{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-06-15T00:16:26.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-06-15T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":1942,"title":"GJam 2014 China Rd B: Party","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2929486/dashboard#s=p1 GJam 2014 China Party\u003e. Small Case.\r\n\r\nThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\r\n\r\nThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\r\n\r\n\r\n*Input:* [M], Bx4 matrix (B\u003c=100). Total B area of \u003c=1000\r\n\r\n*Output:* [x,y,d] where [x,y] is Party House and d is everyone's total distance\r\n\r\n*Examples:*\r\n\r\n  M   [x y d]\r\n  [0 0 2 2] [1 1 12]\r\n  [-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]\r\n\r\n \r\n*Contest Performance:* Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\r\n\r\n\r\n*Commentary:*\r\n\r\n  1) The small can be solved by brute force since fewer than 1000 points require evaluation.\r\n  2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\r\n  3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2929486/dashboard#s=p1\"\u003eGJam 2014 China Party\u003c/a\u003e. Small Case.\u003c/p\u003e\u003cp\u003eThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\u003c/p\u003e\u003cp\u003eThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [M], Bx4 matrix (B\u0026lt;=100). Total B area of \u0026lt;=1000\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [x,y,d] where [x,y] is Party House and d is everyone's total distance\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM   [x y d]\r\n[0 0 2 2] [1 1 12]\r\n[-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\u003c/p\u003e\u003cp\u003e\u003cb\u003eCommentary:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) The small can be solved by brute force since fewer than 1000 points require evaluation.\r\n2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\r\n3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.\r\n\u003c/pre\u003e","function_template":"function [x,y,d]=Party_CH(p)\r\n x=0;\r\n y=0;\r\n d=0;\r\nend","test_suite":"%%\r\ntic\r\nzm=[0 0 30 30 ];\r\nvexp=[15 15 14880];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[0 0 29 29 ];\r\nvexp=[14 14 13500];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[0 1 0 100 ;0 -100 0 -1 ;-100 0 -1 0 ;1 0 100 0 ];\r\nvexp=[-1 0 20400];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[616 34 616 34 ;78 -828 78 -828 ;-762 -671 -762 -671 ;-199 -960 -199 -960 ;427 -575 427 -575 ;448 798 448 798 ;-819 -939 -819 -939 ;852 -564 852 -564 ;-145 281 -145 281 ;694 828 694 828 ;-278 963 -278 963 ;47 813 47 813 ;-393 24 -393 24 ;198 -257 198 -257 ;-393 -177 -393 -177 ;596 237 596 237 ;-678 760 -678 760 ;-180 92 -180 92 ;-590 995 -590 995 ;27 -946 27 -946 ;459 799 459 799 ;-491 -739 -491 -739 ;-691 -922 -691 -922 ;-38 185 -38 185 ;495 -471 495 -471 ;-850 532 -850 532 ;-360 798 -360 798 ;589 -104 589 -104 ;-492 -364 -492 -364 ;-797 415 -797 415 ;105 319 105 319 ;-879 -347 -879 -347 ;-795 172 -795 172 ;529 831 529 831 ;357 -199 357 -199 ;621 959 621 959 ;-475 125 -475 125 ;769 884 769 884 ;172 -706 172 -706 ;618 222 618 222 ;989 734 989 734 ;-273 478 -273 478 ;-548 930 -548 930 ;-634 889 -634 889 ;599 879 599 879 ;836 834 836 834 ;463 901 463 901 ;972 -903 972 -903 ;-319 495 -319 495 ;-727 -368 -727 -368 ;-685 -487 -685 -487 ;834 902 834 902 ;-114 -961 -114 -961 ;-984 193 -984 193 ;-388 867 -388 867 ;712 232 712 232 ;-750 19 -750 19 ;855 -455 855 -455 ;857 996 857 996 ;493 -722 493 -722 ;-582 426 -582 426 ;-824 848 -824 848 ;479 -993 479 -993 ;-976 -820 -976 -820 ;208 443 208 443 ;919 745 919 745 ;-460 -548 -460 -548 ;375 556 375 556 ;-572 980 -572 980 ;345 -411 345 -411 ;-275 613 -275 613 ;718 -895 718 -895 ;-838 -892 -838 -892 ;-241 836 -241 836 ;336 -878 336 -878 ;891 -355 891 -355 ;-986 989 -986 989 ;629 856 629 856 ;-779 787 -779 787 ;970 711 970 711 ;-578 -163 -578 -163 ;779 735 779 735 ;572 -203 572 -203 ;237 192 237 192 ;-427 -213 -427 -213 ;-338 9 -338 9 ;-905 45 -905 45 ;64 -35 64 -35 ;476 -560 476 -560 ;-370 24 -370 24 ;-836 487 -836 487 ;53 50 53 50 ;540 -897 540 -897 ;-179 -8 -179 -8 ;-979 227 -979 227 ;528 257 528 257 ;-876 615 -876 615 ;-342 -895 -342 -895 ;802 -744 802 -744 ;-458 -395 -458 -395 ];\r\nvexp=[-38 185 110298];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[241 -635 241 -635 ;75 -432 75 -432 ;-522 -517 -522 -517 ;-589 -931 -589 -931 ;-903 447 -903 447 ;-555 757 -555 757 ;-584 19 -584 19 ;420 -458 420 -458 ;-127 517 -127 517 ;-417 158 -417 158 ;542 703 542 703 ;865 -531 865 -531 ;-592 -191 -591 -190 ;570 467 570 467 ;-326 -668 -325 -668 ;197 516 197 516 ;238 -442 239 -441 ;-339 -71 -338 -70 ;255 -450 256 -450 ;408 -232 409 -231 ;302 -765 303 -764 ;-575 687 -575 688 ;-352 -651 -351 -650 ;-483 -96 -483 -95 ;285 170 286 170 ;-349 -660 -348 -659 ;518 -419 518 -418 ;555 -506 556 -506 ;900 97 901 98 ;-969 -258 -969 -257 ;-514 -199 -513 -198 ;-422 -197 -422 -197 ;-852 -115 -852 -114 ;166 -651 166 -650 ;628 -930 629 -930 ;-53 853 -52 853 ;484 503 484 504 ;-912 -976 -911 -975 ;-386 -562 -386 -561 ;521 946 521 947 ;717 -799 718 -797 ;-463 -348 -461 -348 ;-14 167 -13 169 ;-346 -677 -344 -675 ;-675 176 -673 179 ;894 807 896 811 ];\r\nvexp=[-338 -71 136630];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[468 377 468 377 ;839 -105 839 -105 ;-871 487 -871 487 ;-307 651 -307 651 ;135 -929 135 -929 ;-411 -829 -411 -829 ;745 -64 745 -64 ;336 784 336 784 ;-875 -84 -875 -84 ;-723 -736 -723 -736 ;701 -818 701 -818 ;-239 210 -239 210 ;-15 614 -15 614 ;362 225 362 225 ;894 443 894 443 ;-352 -303 -352 -303 ;-287 254 -287 255 ;-739 -960 -739 -960 ;110 28 110 28 ;540 434 541 435 ;-103 -962 -102 -962 ;913 -274 913 -273 ;835 -730 836 -730 ;544 866 545 867 ;-97 -358 -96 -358 ;-490 -319 -490 -319 ;-122 700 -122 702 ;37 902 39 902 ;103 266 104 266 ;-581 -714 -579 -710 ];\r\nvexp=[-97 -358 62565];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[28 122 30 124 ;-85 -609 -83 -607 ;763 19 764 20 ;612 -204 613 -203 ;-521 792 -520 794 ;-782 193 -781 195 ;-662 149 -661 151 ;-561 -568 -559 -567 ;-190 -897 -189 -896 ;-725 -317 -723 -315 ;704 -957 706 -956 ;-329 -967 -328 -966 ;-564 -639 -563 -637 ;-603 -86 -601 -84 ;-165 548 -164 550 ;-197 -150 -195 -148 ;-379 -581 -377 -579 ;401 -684 403 -683 ;546 -194 548 -192 ;267 573 268 574 ;-634 288 -632 290 ;593 857 595 858 ;78 -240 80 -238 ;800 981 801 982 ;473 472 474 473 ;-894 469 -893 471 ;582 347 583 349 ;516 189 518 190 ;333 -865 335 -864 ;-192 507 -191 508 ;-310 534 -309 536 ;-783 -487 -781 -486 ;-915 -696 -914 -695 ;-57 872 -56 874 ;717 -423 718 -422 ;509 -810 510 -809 ;-186 -335 -184 -333 ;-403 629 -401 631 ;-598 104 -596 106 ;-149 -210 -147 -208 ;920 911 922 913 ;819 -934 821 -932 ;518 -328 520 -326 ;-630 429 -628 431 ;348 -766 350 -764 ;242 -300 244 -298 ;387 -191 389 -189 ;-19 -871 -17 -869 ;383 723 385 725 ;-742 -327 -740 -325 ;-181 -43 -179 -41 ;799 -46 801 -44 ;729 -373 731 -371 ;-863 -16 -861 -14 ;998 -444 1000 -442 ;242 962 244 964 ;-249 -412 -247 -410 ;116 -14 118 -12 ;871 -455 873 -453 ;669 492 671 494 ;877 -447 879 -445 ;990 -938 992 -936 ;43 522 45 524 ;-70 45 -68 47 ;808 8 810 10 ;-879 -310 -877 -308 ;979 79 981 81 ;-695 202 -693 204 ;-650 469 -648 471 ;690 -624 692 -622 ;-169 -43 -167 -41 ;-81 723 -78 726 ;-789 968 -787 970 ;-913 698 -912 701 ;-597 -970 -595 -968 ;693 -79 694 -77 ;41 847 43 849 ;39 -728 41 -725 ;422 470 425 473 ;-518 -883 -517 -880 ;-858 784 -855 786 ;-246 311 -245 312 ;194 -715 197 -712 ;-370 -868 -369 -865 ;377 174 380 176 ;-697 223 -694 225 ;-489 -957 -486 -955 ;-585 -164 -583 -162 ;-283 -880 -281 -878 ;-141 -729 -140 -728 ;835 447 838 450 ;-424 -612 -423 -610 ;-280 376 -276 377 ;-351 -393 -350 -392 ;-793 -436 -788 -434 ;-548 -180 -547 -175 ;826 775 831 778 ;-664 -604 -658 -602 ;987 -65 988 -57 ;-540 -796 -533 -795 ];\r\nvexp=[-167 -43 874364];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-291 955 -289 956 ;276 -710 278 -708 ;-724 283 -722 285 ;-850 588 -848 589 ;625 -511 627 -509 ;-530 -994 -529 -993 ;-312 -655 -311 -654 ;86 -269 87 -267 ;565 -521 566 -520 ;438 320 440 321 ;-330 985 -328 986 ;-408 -942 -407 -940 ;755 792 756 794 ;847 -794 848 -793 ;436 -1 438 0 ;206 -637 208 -635 ;516 544 518 546 ;77 -200 78 -199 ;-618 276 -616 277 ;380 868 382 870 ;-664 284 -663 286 ;-526 929 -524 931 ;743 -555 745 -553 ;331 145 333 146 ;98 124 99 126 ;220 -661 222 -660 ;-92 498 -90 500 ;646 -552 647 -550 ;-531 -850 -529 -849 ;573 -80 574 -79 ;-317 299 -315 300 ;-963 713 -962 714 ;411 818 412 819 ;-99 -503 -97 -501 ;279 599 280 601 ;793 -237 794 -235 ;-41 -876 -39 -875 ;-550 -478 -549 -477 ;-107 820 -105 822 ;657 886 659 888 ;-460 684 -458 686 ;-80 455 -78 457 ;-779 -528 -777 -526 ;-829 719 -827 721 ;-760 -716 -758 -714 ;39 342 41 344 ;254 447 256 449 ;-272 -705 -270 -703 ;-900 507 -898 509 ;498 327 500 329 ;-669 168 -667 170 ;519 -367 521 -365 ;-674 323 -672 325 ;-724 519 -722 521 ;52 -596 54 -594 ;897 -724 899 -722 ;6 -387 8 -385 ;62 808 64 810 ;-84 -749 -82 -747 ;-475 -379 -473 -377 ;-467 -819 -465 -817 ;-130 232 -128 234 ;218 862 220 864 ;-206 339 -204 341 ;821 658 823 660 ;261 61 263 63 ;-704 869 -702 871 ;788 -490 790 -488 ;482 67 484 69 ;-328 -781 -326 -779 ;150 -117 152 -115 ;946 -90 948 -88 ;-68 477 -65 479 ;-704 915 -701 918 ;979 -761 980 -759 ;328 705 331 708 ;969 951 971 953 ;-638 991 -637 993 ;-621 120 -619 121 ;-546 651 -545 654 ;217 550 218 551 ;-743 196 -740 199 ;-591 847 -588 849 ;-48 -769 -46 -766 ;678 424 680 425 ;-250 268 -248 270 ;964 -389 966 -386 ;193 -818 195 -815 ;-803 107 -801 109 ;16 -725 19 -722 ;-721 -274 -720 -273 ;14 666 17 668 ;-822 933 -820 936 ;-895 -416 -894 -412 ;821 -329 824 -326 ;382 68 387 68 ;590 282 595 284 ;97 -310 103 -307 ;147 933 150 933 ;-772 -42 -765 -33 ];\r\nvexp=[-128 232 914624];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-987 -105 -985 -103 ;-22 -655 -20 -653 ;-622 412 -621 414 ;-526 641 -524 642 ;-694 573 -692 575 ;268 -697 269 -695 ;366 544 368 545 ;648 218 649 220 ;314 443 316 445 ;-589 354 -588 355 ;60 544 62 546 ;21 -444 23 -442 ;175 -224 176 -223 ;-915 -696 -914 -695 ;-417 766 -415 767 ;-874 -599 -873 -598 ;606 921 607 922 ;-672 562 -671 564 ;-17 39 -16 40 ;-708 632 -707 633 ;823 -170 825 -168 ;996 -372 997 -371 ;961 -169 962 -167 ;572 577 573 579 ;53 345 55 347 ;569 453 570 454 ;716 753 718 754 ;-803 -873 -802 -872 ;-110 940 -108 942 ;-943 841 -941 842 ;186 997 187 999 ;-107 388 -105 390 ;193 -54 195 -52 ;-231 -916 -230 -914 ;-962 749 -960 750 ;794 -458 796 -457 ;259 -909 261 -908 ;-719 65 -718 67 ;242 -481 244 -479 ;-528 -223 -526 -221 ;283 955 285 957 ;-888 946 -886 948 ;847 -707 849 -705 ;757 -814 759 -812 ;-940 -941 -938 -939 ;2 -176 4 -174 ;665 -708 667 -706 ;656 170 658 172 ;494 949 496 951 ;994 802 996 804 ;-65 785 -63 787 ;147 684 149 686 ;-488 807 -486 809 ;-875 462 -873 464 ;-152 253 -150 255 ;114 247 116 249 ;760 -206 762 -204 ;-204 569 -202 571 ;89 -752 91 -750 ;-464 -975 -462 -973 ;-783 -545 -781 -543 ;75 -251 77 -249 ;471 -462 473 -460 ;-126 -169 -124 -167 ;-311 615 -309 617 ;-398 -727 -396 -725 ;834 -915 836 -913 ;-87 -21 -85 -19 ;-301 918 -299 920 ;-740 -366 -738 -364 ;24 47 26 49 ;-929 -761 -927 -759 ;-863 -36 -861 -33 ;541 604 543 606 ;-279 -423 -276 -422 ;-620 -116 -619 -114 ;-145 571 -143 573 ;-638 133 -636 136 ;-885 546 -882 549 ;-625 -11 -622 -8 ;-610 -369 -609 -367 ;80 -655 83 -652 ;-398 -183 -395 -182 ;-71 -953 -69 -951 ;-767 939 -766 942 ;-763 -362 -760 -360 ;46 -897 47 -895 ;23 -437 25 -436 ;550 -440 553 -439 ;-660 178 -658 182 ;851 -919 853 -917 ;124 437 125 438 ;-414 -524 -411 -520 ;881 797 884 799 ;-73 -303 -68 -301 ;-373 -585 -369 -584 ;-239 963 -237 968 ;453 965 456 968 ;-742 875 -738 877 ;-894 -954 -884 -944 ];\r\nvexp=[-126 -168 1055075];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-648 -872 -646 -871 ;739 270 741 272 ;-847 -333 -845 -331 ;-510 -174 -508 -173 ;182 -353 183 -352 ;-573 277 -571 278 ;297 245 299 247 ;-223 818 -221 819 ;886 57 887 58 ;888 -773 889 -772 ;-593 513 -591 514 ;-587 -107 -585 -106 ;-564 40 -563 41 ;234 -624 236 -622 ;-82 902 -81 903 ;222 851 223 852 ;-726 476 -724 478 ;-392 -160 -390 -158 ;-153 -484 -152 -483 ;-522 -962 -520 -960 ;66 -926 68 -925 ;-535 28 -534 29 ;-603 -292 -602 -291 ;-981 -471 -980 -469 ;-367 865 -365 867 ;-445 -75 -443 -73 ;300 -40 301 -38 ;-329 -287 -328 -286 ;554 935 556 936 ;593 -932 594 -930 ;206 873 208 875 ;335 574 336 575 ;296 154 298 155 ;323 -423 325 -422 ;-144 472 -143 474 ;-284 211 -282 213 ;-289 -996 -287 -994 ;167 574 168 575 ;65 803 67 805 ;264 173 266 175 ;-820 -637 -818 -635 ;-897 813 -895 815 ;60 -524 62 -522 ;652 850 654 852 ;-837 57 -835 59 ;31 -96 33 -94 ;-607 540 -605 542 ;-240 794 -238 796 ;386 453 388 455 ;-421 -468 -419 -466 ;-838 -196 -836 -194 ;248 -366 250 -364 ;7 -933 9 -931 ;578 742 580 744 ;-634 -828 -632 -826 ;678 16 680 18 ;706 -163 708 -161 ;228 771 230 773 ;-440 -564 -438 -562 ;228 -606 230 -604 ;-361 652 -359 654 ;-608 -741 -606 -739 ;-926 42 -924 44 ;984 147 986 149 ;-132 -334 -130 -332 ;492 870 494 872 ;-470 523 -468 525 ;440 983 442 985 ;-68 -14 -66 -12 ;652 970 654 972 ;-591 -410 -589 -408 ;-252 -573 -250 -571 ;-639 -424 -637 -421 ;-306 -234 -303 -231 ;-720 81 -718 83 ;-645 845 -642 846 ;-938 507 -936 508 ;646 122 648 125 ;-76 864 -73 867 ;777 -142 778 -141 ;267 -756 269 -755 ;-151 -11 -150 -10 ;-568 -929 -567 -926 ;753 -830 756 -828 ;-205 -663 -202 -661 ;329 368 330 369 ;-402 -682 -399 -679 ;-649 463 -647 465 ;995 538 999 539 ;107 817 111 818 ;-546 -441 -544 -437 ;-856 920 -854 921 ;-587 -483 -584 -479 ;717 -641 719 -639 ;-892 -134 -890 -132 ;-300 -887 -296 -883 ;605 -228 607 -224 ;-93 -994 -90 -994 ;-421 -56 -414 -50 ;76 -592 80 -583 ];\r\nvexp=[-303 -231 855861];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\ntoc\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-18T01:44:26.000Z","updated_at":"2026-05-27T13:44:32.000Z","published_at":"2013-10-18T02:33:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2929486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Party\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Small Case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M], Bx4 matrix (B\u0026lt;=100). Total B area of \u0026lt;=1000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [x,y,d] where [x,y] is Party House and d is everyone's total distance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M   [x y d]\\n[0 0 2 2] [1 1 12]\\n[-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCommentary:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) The small can be solved by brute force since fewer than 1000 points require evaluation.\\n2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\\n3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2737,"title":"Prouhet–Tarry–Escott (basic)","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves problem 660.\u003e\r\n\r\nGiven n return two disjoint sets of integers _A_ and _B_ with same cardinality having following property:\r\n\r\n\u003c\u003chttps://i.imgur.com/gSW7nWy.png\u003e\u003e\r\n\r\nfor i = 1:n\r\n\r\nTry to minimize sets cardinality. ","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves\"\u003eproblem 660.\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven n return two disjoint sets of integers \u003ci\u003eA\u003c/i\u003e and \u003ci\u003eB\u003c/i\u003e with same cardinality having following property:\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/gSW7nWy.png\"\u003e\u003cp\u003efor i = 1:n\u003c/p\u003e\u003cp\u003eTry to minimize sets cardinality.\u003c/p\u003e","function_template":"function [A, B] = prouhet(n)\r\n  A = 1:n;\r\n  B = -A;\r\nend","test_suite":"%%\r\nn = 1;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 2;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 5;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 7;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\n%n = 9;\r\n%[A, B] = prouhet(n);\r\n%assert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\n%assert(isempty(intersect(A, B)));\r\n%assert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\n%assert(isequal(sum(uint64(A(:)).^uint64(1:n)), sum(uint64(A(:)).^uint64(1:n))));\r\n%disp(sprintf('Each set has %i elements.', numel(A)))\r\n%if numel(A) \u003c=20\r\n%    disp('A:')\r\n%    disp(A)\r\n%    disp('B:')\r\n%    disp(B)\r\n%end\r\n%%\r\n% test info\r\n%\r\n% larger n will be added later\r\n%\r\n% scoring function will be added later as well\r\n% scoring will be entirely based on size of output: smaller output == better score\r\n% something like this:\r\n%\r\n% score = 0;\r\n% for n = 1:25\r\n%   [A, B] = prouhet(n)\r\n%   assert(...);\r\n%   score = score + numel(A);\r\n% end\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2016-10-08T00:11:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-08T09:56:20.000Z","updated_at":"2026-06-08T14:44:05.000Z","published_at":"2016-10-07T08:07:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 660.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n return two disjoint sets of integers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with same cardinality having following property:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor i = 1:n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry to minimize sets cardinality.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.JPEG\",\"contentType\":\"image/JPEG\",\"content\":\"data:image/JPEG;base64,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\"}]}"},{"id":61269,"title":"Precise Almost Pythagorean Triples ","description":"This  is essentially the same as:  Problem 52834. Easy Sequences 32: Almost Pythagorean Triples; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\r\nRepeating the original problem description:\t\t\t\t\r\nAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is 1 less than the sum of square of the smaller elements (shorter sides). This means that if c is the hypotenuse and a and b are the shorter sides, , satisfies the following equation: \r\n        \r\n        where:  \r\nThe smallest  is the triple , with  and perimeter (the sum of the 3 elements)  of . Some researchers consider  as the smallest , but here, we will only look at 's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of 's are , and . \r\nUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible 's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with 's with a known ratio between the hypotenuse and the shortest side: . \r\nGiven the value of r, find the perimeter of the  with the r-th smallest perimeter. For example for , that is , the smallest perimeter is  for  , while the second (r-th) smallest perimeter is , for the  with dimensions . For , the third smallest perimeter is  for  . \r\nThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\r\nFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 334px 334.917px; transform-origin: 334px 334.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 42px; text-align: left; transform-origin: 310px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.675px 7.91667px; transform-origin: 102.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis  is essentially the same as:  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52834\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 10.5px; text-align: left; transform-origin: 310px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.933px 7.91667px; transform-origin: 201.933px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepeating the original problem description:\t\t\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 86.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 43.4583px; text-align: left; transform-origin: 310px 43.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303.05px 7.91667px; transform-origin: 303.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.45px 7.91667px; transform-origin: 12.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eless\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.8917px 7.91667px; transform-origin: 94.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 7.91667px; transform-origin: 3.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 7.91667px; transform-origin: 72.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hypotenuse and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 7.91667px; transform-origin: 49.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the shorter sides, \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.692px 7.91667px; transform-origin: 102.692px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, satisfies the following equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 12.4583px; text-align: left; transform-origin: 310px 12.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 7.91667px; transform-origin: 15.5333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"99\" height=\"19\" style=\"vertical-align: baseline;width: 99px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 23.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 11.9583px; text-align: left; transform-origin: 310px 11.9583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.425px 7.91667px; transform-origin: 40.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        where:  \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"62\" height=\"18\" style=\"vertical-align: baseline;width: 62px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 96.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 48.3333px; text-align: left; transform-origin: 310px 48.3333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.725px 7.91667px; transform-origin: 37.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the triple \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGEAAAAlCAYAAABSz4fZAAACsklEQVRoge2a0ZGDIBRFTw92YAM2kApSQTqwAztIC9awJdhDWrCGtJD9wDcSFQTDI+4OZ4afDAJ5Fy48FAqFQuH0dI5y+eag/gAX3LGL5gU8gGFRbilG+o+5sY7ZAxPPaF6UWZ+KC5lEqKb6W+UK3I8MwkPj6a8H6g/b9/2frVJ52somQjc94yopV1UFPD19DQn6uHnaX5YnftGziJAjKDY5BBcfDyl7/y+LCB0w4l+SqRDBW8U+JGh7h5B7YL0sIjxJ7/kuWvaX/6f0hIk8Bo5FXQTxzhazWWozYqxibzP8hJBjeEO41aqLMLLepHp0BNnaLB/T7zms0EasKCQJUxVh7wTRkzY4S8GX4ufMa2QsIbaovhLqqV4L/LB9ckgphJ13bIlyTdiXC7GiR2D9bHmCULMW49C9SSA33o/HT/StKcaK4AsiCLZVaQem4v1cryk6xFkRfFEEmGdMjnuomnlFpE4ObWKtCL4sQs0sgmZyJfTMK0+LWCuCL4sAs03kEOGKvgixVgQnEGEgLLVPgfzZUbn9GCuyn4sm9UrQvGYQZCX0Su2L3cVu/KfYE2JnzlEkSFq5gmz8sRNKVYRmp44EZatOhdknOsKuOOQliysAIrjrZCTvfo9eccgqO2J1aiK0zCefkXUgJU9wLV0RSMqeEHZC1vEeSMkTHo527FPaC5NMxiLjPXJbrCaCNLy8K+ows3HEbwvLrHrPxwfe649TX3fmS0PXDG9YjzXWUmQSHLFoVTuqMUGwvyyQJb9HgxFiYA7iHjfrmYFZ9JCAyuQ4clBopmePrCA4wekohJyf0lzQO8L6+jy1CA35Xo2Cmc05EkebU4vQ4N5MNejJ9xrW5iMRWtbf16RKuipMQHIkcWDsLoflyfsVu8hJMhrXGyzta+K/ju9znEKhUCgUCmfnFzTbYsvcMy9LAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 7.91667px; transform-origin: 18.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"100\" height=\"19\" style=\"vertical-align: baseline;width: 100px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.508px 7.91667px; transform-origin: 101.508px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and perimeter (the sum of the 3 elements)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.91667px; transform-origin: 7.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6UlEQVRYhe2WQQ3DMAxFP4cwCIESGIIiKIMxKINSKIZBKIdRKIZR6A6ztWiHxkm+qkjzl6xenOQpL5UMeDyevhIBhEzPAOBmrKEFZAVwGDbZpc9SSylISEC0zoDGApgDn1syZwQwy/dpBNqk4klPkH32EpjfzAagKIfk3tiESl01QBYFD1ToqgGyRHW9kL/JS4BU19oCwwRSXWMPQDRdLCCaLhYQTRcDiKqLAUTVxQDaQNTVChRB1tUKdAdZVyuQTgpTD0CprrORpCg6VijQXLBWdW0skAXfoSutVQ7LRdfT/i6Px+P5u7wB3c96XQFb71kAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.4083px 7.91667px; transform-origin: 91.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Some researchers consider \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 7.91667px; transform-origin: 50.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as the smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7917px 7.91667px; transform-origin: 70.7917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but here, we will only look at \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.942px 7.91667px; transform-origin: 243.942px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.8333px 7.91667px; transform-origin: 18.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's are \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"56\" height=\"18\" style=\"vertical-align: baseline;width: 56px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 35.875px; text-align: left; transform-origin: 310px 35.875px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 269.142px 7.91667px; transform-origin: 269.142px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.9417px 7.91667px; transform-origin: 21.9417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.775px 7.91667px; transform-origin: 6.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"50\" height=\"18\" style=\"vertical-align: baseline;width: 50px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 95.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 47.8333px; text-align: left; transform-origin: 310px 47.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2083px 7.91667px; transform-origin: 62.2083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 7.91667px; transform-origin: 2.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.925px 7.91667px; transform-origin: 85.925px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the perimeter of the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3167px 7.91667px; transform-origin: 30.3167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003er-th smallest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3417px 7.91667px; transform-origin: 37.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e perimeter. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 7.91667px; transform-origin: 12.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.4917px 7.91667px; transform-origin: 24.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"43\" height=\"18\" style=\"vertical-align: baseline;width: 43px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 7.91667px; transform-origin: 81.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABLUlEQVRYhe2WUbHDIBBFjwccYKAGoiAK4qAOcBAL0RAJeKiFaoiFvg+WmX2dPEIC5fWDO7Nfu1lOLiwJdHV1fZcsYE4+M0jcaoMswCuzsQFm4Ak4iafEvQTEKJAYR0AWeMji726u0sPv5A41Et5slAVygWKt28kZYEvks+UygaaMOu34aZfOAsUt2RI1GvqyS7lAcTtSQIPqtX4aKNakgGxmXVWgo/PRDMiruvEbgO4cn4+mW2YIF2LKJT32j08DIXkN5eX5meDIqnJLCyAITk2yoBcIR9iumbxzVhUoBRrvqr1vXXMg3Wcq6FMF6MbxBDYD0tN36dejJpCeurUGjOX3GJ/5QjvCId4o/FOMIDPB4vdY/ljAEEY53jle6opduSorAMN/QnR1dXWV6Ae9sZqCc2SAGwAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.9583px 7.91667px; transform-origin: 57.9583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, while the second (r-th) smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2WUQ2DMBCGfw91UAMYmIIqwMEc4AAL1TAJ9TALaJgF9sBd0i2DXQ9u4+G+5MIDBT74QgBwHOc/dAAuwumE54wAglZoAjALZxSIZForlX8hNcjMWJ7SJ0IlwqMSKjRxY02gC0wr+xOAgbb3PUKRLvKtdQ9ZLpDYLqG1BDU3bOc6TEgC53pA9taYC3GuLFxvLsS50hmEWnOZC7XmMhdqzWUqpMllKqTJZSpU0J7LTChCl8tM6ApdLjMh/mL3ZxCqc239kvxMiHMVxbH8O8NCwxFCI8m0vF2xOu59MpabdBzHcSQ8AUZlel3qgGXQAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6583px 7.91667px; transform-origin: 25.6583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6833px 7.91667px; transform-origin: 53.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with dimensions \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAlCAYAAACUJtElAAAEa0lEQVR4nO1bbZHrMAxcDmFQAiEQBEUQBmVQBqUQDIUQDqVQDKXQ98PRZOvKsp2vJve8M565mUtsWVpLsqICBQUFBQUFh8U1MJpfClWwChqE7Z2NN4AHgN4b7RKSFuwKLb7t/IDjQDbeKN7lf0aDHxGnzni2GtbSxhnAbYYcIcj8OXJqqOFcejeM88z5fLBupkDePU14b1PitACeAO4Z71yH9UJjKc9XwRnXn/8F4JI5zxVun+/h71zDxHDGGC543Ib1LZzg9vnCmKs84UJQ6kHZjDhnjIp8I504FdwGQ6TpM2SwcIqsI0aJoca4zx7LEwZwh0/mvw5ysW4tndRw+3zikyQVzZHiFTchzg3uxF6QTxw5DbFTNBf9sA4n9zW+PZCl1BZ5J38KmkFOTQ6WVbMNk0PzoEKGN+Kybx6qconzwjo5DOM8rBNy0xwqQ3Kz0nusR3QrnJxIBo0Yso8Xwp5QiBWzz66JIyf4gvlJqoU77Bymwme+o/3/hbhR5qJCvNxheUaR8WG8z17LIv+uicNxW4zSYXkSdYgbu0eYOKzstb2jBfE4Wmg/Y5SxM+bgdMIi6W6Jw/mCNjqsn/cwhDh+4sne6I2RgDWmXXPnQEKR5m043FrelUOuRbDdEgdwSm/gNnrHN3nWzCV8hJJKPqFPOAP5t7On8t7SaId1Q8k76y+VOFZI2zVxfJzwTaBJ30smrCsE8D2IL48U+RqMNas1w1jtyRCqOfXIJ44Wlv3nsvEL4gg4jL2wvtcRN68pnItw2v8r75klK8c3jGUE3xv7JGXixHLEP0scwCnGqlksBbkxhYpqrORQPsOJ6VIFSx+aN2aCMHEsfcVukILDEidWs1gKdziPEfJqKUr2n1vTQ/KB4jBeQhVBQsBaxLnguzTvg+s3FnJCxRywx2AdT7lVWTY6NHHEGGv0AEliGzMy13csT7IVcXgt1jHnhanEsZL5QxNHPM7StZJU0gCfocF6PpVgS0DWYoJwaLd0z57JSuQPSxxRhFVrmAL5im+RoMZnoU/2ZHk+ufksLW9oLS1ZF0I9jXfv9MwhPzlI5TUEKfOHvgJf4E5PTliQloPYreOBT6OI5wuRgvMOn1zSz9tiGU8kBtXCDIehkN5SLxy7JI5fjfWNL/E6VPzzWyFSyCOkeSDcmM0NTww2iOZ1xP3773H4SDlM3DOktW3IHqyKuoRWba2QnBo2JQ7HT60K6wvFoxvel4KXFX+1aq4FUbi/Zmhoa7c0B3sPOQR36Ib257byNZ9o0nIirampnzbkYDH5RM7UzzibEKeFU5zfKS8dbJpHOGGsjPKzKTcoKcP3GL+oWwjJpg2NAAIJkTxf7CdDchhSE/1m2A/Lc0V+RbrBp35vmXP8rFl9KxzlJzvS2XcU/GniSP/vlu0XUxFrJtsb/ixxajj3v3axbQl0+G0D2BTMIs4F379z2rJxKYQKzhB7kCWGFvsPpdIXxUOS6WyEbhxb9McUbAvrd20FBQUFBQUFBQUFBRb+AeqNb10z+oPdAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.325px 7.91667px; transform-origin: 16.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 7.91667px; transform-origin: 31.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the third smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"33\" height=\"18\" style=\"vertical-align: baseline;width: 33px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"101\" height=\"18\" style=\"vertical-align: baseline;width: 101px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 305.717px 7.91667px; transform-origin: 305.717px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 282.908px 7.91667px; transform-origin: 282.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function function perimeter = rthPerAPTdbl(r)\r\n  perimeter = r^2;\r\nend","test_suite":"%% Test Case 1\r\nr = 2;\r\np_correct = 71;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 2\r\nr = 3;\r\np_correct = 1393;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 3\r\nr = 5;\r\np_correct = 1046629;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 4\r\nr = 10;\r\np_correct = 737287485879;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 5\r\nr = 100;\r\np_correct = 16183149010201;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 6\r\nrs = 101:150;\r\nps = arrayfun(@(r) rthPerAPTdbl(r),rs);\r\nps = mod([sum(ps) ps(5:5:end) floor(std(double(ps)))],1e6);\r\nps_correct = [12636 824229 203679 227761 926641 15749 664839 210241 515881 139269 477199 789840];\r\nassert(isequal(ps,ps_correct))\r\n%% Test Case 7\r\nr = 1000;\r\np_correct = 499499001002001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 8\r\nr = 10000;\r\np_correct = 100020001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 9\r\nr = 123456;\r\np_correct = uint64(76696064606196865);\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 10: Forbid java and BigInteger\r\nfiletext = fileread('rthPerAPTdbl.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":2404920,"edited_by":2404920,"edited_at":"2026-03-04T15:24:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-04T14:14:29.000Z","updated_at":"2026-06-06T17:53:55.000Z","published_at":"2026-03-04T15:24:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis  is essentially the same as:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52834\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e; it even presents the same set of test problems.  The difference is that the \\\"correct\\\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepeating the original problem description:\\t\\t\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn Almost Pythagorean Triple (abbreviated as \\\"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eless\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the hypotenuse and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are the shorter sides, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, satisfies the following equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"99\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"62\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the triple \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"100\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and perimeter (the sum of the 3 elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Some researchers consider \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but here, we will only look at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's where the hypotenuse is \\\"strictly\\\" greater than the other shorter sides. Other examples of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"56\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId9\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"50\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the perimeter of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er-th smallest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e perimeter. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"43\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId12\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId13\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId14\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while the second (r-th) smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId15\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId17\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the third smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"33\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId18\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"101\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId19\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not 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Power Steering (EPS) Motor Torque with Efficiency","description":"In EPS systems, the motor must generate additional torque to compensate for system losses.\r\nGiven Required assist torque at rack Ta and Mechanical efficiency η (0 \u003c η ≤ 1)\r\nCompute required motor torque Tm.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Required assist torque at rack \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMechanical efficiency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eη (0 \u0026lt; η ≤ 1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute required motor torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Tm = epsMotorTorque(Ta,eta)\r\nTm = 0;\r\nend","test_suite":"%%\r\nTa = 10; eta = 0.9;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 15; eta = 0.85;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 8; eta = 0.8;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:46:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:46:15.000Z","updated_at":"2026-06-09T08:08:23.000Z","published_at":"2026-04-28T09:46:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Required assist torque at rack \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eMechanical efficiency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eη (0 \u0026lt; η ≤ 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute required motor torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1440,"title":"USC Spring 2013 ACM: Snow Cones","description":"This Challenge is to solve the \u003chttp://contest.usc.edu/index.php/Spring13/Home USC Spring 2013 ACM Contest\u003e Problem F, Snow Cones.\r\n\r\nSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O.\r\nInput is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child. \r\n\r\nDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\r\n\r\n\r\n*Input:* From XXO to  OXX   *Output:* 2\r\n\r\n*Input:* From OXOX to XOXO  *Output:* 1\r\n\r\nOnly two competitors solved this challenge.\r\n\r\nA little complex requiring a Matlab 3-Liner solution versus \u003chttp://contest.usc.edu/index.php/Spring13/Home?action=download\u0026upname=cones.zhengcao.cpp.txt Cao's C solution\u003e ","description_html":"\u003cp\u003eThis Challenge is to solve the \u003ca href = \"http://contest.usc.edu/index.php/Spring13/Home\"\u003eUSC Spring 2013 ACM Contest\u003c/a\u003e Problem F, Snow Cones.\u003c/p\u003e\u003cp\u003eSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O.\r\nInput is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child.\u003c/p\u003e\u003cp\u003eDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e From XXO to  OXX   \u003cb\u003eOutput:\u003c/b\u003e 2\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e From OXOX to XOXO  \u003cb\u003eOutput:\u003c/b\u003e 1\u003c/p\u003e\u003cp\u003eOnly two competitors solved this challenge.\u003c/p\u003e\u003cp\u003eA little complex requiring a Matlab 3-Liner solution versus \u003ca href = \"http://contest.usc.edu/index.php/Spring13/Home?action=download\u0026upname=cones.zhengcao.cpp.txt\"\u003eCao's C solution\u003c/a\u003e\u003c/p\u003e","function_template":"function swaps=snowcones(v1,v2)\r\n% v1 is a string of Xs and Os (not zeros)\r\n% v2 is string of desired sequence\r\n swaps=0;\r\nend","test_suite":"i='X'; %1\r\nd='X';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XO'; %2\r\nd='XO';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XO'; %3\r\nd='OX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XX'; %4\r\nd='XX';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXO'; %5\r\nd='XOX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXO'; %6\r\nd='OXX';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XOX'; %7\r\nd='OXX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXXXOOOO'; %8\r\nd='OOOOXXXX';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XOXOXOXO'; %9\r\nd='OXOXOXOX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOXXO'; %10\r\nd='XXOXXOO';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOOOOXX'; %11\r\nd='OOXXXXOO';\r\ne=3;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOXOXOXOXOX'; %12\r\nd='XXOOXXOXXOXOO';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXXOOXOXOXXXO'; %13\r\nd='OXOOXXOXXOXXX';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOOXXOXXOXXX'; %14\r\nd='XXXOOXOXOXXXO';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOOOOOXOXOXXXXXOOXX'; %15\r\nd='OXOOXXOXXOOXOXOOXOXX';\r\ne=5;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOXXXXOXXOXXXXXXXXX'; %16\r\nd='XXXXXXXOOXXXXXOXXXXX';\r\ne=5;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOXOOXXOOXOXXOXOXOO'; %17\r\nd='XOXOXXOXOXOOOXOXOOOX';\r\ne=3;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOOXXXOOXXXXXXOXXX'; %18\r\nd='OXOOXOXXXXXXXXXXOOXX';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOXXXXXXXOXXXOOXXOO'; %19\r\nd='XXOXXOXOXXXXOOXXXXXO';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%20\r\ni='XOOXXXXXOXXOXOXXXOOOXXOOXXOOOXXXXOXXXXOOOOXOXXXXXOXOOOOXXOOOXOXOOXOXOOOOOOXOOOXOOXXXXXXXOXXOXXXOXXOXOOOOXOOXXXXOXXXXXXXXOOOOOXOXOXXXOXXOOOXOXXOOOOOXOXXXOXXOXOXOOOOXXOOXXOXOOOOXOOXOOXXOOXXOOOXOXOXXXXOOXXXXXOOXOOXOXXXXXXOOOOOXOXXXOOOXOOOOOOXXOXOOXXOOOOXXXOXOXOXXXOXOOXXOXXOXOXOXXOXOXOOOOXXOXXOXXXXOXOXXOXOOOOOXOXXOOXOOXXXOXOXXOXXOXXXXXOXXOOOOOOXOOOOXOOOOXOXOXXOXOXXXOXOOOOXXOXXXOXXXOXXOOXXXOOXOXXOOXOOXOXOOOOXOOOOXXOXXOOXXXOXXOOXXOXOXXXOXOOOXXOXOOXXOOXOOOXXOOXXOXOXOXOOOOOOXXXXOXXOXOOXOXXOOOOXXXOOOOOOOOXOOOOOOXXOXXOXOOOOOOXOOOOOXOOXXOOXXOXXXOXOXOXXXOOOOOOXXOOOOXOXOXOOXXOOXOXXXOXOOXXOXOXOOXOXOXOXOXOOOXOOXXXOOOXXXOXOOOXOXXOXXOXXOXXXXOXOOXXOXOXXOOOXXXXXOXXXXOOOOOOOOXXOOXOOOXXXXXOOOXOOXOOOOOXXOOXXOOXXOXXXOXOXOXOOOXOXXOXXOOOOOXOOOOXXXOOXXXOOXOXOXXXXXOOXXOXOOOXOOOXXXOXXOXOXXOXOXOOXOOXXXOOXOOXOXOOXOOOOOOOXXOOOOOOXOOOOOOXOXXXXOOXOXOOXXXOXOXXOXOOOXOOOOOOXOOXOXOOXXOOXOOXXOXOXOOOOOOOOXOXXOXXXXOXXXOOXXOXOOXXXOXOXOOOOXXOXXOXOXXOXOXOOXXXOXXXOOXOOOXOOOXXOXXOOXXXXOXOOXOXOXXOOXXOXXXXXXXXXXOXXOOOOXXXOOXXOOXOOX';\r\nd='OXXXXOOOOXXOOOOXOXXOXOXXXOXXOOOXXOOOXXOXOOXXXOOOOOXOOXOOXXOOXOOOXXOXOOXXXOXOXOXOOOOOOOXOXXXOOXOOXOXXOXXXOXXXXOXXXOOXXXXOXXXOOXOXXXOOXOXXOXXOXOOOXXOOXXXOOXXXXXXOOXXXOXOXXOOOOOXOXOOXOOOOXXXOOOXXXXXOOXOXXXOOOOOXOOOOXXXOOOXXOOOOOOOXOOXXOOOOXOXXXXXOOXOXOXOXOOOXOXOOXOOXOOXXXOOXXXXOOOXXOXXOOXOOOOXOOOXOXOOXOXOXOXXOXXOOOOOOOXOXXOXXOOXOXOXOXXOXXOOOXOOOOOOOOOXOOXXOXOXXOOOOOOXOXOOOOOXXOXOXOXXOXOXXXOOOXXOOXXOXXOXOXXOXXXOOOOOXOOOOOXXXXXOXXOXOOXXOXXXXXOOOOOXOXOXOOXXOXOOXXOXOXXOOXOOXOXOXXOXOOOXXXOXXOXXOOXXXXXXOXOXOXOXXXOXXXOOOOOXXXXOXXXOXOXOOXOXOOXOOOXOOOOXOOOXXOXXXXOXXXXOOOOOXOOOOOOXXOOXOOXXXOXOXOXOXOXOOOOOXOOXXXXOOXOXXOXOOXOOXOXXXXOOOOXXOOXOXOOXOOXOOOOXXXOOOOOOOOXOOXXOOXXOOOXOOXXXXXXOOOOXOOOOXXOXXXXXXOXXXOXOXXXOXXXOXOOOXXOOXOOOOXOOOXOXOXOOOXXXOXOOXOXOOOXXXOOOXXXOXXOOOOOOXOXXOXXOOXXOOXOXOOOXXXOOOOOXXOOXXOXOXXXOXXOXOOXXOXOOOXXXOXXOOXOXXXOXXOXXOXXOOXXXXXOXXOXOOOOOXOXXOOOXOXOOOOXXXXXOOXOOXXOXXXXOXOOXXOXXXOOXXOXOXXOOXOXOOOOXXXXXXXOXOXXOXXXXXOOOOXOOXOXOXOOOXXOXOXOOOOXOXOOOXXOOOXXXOXXOXOXXXXXXOXOXOOOOXOOXX';\r\ne=47;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%21\r\ni='XOXXOXXXOXOOXXOOOXXXOOXXOOOXXOOXXOOXXOXOXXOOXOXXXOOOXOXXXXOOOXXOOXOXOXXOOOOXXOOOOXOXXOXOXOXOXXOXXXOXXXOOXOOOXXXOXOXXOOOOOXOXXOXXXXXOXOXXXXXOXXOOXXOXXXOOOOXOOOOOOXXXXXXXXOXXXOOXXOOOXXXXXOOXXXOXXOOXXXXXOXOXOOXOXOOXOOOOXOOXXOXXOOXXOOXXOXXXXXXOOXOOXOXOOOXXOOXXOOOOOOXXXXOOXOXXOXOOXXOOXXXOXXXOOOXXOOXOXXXOOXXOOOOOOXOXXXOXOOOXOOXOOXOXOXXOXOOXXOOXXOXXXOXOOXOXXOOOXXXXOXXOOXOOXXXOXXXXXOXOOOXOOOXXOXOXXXXOOOXXXXOXOOXOXOOXOXOXXXOXXXXXXOXOOXOOXOOXXXOXOOOOXXXXXOXXXXOXOXXOOOXOOOOOOOOXXXOXXOOXXXXOXXOOXOXXXOOOXOOXOXXXOXOXXXXXXXOOOXOOXOXXXXOXXOOOOOXOOXOXOOXXXOXXOXXOXXXXXOOXOOOOOXOOOXXOXOXXOOOOXXOXXXXOOOOXOOXOXOOOOXXXOXXXXXXXOXOOXOXOOXOOXOOXXXXOXOOOXXXOXXXXOOOOOOXXOXOXXOXOXXXXOXXOXXXOXOOXXOXXXXOXXXOXOOOXOOOXXOXOXOOOXXOOOOOOXOXOXOXXXXOXOOOXXOOXOOXXXOXXOXXXOXOXXOOOXXXOOXOOXXOOOOOOOOOXXOOXOXXOOOXOXOXOXXXOXXXOOOXOXOOXOOXOXXXOOOOOXOOOXXXOXOXOXOOOOOXXOXXXXXOXXOXXXXXXXOOOOOXXXOXXOOXOXOXXOXOXOOXOOXXXOOXXXXOOOOXXOOOOOOXOOOXXOOXOXOOOOOOXXXOXXOXXOOXXOXXXXXOOOOXOXOOXOOXXOOXXXOXXXXXOXOXOXOOOOOXXOXXXOOOOOOXXXOXOXXOOXXOO';\r\nd='XXXXOXOXOOXXXOOOXXXOXXXOXXXXXOOOXOOOXXOOOOXOOOOOOOOOXXXOOXOOXXXXOXXOXOXXXOXOXOXOOXOOOXXOXXOXOXOXXXXOOOOXXOXXXOOOXOXXXOXOOOOXOXOOOXOOOOXXXOOOOXOOOOXOOXOXXOXXOOXXOXOXXXOOXOXOOOOXOOXXXOXOOOOOOXOXOXXXXOOXXXOXXOXOXXOXOOOXOXXOOXXOXXOXXOXXXXOOOXXXXXOOOOXOXXXXOOOOOXOOOXOOXXXOOOOOOOOOOOXOOOOOOOXOXXOXOOXOOXXXOXXOXXOOOOOXOOOXXOXXXOXOOXOOOOOOOXXOXXOXOXOOXXXOOOXOOXXOOXXXXXOOOOOXXOOOOOXXOXXOXXXXOXXXXXOXXXXOOXXXOXXXXXOXOOXOOOOXXXOOOOXXXOXOOOXOXOXOXOOXOXXXXXOXXXOXOOXOXOXXXXOXOOXOOOXXOOXXOXXXXXXXOXXXXXXXOOXXXXXXOXXOXXXOOXOOOOXXOOOOXOXXXXXOOOXOXXOOXOXOXXXXOOXOOXOOOXXOOOOOXOOXOOXXXXOOXXXOOOXOOXOXXXOXOOXXXXOXXXOXOXXOXXXXOXXXXOOOXXXOOXXXXOOXXOXOOOOXXOXXXXOOXOXXXXXOOXXXXOOXXXXXOXXXOXXOXOOXOXXXOXOXXOOXOXXXOXOOOOXXOXOOXXOOOXOXXOXXOOXXXOOXOOOOXOOOXXOXOXOXOXOXOOXXOOXXXXXXXOOOOOXXXXOOXOXXXXXOXOXOXXXOOXOOXXXXOOXXOXXOXXXXOOXOXXOOXXXXOOXOOXOOXXXOXOOOXOOXOXXXXXOOOOXOOOXOOXOXXOOOXOXOXOOXOXXXOXOOXXXXXXXXXOOXOOXOOOXXOXXOOOXXXOXXOXXOOOXXOXOXOXOXXXOOXOOXXOOXXOOXOXOOOXXXOXOOXOXXOXOOXXOOOOXOXXOXOOOXXOOXOOOOXXXOOXXOXOXOOXOX';\r\ne=60;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%22\r\ni='XXXXOOOXXOXXOXXOOXOXXOXOOOXOXOOXXXOOOOOXXOOXXOXOOOXXOOOOXOOOOXXXXOXOOOOXOXXOOOOXOOXOXXXXOXOXXOXOOOOXXXOXXOOOOXOOXOOXXOOOOOXOXOOXXXXXOXXXOXXXOOXOOOOXOXXOOOXXXXOOXOOOOOXXOXOXOOXOOOXOXOXXXXXOOOXXXOXOOXXOOXXXXXOXXXXOOXOXXXXOXOXXOOOOOXOXXXXXXOXXOOOXOOXXXOOOXXOOXOOXXOOOOXOXOOXOOXXXOXXXXXOOXOXOXXXXXXXXOOXOXXOOOXOXOOXXOOOOXOOOOOXOOXXOOXOOXXXOXXOOXXOXOXOXOXXOXXOXXOOOXXOOOXOXOOOOXOOOOXOXXXOXOOOOXXXXXXXXOOXXOOOXXOOXXXOOXXXXXOXXOXOXXXOOOXOOXXOXXOXOXXOXXOOOXOXXOOOXOXXXOXXXOOXXOXXXXXXOOXXXXXOOOOXOXOXOXOOOXOOOXXXOXOOXXXOOXXXOOOOOXXOXXOXXOOXOXXXOOOXXXOXXXOOOXXXXXXXOOOXOOOXXXXXXOXXOXOXXOOOXXOOXOOOXOXOOOXOXXOXXOXOOXOOXOOOXOOOOXOXOXXOOOXOXOXOXXXOOOXOOOXOOXXXOOXOXOXXOOXXXOOOOOOXXXXXXXOOOXXOXOXXOOOXOXOXXOOOOOOXXXXXXOOXOOXXXXOOOOOOOXOOOOXXXXOXOXOOXOXOOOOXOXXXOOOOXXOXOXOXOOXXOOOOOOXXOOOOOXXXXXXOOXOOOOOOXXXOOXXOXXOXXOOOOOXOXOXXOXXOXOXOOXXXOOOOOXOOXXXOXOXOOOXXOXOOOOOXXOXOOOXOXXOOXOXXXOOXXOXXXXXOXOOOXXOXXOOOOOXXXOXXOOOXOOOXOOXOOXXOXXXOXXXOOXXXXOOXXXOOXXXXOXXXXOXXXOOXXOXOOXXOOXOXOXXOXXOXOOXOOOXOXXOOOOOOOXOOOOXOX';\r\nd='OXOXOXXOXXXXOOXOOXOOXXOXXOOXOXXXXXOOOXXOXOOXOXXOXXOXXOOXXOXXOXOOOXOOOOOOXXOOOOXOXXOOXOXOXXOXXXXOXOXOOXOXXXOXOOOXOXOXOOOOOOXOXOOOOXXOOOOXOXOOOOXXOOOXXOXOXOOXXOOXOOOOXXOOXXOXXOOXXOOOOXOXXXOXXXXOOXXOXXOOOXOXXXOOXXXOOXOXOOOXXOOXOOXXXXOOXXOOOOOXOOXOXXXXXOOOXOOXXOOOOOXXXXOXOXXXXOXXOOXOOOOXOOOOOXXOOXOXOOOOOXOOXXXOOXXOOOOOXXXXOXXXOOXXXXOXOXOOXXXOXOXOXOOXOOXOXXOOXOOOOOOOXXXOOXOXOXOOOOOOXOXXOOXXOXXXXOXOXOOOXOXOXOOOXOXOXOXXXXXOOOXXXOXOXOOXXXOXOXOOOOOOOXOOXXXOOXXXOOOOXOOXXXOXOOOOXOOOXXOXOOXXXXXXOXOOXXOOXXXXXOXXXXXXOOOXOXOOOXOXOXXXXXXXOXOOXXOOXXOXXOXOOXXXXOOXOXOOOOOOXOXXOOOXOXXXXOXOXXOOXOOXXXOOOOXOXOXOXXXOOXOOOXXOOOXXOXXXXXOXOXOOXOXOOOXOXXXOOOXOXOOOXXXOXOXOXOOXOOXOOXXOOXXXOOXOOOOXXOOOXXXXOOXOOXXXXOOXXOOXOOXXOOXXOOXOOXXOXXOXXXOXXOOXXXOOOXXOOOOXOXOXXOXOXOXXXOOXXXXOXOXXXOOOXXXOOXOOXOOXXXXOOOXXOOOOOOXXXOOOXOXXXOOOXOOXXXXOOXOXXOXXOOXOOXXXXXOXXXXXOOXOXXOXXOXOXOXOXXXOOXOXOXXOOOOXXOOOOOOOOOOXOOXOOOXXXOXXXXXOXOXXXOOXOOOOOOXXXXXXXOXOOOXXOOOOXXXXOXOXOXXOOXXOOXXOXXOXOXXOXXXXXOXXOXOXXXOOOOXXXOXOXOXOOOOXXOXOOXXO';\r\ne=47;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%23\r\ni='OXXXXOOXXXOOOOOOXXXOOXXXOOOOOXOOOOXOOXXOXOOXOOXOXOOOOOOXXXOOXOOXXXOOXXOXOOOXXOXOOOOOOOOXXOOXOXOXXXOXOOOOOXOOXXOOOOXXOXOXXOXOXOXXOXXXXOXXXOXOXXXXXXXOXXOXXXOXXXOOOOXOXOXXOOOXXXXXOOOXXXOXXOXOOXXOXXXOXOXOOOOXXXOOXXOOOOOOXOXOOOXXXXOXOXOXXXOOOOXOOOXOXOXOOOXOOXOXOOOXOOOXXXOOOXXXXXXOXXXOXOXOXOOOOXXOXOOOXXOXXOOOXOOOXOOXOOOXXOOXXXXXOOXOXXXOOOXXXOOXXXXXXOXXOOOOXXOOXXXXXOOXXXOXXXXXXXXOOOOOOXOXXOOOOOXXXOXXOOOOXOOOXXOXOXXOXOOOOXXOOXOXOOXXOXOXOXOOXOOXXXXXOOXXOXXXXXOOXXXXOXOOOOXXXXOOXXXXOOOOXOOOOOOOOXXXOXXXXOOXXXOXXXOOXOXXOXOXXXXOXXOOOOOXOOOOXXOOOXOOXXXOXOXXOOXOOXXOOXXOXOXXXXOXOXXXXOXXOXXXOXOOOOOOOOOXOOOOOOXOXXXOXOXOXXXXXOXOXOXOOOXOOXXOXXOXXOXXXOOOXXOOOOXOXOXXOXOOOXXOXXXOOXXOOXOXXXXOXXXOXXXXOXXXXXXOOXOXOXXXOOOXXXOXOOXXOOOOOXOXOOXOXOXXXOOOXXXOXOXXOOOXOOXXOOXOOXOXOXXOXXOOOXXOXOXXXXXXXXOOXXOOOXXOXOOOOXOOOOXOOOXXXXOOOOXOOXXOXXOXOOOXOXXOOOOXXOOOOXOOXXXXXOOXOOXXOXOXOOXXXOOXXOOXXOXXOXXOOOXXXOXOOOXOXOXXOXXXXXXOXOOXXOXXOOXXOOXOXXXOXOOOOXOXOOXXOXXOXXOOXOXXXXOXOXOOOOXOOOOXXXOOOOXXXXXXXXOXXOXXOXXXXXOXXXOXXOOXXXXO';\r\nd='XXOOXXOXOOXOOOOOXOXXXXXXXOOOXXXOOXOXOXOOOXXOOXXXOOXXXXOOOOXOOOOXOOOXOOXOXXOOOOOXXXOXOOXOXOOOOXOOOXXOOXXOXOXOXOXXOOOXXOOXOXOXOXXXOXXXXOOXXXXOXXXOXXOXXXOOXXXOXOXXOOXXOXXOXOOOOOXXXOOOXOXOOXXXXOXXOXXOXOXXOOXXOOXXXXXOXXXOXXXXXXOOXOOOOXOXOOXOOOXOXXXOXOXOOXOOXXXOXXXXXXXXOXXXOOOXXXXXXOXOOXXXOXXXOOXOXXOOXXOOOOXOXXXOOOXOOXOXOOOXXXOOXXXOOOOOXOOXXOXXOOXXXXXXXOOXOOOXXXOXXXOOXOOOOOOXOXXOOXOOOOOXOXXXOXOXOOOOXXOXXXXOOOXOXXOOXXXOXOXXOOOXXXOXXXXOXOOOOXOXXXOXOXOOXOOXOXXXOXOXXOXOXXXXXOXOOOXOXOOXXXXXOOOXOXXOXXXXOOXOXOXOXXOOOXXXXOOOOOOOOOOOXOOXXOOOOOXXOXXOXXOOOOOXXOXXXXOOXOOXXOXOXOXXXXXOOXOOOOOXOXXOXXXXXOXXOXOXXOOXOOXXXXXOOOOOXOOOOXOXOOOXOXXXOOOOXXOOXOOOOOOXXOXXOXOOOOXOOOXXXXOXXXOXOXXOXXOXXOOXOOOXXXXXXXOXOXXXOOOOOXOOOXXOXXOOOXXOOXXXOXXOXOXXXOOOOOOXXOXOOXXOXXXOXOXXOXOOOXOOXXOXXOXXXOXXOOOOOXOOXOXXXXXOXOXOXOOOXXXOXOXOXXOOXOOOXXOOOXXXOOOOOOOOOOOOXXOOOOXXOOXOOOXXOXOXXOXOXXOXXXOOOXXXOXOOXOOOXXOOXXXOOOOOXXXXOXXOXXXOXOXXXOXXXOXOOOOOXOXXXXXXXOXOOXOXOXXXOXXXXOOXOOXOOXOOOXXOOXXOXOXOOXOXXXOOXXOXXXXOXXXOOXXOOXOXXOXOOXOX';\r\ne=42;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%24\r\ni='XOOXXOOXOOOXOOOOOXOOOXXOXXOOOXOXXOOOOXXXOXOOOXXXOXOOXXXOOXOOXOXXXOOOOXOXXOOOXOXXOXXXOXXXXXOOOOXXXOXOOOXOXXXOXOXXOOOOOOOOOOOOOXOXOXXOOXXOXXOXXOOXXOXXXOXOXOXXXXXXOXXOOXXXOXOXXOXXXXOOXXXXOXOXXOOOXOXXOXOOOXXOXOXXXXXOOOOXXOOXOXOOXXXOOOXOOXOOXOXXOOOOOOXXXOOOOOOXXOOXOXXOOXXXXOXXXOOXXOOOOXXOXXXOOXXXOXXOXOOXXXOXXXXOXXXOXXOOXXOXXOXXXXXOXXOXXOOXOXOXXOXOXXOOOXOXXOXXOOOOOOOOOOOXXOOOXOXXOXXXXXOXOOXXXOOOOXOXOXOOXOOOOOOXOXOOOXOXXOXOXXOOXOOOXXOXOOXOXXXXXXOOXOXOOOXXOOOOXOXOXXOXXXOOOXOOXOOXOOXXXXOXOXOOOXXXOOXOOXOXXOOOXXXXXXOXOXOXXOOOXXXOOXXOXOXOOOOOXOOXOXXOXOXXXOXXOXXOXOOOOXOXXOXOXXOOXXXOOXXXXXXOXXXXXXOXOOXXXXOXXOXXXOOOXOXOXXOOOOOOXOOOXXXOOXOOXOOOOOOXXXXXOXXXXXXXXXXXOOOXXOOXXXOOXXOOOXOOXOOXOXOXOOOOXOOXOOXXXXOOOXOXXXOOOOOXXOXXXXOXXOXOOXOXXXXOOXXOXOOOXXOOOOXXOXXXOOOXXOXXXOOOOOOXOOXOOXOXXXOOXXXXOOXXOOXXOOOXOOOOOXOXXOOOXOXXXXXOOOOOXXXXOXOOXXOXOXOOXXXXOOXOXXXXXXXOXXOXOOXXXXXXXOOXXXXOOOXOXOOOXXXXOXXXXXXXOXOXXXXXXOXXXOOXOOXXXOXOXXXXOOXXXXXOXOXXOOOOXXOOOXXOXOOXOXXXOXOOOXXOXXXXOOXXOXOOXOXXXXXOXOXXXXXOXOXOXOXXXOXO';\r\nd='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';\r\ne=64;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%25\r\ni='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';\r\nd='XXOXXXXOXOOOXOOOXOXOOOOXOOOOOXXXXOXXXXOOOXXOOXOXXOOOXOXXOXXOXXXOOXOOXOOOXXXXOOOOOOOOXXXXOOXXXXXXOXOXOOOOOXXXOXOOXXOXXXOXXOXOXOXXOOOXXXXOOXOXXXOXOOXOXOOXOXXOXOOXXOOXXXXOOOXXOXOXOOOOOOXXXXOXXXXXOXXOOOXOXXOOOOOOOOXOOOOOOXXXOXOOOOOOOXOOOXXXXOOXOXXXOOOOOOOOOXXXXOOOOXXOOOOOOXOOOXOXXXOOOXXXOOOXXOOXXOOOOXXXOXOOXOXXOXXOXXOOXXOXOOXOXOXOOXXOOOXXXXOXXOXOXXXOXXOXOOXXXOXOXXOXOXXOXOOOXXXOOOOXXXXOXOOOXOXXOOOOOOOOOOOXOOXOXOOXXOXOXXOOOOOXXXOXOXXXOXXXOOXXOOOOXOOOOOXXXXOOOXXXOXXXOOXOXXXOXOXOXXXXOXXOOXXOXOXOXOXOXXXOOOXXOOOXOOXOOOXXOOOXOOOXXOXXXXOOOXOOXOXXXXXOOOXOOOXOOXXXXXOXXOXOXXOOXOOOOXXOOOXOOOOXOXXXOOXXOXXXOOXOXOOOOOXOXXXXOXOOOOOXXXOOOOOOOXXOXXOXOXOOOXXOXOOXOOOOXXXOOXXXXOXXOOOOOOOXOXOXOXOXXXOXOOOXOXOXXXOXXXXXXXXXOXXOXOOOXXXXOOOOXXOOXXOOXOXXOXOXXXXOXOOXOXOOOXXXOOOXOXOXXXXOOOXXOXXOXXOXXOXXXOXXOXXOXXOXXOOOXOOXXXXOOOOOXOXXXXXOOOOXOXXXOXXOXOXXXOOXXOOXOOXOOXOOXOOOXOOXXOOOXXXXXOOOOXOOXOOXXOOXXXXXXOOXXOXOXOXXXOXOXOOOXOXXXOOXXOXXXOXXXOOOOOOOOXXOXXXOXOOXOOXOXXOXOXOOOOOOXOXOXXOOXOOOOXOOXXOXOOOXXXOOOOXOXXOXXOXOOXO';\r\ne=23;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%26\r\ni='OXXOOOOOOXOOOOOXOOXXXXXOXXOOOXOOXXXOOXOXOOXOXOOOXXXOXOXXOOOOXXXXOOXOOXXXXXXOXXXOXXOOXOOXXOXXOXXOXXOXOOOOXXXXXOOOOXXOXXOOOOOOOXXXOOXXOOOXXOOXXXOXOXOXXXOXOOOOXXOXOXXOXOOOXOXXXOOXXXOXXXOXXOOXOXOOOOXXXOXOOXOXXXXXOXXOOOOOOXXXXOOXOXXXXOXOOOOOXXOXXXXXOOXXXXOXOOXXXOOOXXXXOXOXXXOOXXOXOXOXXOOOXXOOXXXXOOXXOOXOXXXXXXOOXXOXOXOXXOOXOOXXOXOOOXOOXXOOXXOXXOOXOOOOOOOXOXOOXOOOOOOXOXXOXXXXOOOXXXXXXXXOXOOXXXOXOOOOOOXOOOOOOXXOOXOOXXOXXOXXOOXXXOXOOXOOXXXXXOOXXXOXOXOXXOXOXOXXXXOXXOOXOXXXOOXXXXOOOXXOXOXXOOXOXXXOXXXXOOXOXOOOXXXXXXOXOOOXOOXXXOXOOOOXXOOOOOOOXOOOXXOOXXOOXOOOOOXXXOXOXOXOOXOXOOXXOOOOOXOOOOOXOOOOXXOOOOOXXXOXXXXOOXXOXOOOXXOXXXXOOXXOOOOOXOOOXXOXOOOOXOOXOOXXOXOXXXXXXXXOOXXOXXOOOXOXXOOOOXOOXOOXOXOXOOOXXOXXXOOOOOXOXXXOXOOXXOXXXOOOXXXXOXXXOXXOOOOXOXXXOXXOOOOOOOXOXOXXXOOXOXXXOXOOOOXXXXOXXXXXXXOXXXXOXOXOXXOXOXOOXOXXXOXXOXXXOOXXXOXOOOXXXOXOOXXOXOOOOOOXXOXOXXXOXOXOOOOOOXOXXOOXOXXOOOOXOOOOXXOOXOOXXOXXOXOXXOOOOXXOXXOOXXXOOOXXXOOXXOOXXOOOXXOXXOXXXXOOXOOXOOXXOOOXXXOXXOXXOOXOXOOXXOOOOOOXXOXOOXXOOXXXXOOXOXXOXOXXOXX';\r\nd='XOOOOXXOXXXOOXXOOOXOXOXXXXOXOOXXXXXOXOXOXXXXOOOOXOOOOXOOXOXOXXXXOOOXOXXOXOOXXOOXOOXXOOXOXXOXXXOOOOXXXXOOXOXXOOOXXXXXOXXOXXOXOOXOOOXOOOXOOOOOXOXOOOXXOOXXXXXOOOOOOXXXXOOOXXXOOOXXXOXOOXXOXXOOOOOOXOXOOOXXXXOXXXXXXXXXOXXOXOXOXXOOXXXXXOOXOOOOXOOOOOXOOOOOXOXXOOOXXXXOOXXXOXXOOXXOOOOOOOOXXXXOXOOXXOXOXOOXOXOOXXOOOXOXXOXOXXOXOOOXOXOOOOOXOXXOOXXXOOXOXOOOOOXXXOXOXXXOOOOXXXXOXOOXXOXXXOOOXXOXXOOXXOOXOXXOXOXXXXXXOOXOXXOXOXOOOXXOXXOXOXOOOXOOXOOOOOOXOOOOOXXXXXXOOXXXOOXXOXXOOOOXXXOXXOXOXOXOOOOXXXOOXOXXOOOXOOXOXOOOXOXOXXOOXXOOOXOXOXOXXXXOXOXOOXXXXXXOOXOXXOXOXOOOXXXOOOOXXOXXXOXOXXOXXOOOXXXOOXOOXOXXXXOOXOOOOXOOOOOOXXOXXXXOOXOXXXXXXOXXOOXOOOOXXXXOXOOXOOOOOXXXXXOOOXXOXXOXXXXXXXXOOXOOOOOXXXXOOOOOXOXOXOOOXOOOOXOOOOOOXXXXXXOXOXOXXOOXXXOXXOXOOXOXXOOXXXXXOXOXXOXOOXXXXXOOOXOOOXXOOOXOXOXOOOOXOOXXXXOXOXOOXOXXXOOOOXXOXXXXXXOXXOXOXOXXXXXXXXOXOXXXOOXXOXXOOXXXXXXOXXXXXOXOOOOOXXOXOOXOXXXXXXXOXXOXOOOXXOOXXXOOXXOOOXXXXOOOOOOXOOXOOOOXOOOXOXOOXOOOXOXXXOOXOXOXXXXOXOXOOOXOOOXXXOOOXXOXXXXXOXOOOOXOOOOOXXXXOOOXXOXOXXXOOXOOOOXXOOX';\r\ne=38;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%27\r\ni='XOXOXOOXOXXOXXOOXXOOOXOOOXOOXOXXXXXXXXOXXOOOOOXOOXOXXOXOXXOOXXOOOOXXOXOXOOXOXOOXXOOOXOXOOXOOXOOOOOOOOXXXXOOOOXOXXXXXOOXOOOOXXOOOXXXOOOXXXXOOXOXOXXOOOXXOXXXOXOXOOOOXXXXXOXOOOXXXXXXXOOOOXXOXOOXXXOXXXOXXOXOOXXXOXOXXOOXOXXOXOXOXOOXOOOXXOXXXOXXXXOXXOOOOXOOOOXXXXXXXXOXXXOXXXOXOOOXXXXOXXXOXOXXXXOXOOXOOXOXXXXXXOOXOXOXXOOOOOXXOXOOXXOOOOXOXXOOOXOOOOXOXXOXOXOOOXXXOXOXOOXOOXOOXOXXXXXOOOXOOXXOOXOOXOOOXXXOOXXOXOOXXXXXOXXXXOXXOXXOOOOOXXXXOOOXOXXXOOOOXOXOOXXOXOXOXOXXOOXXOOXOXXOXXOXOOXOOXOXOXXOOXXXOXXXXXXXXXXOXOXXXOXOXXXOXXOXXXOOXOXOOXOXOOXXOOOXOXXOXOXXOOXXOXOXXOXXOXXXXOXOXOXXOOXOOOXXOXOOXOOXXXXXOXOOOXXOOOOOXXXXXOXOXXOXOOXOXOXXOXOOXXOOOOOXXOXXXXXOOOXOOXOOOXOXXXXOXXXXOOXXXXOXXOXXXXXOOXOOXOXXOXOOXXOOOOOXOOXOXOXXXOXXXOXOXXXOXOXXOXXOXOXOXXOXXXOXXXXOOXXXOXXOOXOOOXOXOOOXOOXXOXXXXOOOXOOXOOOOOOOOXXOOXXOXOOOOXXOOOXOXOOXOOXXXXOXOOXXXXXXXOXOXOXXOXOXXOOXOXOXOXXXOOXXOOOOXOOXOOXXXOXOXOOOXXOXOOXXXOXXOXOXOXOXXOXOOOOXXOOOOXXXXXOOXXXOOXXOXXXXXOXOOOXXOXOXOOXXOOOXXXOOOOXOXXXOXXXOXOXOXOOOOOXXXOXXXOOXOXOXXOXOOOXXXXOOXXXXOO';\r\nd='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';\r\ne=36;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%28\r\ni='XXXXOXOOXXOOXOXXOXOXOOXXXOXOXOXOOOOOXOOOXXOOXOOXOXOXOOXOOXXXXOOXXOOXXOOOOXOXOXOOOXOXXXOOXXXOXXOOXXXOXOOOOOOOOXXOXOXXOOOXOXOXXOOOXOXXOXXOOOOXOXXXXOXOOOXOXOOOXXOXXXOXXXOXOXOXXOOOOXXXXXXOXOOOOXOXOXXXXOXOXOOOOXOOOOOOOOOOOXOXXXOXOXOXXXOXOOOOOOXXXXOXOOOOOOXXXXOXXXXXOXOOOOOOOXXXOOOOOXOOXOXXOOXXOOOXOXXXOXOOXXOOXXOXXXOOOOXXXXXOOXXOOXOOOXOOOXXXXXOXOOXOOOXOXOOOXXOOOOXXXOXXOXOOOXOXOOOOOOOXXXOXXOXXOXXOXXXOXOXXOXOXOXXOXOOXOXXOXOOOXOOOOXOXOXOXOXXXXXOXXOXOOXXXXOXOOXOOXOOOOOXXXXXXXOXOOOXXOOOOOXXXXXOXXXXXOOOXXOXOXOOXXOOXOXOOXXOXOXOXXXXOXOXXOOOXOXOOOOOOXOXOXXXXOOXXOOOOXOXOXXOOXXXOOOXOXXXOXOXXXOXXOOXOXOOOOOXXXOOXOXOOXXXOOOOXOXXXXOOOXXOXOOXOOXXXXOXOOXXXXOOXOXXOOOXOOXXXOXOXXXXXOOOOOXXXOXOOOOXOXOOOOOXXXXXXOXOXOXXXOOXOOXOXXOXXXOXXOOOOOXXXOXOXOOOOOXXOXXXOOXXXXXOOXOOOOOOXXXOOOXXOXOOOOOXXOXOXOXXXOOXXOXXXOOOOXOOOXOXOXOXOXOXOXXOOOXXXOXOOOXXOOXXXXOOOOXXOOXOOOOXXXOXXXOXOOOOOOXXOOOOOXOXXXXOXOXXXOOXOOOOXXOXOOOOOXOXOXOXXOXXXXOOOXXXXOOOOXOXXXOOOXXXXOOOXOXXXXXOOXXXXOXXXXOXXOOXOXOOOXOOOOXOOXOXOOXXXXOOXOXOXXXXOXOOOXOOOOOO';\r\nd='XOOOXXXOXXOXXOOXOOXOXOXXOOOOOOXOXXXXOOOOXXOOXOOXXOOOOXXXOOOXXXXOOOOOOOOXOXXXOXOXXOXOOOOOXOXXXXXOOOOXXOOXXXXXOXXXXXOXXXOXOOOOOXOOOXOXXXXOXXXXXOOOXOOXOXXOOOXXOXOXOOOXXXOOOXOOXOOOXXOXOXXOOOXOXOXXXOXXXXXOOOOXXOXOOXOOOOXXXXXOOOXXOXXXXOXOXXXXOXOOOOOXOXOXXOXOXOOOXOXOXXOXXXXOOXXOOXOOOOOXOXOXXXOOXOXXOOOOXOXXXXOOXXOXOXOXXXOXOXXOXXXXXXOOXXOOOXXXOOXOXOXOOOOOXOXOXXOOOOXXXOOOXXOOOXOXOOXOOXOXOOXXOOOXXXXOOOOOOOXOOOXOOOOOXXXXOXOXOXXOXOOXXXXOOXOXOXXOXOOXOOOXOXOXOOXXXXXOXXXXXXOXOOOOXXXOOOOOXXOXXXXXOXXOXXXOOOXOOOXOOXOXXXXOOXXOXOOXOOOXOOOOXOXOXXXOXOOXOOXOXXOOXOXXXOXOOOOOOOOOOXOOOXOOXXOOXOOXOXOOOXXXOXXXXOOXOXOXOOXXXXOOOXOXXXOOXOXOXXXOOXXXXOXXXXXOXOXOXOXXOOXOXXOXXOOXXOOOOOXOXXXXXXXXOXXOOXXXOXXOOOXOOOOOOOOOXOXOOOXXXXXOXOOOOOOXOXOXOXOOOOXXOOOXOOOOOXXOXOOOXOOXXOXOXOOOXXXOOOXOOXOOOOXXXXXOOXXOOXXXXXOOOOOXOXOOXOXOOXOOOXOOOXXOOXOOOXOOXXOOXXXXXXOOXOXOOOOXXXOOXXOXOOOXXOXXOXOXXOXOXXXOOXOXXXOOXXXXOXXOOXOOOXXOXOOOXXXXXXOXXOOOXOOXOOOXXXOOOOOXOOXXXXXOOXXXOOXOOXXOOXOXOOOXOXOOOXOXXXOXOOXOOXXOOXOOOOOOXXXOXXOXOXOXOXOXXOXXOXX';\r\ne=32;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%29\r\ni='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';\r\nd='OXXXOXXOXOXXOOOOOXOOXXOXOXOOOOOXOXOOXXXOOXOOOXOXXOXXXOOXOXXXOOXOXXXXXOOOXXXOOOOXOOOOOOOOOXXOXXOXXOOXXOXOXXXOXXOXOOXXXOXXXOXXXXXXOOOOXOXXXXOOOXXOOOOXOOOXXXXOXXXXXXOXXOOOXXOXXXXOXOXXOXXXOOOOOXXXOOXXXXOXOOOXXOXXOOXXOOXOOXOXOOOOXXXOOXOOXOOOXXXXXOXOOXXXOOOXXOOOXXXXOOXOXXXOXOOOXXXXOOOXXOOOOXXXXOXXXXOXXOXOOXOXXOOXXXOOXOXXOXOOOXOXOXXXXOXXOXXXXXOOOXOOOXXOXOXOXOXOXOXXOXOOOOOXOOXXOOOXXXOXXXXOOXOOXOXOOXOXOXOOOOXXXXOXXOXXXXXXXOXXXOOXXOOXOXXXXOXOXOOXOOXOXXOOXXXXXXXXXOOOXOXXOXXOXXXOOOOOOOOOXOOOOOXXXOXXXOXXXOXOOOXXOXXOXOXOXXXXOXOXXXXOXOOOOXOXXOXXXXOXXOXXXXOOXXXXOOXOXOOOXXXXXXXXXOOXXOXOXXOXXXOXOOOXXOOXXXXXOXXOXOOXOXXXXOXOOXOOOOOXOXXXOXXXOXOXXOXXXXOOXXOXOOXXXOOXXOOXOXXOXOOOOXOOOXXXXXOXXXOXXOXXOOOXXOXXXXOXXOOXOXXOOOXOXOXOXOXOXOXOOOXOOXOOXXOOXOXOXXXXOXXOXOOOOOOOOOOOOOXXXOOOXXOXXXXOXXOXOXOOXOOXOOXOXOXXOOXOXXXXXOXXOOXOXXOXOXOXXOXOXOOXOXOXOXOOOOOOXOOXOXXXOOOOOOXXXXXXXXOXXXXOXXXXOXOOXXXOXXXOOOXXOXOXXOOOOOOOXOXXXOXXXXOXXXOOXOXOOOXXOXOXOOOXXXXXXOOOOXXOOXOXXXXXXXXXOOXXOXOOXXXOXOOOXXXOXXOXOOOOXXOOOXOOOOOOXXXXOXO';\r\ne=27;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%30\r\ni='XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO';\r\nd='OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX';\r\ne=999;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OOOOXXOOOO'; %31\r\nd='XOOOOOOOOX';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-21T20:43:53.000Z","updated_at":"2026-06-09T10:32:06.000Z","published_at":"2013-04-21T21:37:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://contest.usc.edu/index.php/Spring13/Home\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eUSC Spring 2013 ACM Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Problem F, Snow Cones.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O. Input is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e From XXO to OXX \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e From OXOX to XOXO \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly two competitors solved this challenge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA little complex requiring a Matlab 3-Liner solution versus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://contest.usc.edu/index.php/Spring13/Home?action=download\u0026amp;upname=cones.zhengcao.cpp.txt\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCao's C solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":988,"title":"Convert a substructure reference string into a valid definition structure for subsref and subsasgn","description":"You have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. \r\nTherefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\r\n\r\nFor example, to reference the value a(12), you would have to convert '(12)' into \r\n\r\n  def = \r\n    type: '()'\r\n    subs: {[12]}\r\n\r\nAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into \r\n\r\n  def(1) = \r\n    type: '()'\r\n    subs: {[12]}\r\n\r\n  def(2) = \r\n    type: '.'\r\n    subs: {'field_b'}\r\n\r\n  def(3) = \r\n    type: '{}'\r\n    subs: {[1]  [3]}\r\n\r\n  def(4) = \r\n    type: '{}'\r\n    subs: {2}\r\n\r\n  def(5) = \r\n    type: '()'\r\n    subs: {[3 4]  ':'}\r\n\r\n  def(6) = \r\n    type: '.'\r\n    subs: {'c'}\r\n\r\nThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\r\n\r\nNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.","description_html":"\u003cp\u003eYou have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. \r\nTherefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\u003c/p\u003e\u003cp\u003eFor example, to reference the value a(12), you would have to convert '(12)' into\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edef = \r\n  type: '()'\r\n  subs: {[12]}\r\n\u003c/pre\u003e\u003cp\u003eAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edef(1) = \r\n  type: '()'\r\n  subs: {[12]}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(2) = \r\n  type: '.'\r\n  subs: {'field_b'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(3) = \r\n  type: '{}'\r\n  subs: {[1]  [3]}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(4) = \r\n  type: '{}'\r\n  subs: {2}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(5) = \r\n  type: '()'\r\n  subs: {[3 4]  ':'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(6) = \r\n  type: '.'\r\n  subs: {'c'}\r\n\u003c/pre\u003e\u003cp\u003eThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\u003c/p\u003e\u003cp\u003eNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.\u003c/p\u003e","function_template":"function def = subsdef(defstr)\r\n  def = substruct('()',{1});\r\nend","test_suite":"%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = 1i;\r\nb(12) = y_correct;\r\ndefstr = '(12)';\r\nassert(isequal(subsref(b,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = -4i;\r\nc{1,2,3,4,5}.field_b = y_correct;\r\ndefstr = '{1,2,3,4,5}.field_b';\r\nassert(isequal(subsref(c,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = 3i;\r\na(12).field_b{1,3}{2}((3),1).c = y_correct;\r\ndefstr = '(12).field_b{1,3}{2}((3),1).c';\r\nassert(isequal(subsref(a,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = repmat(2i,3,1);\r\nd{2}.a(1:3,:) = y_correct;\r\ndefstr = '{2}.a(1:3,:)';\r\nassert(isequal(subsref(d,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2012-10-11T14:58:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-11T14:55:15.000Z","updated_at":"2026-06-02T03:44:46.000Z","published_at":"2012-10-11T14:55:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. Therefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, to reference the value a(12), you would have to convert '(12)' into\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[def = \\n  type: '()'\\n  subs: {[12]}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[def(1) = \\n  type: '()'\\n  subs: {[12]}\\n\\ndef(2) = \\n  type: '.'\\n  subs: {'field_b'}\\n\\ndef(3) = \\n  type: '{}'\\n  subs: {[1]  [3]}\\n\\ndef(4) = \\n  type: '{}'\\n  subs: {2}\\n\\ndef(5) = \\n  type: '()'\\n  subs: {[3 4]  ':'}\\n\\ndef(6) = \\n  type: '.'\\n  subs: {'c'}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42685,"title":"Cody meets Xiangqi: foresee the unseen (Part 2)","description":"This is the second part of the Xiangqi series. The first part in this series is: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen Cody meets Xiangqi: foresee the unseen (Part 1)\u003e\r\n\r\nBeing increasingly interested in \u003chttps://en.wikipedia.org/wiki/Xiangqi Xiangqi\u003e (a.k.a., *Chinese Chess*), Mr. Cody has designed a new Xiangqi match for \u003chttps://en.wikipedia.org/wiki/Xiang_Yu Xiang Yu\u003e and \u003chttps://de.wikipedia.org/wiki/Han_Gaozu Liu Bang\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\r\n\r\nOnce\r\n\r\n   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \r\n\r\n*whichever comes first*, Mr. Cody announces the outcome accordingly as follows:\r\n\r\n   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\r\n\r\nAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\r\n\r\n                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n\r\nwhere \r\n\r\n* a: the probability that Xiang Yu wins one individual game\r\n* b: the probability that Liu Bang wins one individual game\r\n* Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n* Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n* Nc: # of consecutive ties required to result in a final draw\r\n* Pa: the probability that Xiang Yu wins the match\r\n* Pb: the probability that Liu Bang wins the match\r\n* Pc: the probability of a final draw\r\n\r\nThe main focus of this problem is on *Monte Carlo simulations*, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\r\n\r\n1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u003c tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected. \r\n\r\n2) Check if your solution is based on *pure Monte Carlo simulations* or *analytical approaches*. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations. \r\n\r\n3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get. \r\n\r\nIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks. \r\n\r\n ","description_html":"\u003cp\u003eThis is the second part of the Xiangqi series. The first part in this series is: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\"\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eBeing increasingly interested in \u003ca href = \"https://en.wikipedia.org/wiki/Xiangqi\"\u003eXiangqi\u003c/a\u003e (a.k.a., \u003cb\u003eChinese Chess\u003c/b\u003e), Mr. Cody has designed a new Xiangqi match for \u003ca href = \"https://en.wikipedia.org/wiki/Xiang_Yu\"\u003eXiang Yu\u003c/a\u003e and \u003ca href = \"https://de.wikipedia.org/wiki/Han_Gaozu\"\u003eLiu Bang\u003c/a\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/p\u003e\u003cp\u003eOnce\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \u003c/pre\u003e\u003cp\u003e\u003cb\u003ewhichever comes first\u003c/b\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\u003c/pre\u003e\u003cp\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/p\u003e\u003cpre\u003e                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\u003c/pre\u003e\u003cp\u003ewhere\u003c/p\u003e\u003cul\u003e\u003cli\u003ea: the probability that Xiang Yu wins one individual game\u003c/li\u003e\u003cli\u003eb: the probability that Liu Bang wins one individual game\u003c/li\u003e\u003cli\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/li\u003e\u003cli\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/li\u003e\u003cli\u003eNc: # of consecutive ties required to result in a final draw\u003c/li\u003e\u003cli\u003ePa: the probability that Xiang Yu wins the match\u003c/li\u003e\u003cli\u003ePb: the probability that Liu Bang wins the match\u003c/li\u003e\u003cli\u003ePc: the probability of a final draw\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe main focus of this problem is on \u003cb\u003eMonte Carlo simulations\u003c/b\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/p\u003e\u003cp\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/p\u003e\u003cp\u003e2) Check if your solution is based on \u003cb\u003epure Monte Carlo simulations\u003c/b\u003e or \u003cb\u003eanalytical approaches\u003c/b\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/p\u003e\u003cp\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/p\u003e\u003cp\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/p\u003e","function_template":"function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n% a: the probability that Xiang Yu wins one individual game\r\n% b: the probability that Liu Bang wins one individual game\r\n% Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n% Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n% Nc: # of consecutive ties required to result in a final draw\r\n% Pa: the probability that Xiang Yu wins the match\r\n% Pb: the probability that Liu Bang wins the match\r\n% Pc: the probability of a final draw\r\n    Pa = ;\r\n    Pb = ;\r\n    Pc = ;\r\nend","test_suite":"%%\r\n% Thanks to Alfonso Nieto-Castanon\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path;\r\n\r\n%%\r\nfh = fopen('EvaluateSolution.p','wb');\r\nfwrite(fh, hex2dec(reshape('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',2,[]).')); rehash path; fclose(fh);\r\n\r\n%%\r\nfid = fopen('Xiangqi2.m');\r\ndelim = {' ', '\\n', ',', '.', ';', '''', '@', '+', '-', '*', '/', '\\', '^', '\u003e', '\u003c', '=', '\u0026', '|', '~', '{', '}', '[', ']', '(', ')'};\r\nfile = textscan(fid, '%s', 'CommentStyle', '%', 'MultipleDelimsAsOne', 1, 'Delimiter', delim); fclose(fid); \r\nassert(~any(ismember({'rng','RandStream','seed','state','twister','shufle','default'},file{1})));\r\n\r\n%%\r\na = 0; b = 0; Na = 2; Nb = 3; Nc = 2; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0; b = 1; Na = 1; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 1; b = 0; Na = 3; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0.15; b = 0.85; Na = 4; Nb = 2; Nc = 1; tol = 1e-4;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.9; b = 0; Na = 3; Nb = 1; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.65; b = 0.3; Na = 3; Nb = 2; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\nNa = 3; Nb = 2; Nc = 1; tol = 2e-3; \r\np = sort(rand(2,30)); \r\np = sort([p(1,:);diff(p);1-p(2,:)]);\r\nfor k = size(p,2):-1:1\r\n    a = p(3,k); b = p(2,k);\r\n    score(k) = EvaluateSolution(a, b, Na, Nb, Nc, tol);    \r\nend\r\nSetSolutionScore(round(mean(score)));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2015-11-12T00:41:35.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-08T20:51:55.000Z","updated_at":"2026-06-01T20:51:40.000Z","published_at":"2015-11-10T00:22:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second part of the Xiangqi series. The first part in this series is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeing increasingly interested in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiangqi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiangqi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (a.k.a.,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eChinese Chess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), Mr. Cody has designed a new Xiangqi match for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiang_Yu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiang Yu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://de.wikipedia.org/wiki/Han_Gaozu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLiu Bang\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu wins Na games consecutively,\\n   2) Liu Bang wins Nb games consecutively, \\n   3) No ties occur consecutively,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhichever comes first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu is the final winner,\\n   2) Liu Bang is the final winner, \\n   3) They end up with a final draw.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea: the probability that Xiang Yu wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb: the probability that Liu Bang wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNc: # of consecutive ties required to result in a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePa: the probability that Xiang Yu wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePb: the probability that Liu Bang wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePc: the probability of a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe main focus of this problem is on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMonte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Check if your solution is based on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epure Monte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eanalytical approaches\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":811,"title":"Genome Sequence 004: Long 3rd Generation Segment Correction","description":"The Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003chttp://www.pacificbiosciences.com/ PacBio\u003e. The \u003chttp://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar Assemblathon Genome Contest\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003chttp://www.sciencedaily.com/releases/2012/07/120702210229.htm Sequence Parrot DNA\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\r\n\r\nThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u003c1% error rate. Jarvis and his team combined this data to achieve \u003c 0.1% error rate.\r\n\r\nGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\r\n\r\n*Input:* \r\n\r\nCall 1: empty array, segment Width, Flag=0\r\n\r\nCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\r\n\r\n*Output:* \r\n\r\nCall 1: empty vector, Number of Requested Vectors\r\n\r\nCall 2: Corrected DNA vector, Number of Requested Vectors\r\n\r\n*Score:* Number of N vectors used to produce correct vector for w=1024 case\r\n\r\nThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\r\n\r\nThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\r\n\r\nThe response to the second call is the fixed DNA sequence, vector of width w.\r\n\r\n*example:*\r\nFirst call return : N=3\r\n\r\n  01230123111122223333 Truth\r\n  Input example\r\n  01232123112122221332 Injected errors\r\n  01130123111122123323\r\n  11230133121122223333\r\n\r\n  Output: \r\n  01230123111122223333 Truth, hopefully\r\n\r\n\r\nThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned. \r\n\r\nThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\r\n\r\nFollow-Up Challenges: Sample Data from the PacBio site for \u003chttp://www.cbcb.umd.edu/software/PBcR/ Lambda Phage\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\r\n","description_html":"\u003cp\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003ca href=\"http://www.pacificbiosciences.com/\"\u003ePacBio\u003c/a\u003e. The \u003ca href=\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\"\u003eAssemblathon Genome Contest\u003c/a\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003ca href=\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\"\u003eSequence Parrot DNA\u003c/a\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/p\u003e\u003cp\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/p\u003e\u003cp\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty array, segment Width, Flag=0\u003c/p\u003e\u003cp\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003e\u003cb\u003eScore:\u003c/b\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/p\u003e\u003cp\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/p\u003e\u003cp\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/p\u003e\u003cp\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/p\u003e\u003cp\u003e\u003cb\u003eexample:\u003c/b\u003e\r\nFirst call return : N=3\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e01230123111122223333 Truth\r\nInput example\r\n01232123112122221332 Injected errors\r\n01130123111122123323\r\n11230133121122223333\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: \r\n01230123111122223333 Truth, hopefully\r\n\u003c/pre\u003e\u003cp\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/p\u003e\u003cp\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/p\u003e\u003cp\u003eFollow-Up Challenges: Sample Data from the PacBio site for \u003ca href=\"http://www.cbcb.umd.edu/software/PBcR/\"\u003eLambda Phage\u003c/a\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/p\u003e","function_template":"function [M_fix,N]=PacBio_fix(M,w,flag)\r\n% 1st Call\r\n% M is empty\r\n% w is width of segment\r\n% flag is 0\r\n% Ouput is N, the number of segments requested to fix the segment\r\n% 2nd Call\r\n% M is an Nxw array of values [0:3]\r\n\r\n M_fix=[];\r\n N=1; % needed for 2nd call with flag==1\r\n if flag==0 % Requested number of Segments\r\n  N=1;\r\n  return;\r\n end\r\n\r\nM_fix=M(1,:);\r\n\r\n\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',0);\r\n%%\r\nM=[];\r\nflag=0;\r\nw=100;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n%%\r\nM=[];\r\nflag=0;\r\nw=6144;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\n%%\r\n% Size Performance is based on w=1024 case\r\nM=[];\r\nflag=0;\r\nw=1024;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,not_N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\nfeval(@assignin,'caller','score',min(20,N));\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2012-10-08T02:30:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-01T05:26:57.000Z","updated_at":"2026-05-31T11:18:13.000Z","published_at":"2012-10-08T02:29:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.pacificbiosciences.com/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePacBio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAssemblathon Genome Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e led the team of Phillippy, Koren and Jarvis to successfully\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSequence Parrot DNA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty array, segment Width, Flag=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScore:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e First call return : N=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[01230123111122223333 Truth\\nInput example\\n01232123112122221332 Injected errors\\n01130123111122123323\\n11230133121122223333\\n\\nOutput: \\n01230123111122223333 Truth, hopefully]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-Up Challenges: Sample Data from the PacBio site for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.cbcb.umd.edu/software/PBcR/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLambda Phage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61337,"title":"Volumetric efficiency","description":"Volumetric efficiency measures how well an engine breathes.\r\nThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \r\nNaturally aspirated engines typically achieve 80–95%.\r\n\r\nGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 317.18px; transform-origin: 467.496px 317.191px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVolumetric efficiency measures how well an engine breathes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 514.477px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 257.227px; text-align: left; transform-origin: 443.508px 257.238px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function eta_v = volEfficiency(m_actual, rho, Vd)\r\neta_v = 0;\r\nend","test_suite":"%%Test 1\r\nm = 0.00180; rho = 1.2; Vd = 0.002;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 2\r\nm = 0.00252; rho = 1.2; Vd = 0.003;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 3\r\nm = 0.00096; rho = 1.15; Vd = 0.0012;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-21T09:48:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:45:01.000Z","updated_at":"2026-06-09T14:09:19.000Z","published_at":"2026-05-21T09:48:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVolumetric efficiency measures how well an engine breathes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-06-09T14:10:05.000Z","published_at":"2026-05-21T09:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61342,"title":"Swept Volume and Clearance Volume","description":"The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \r\nThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\r\n\r\nGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 312px; transform-origin: 468.5px 312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 513px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 256.5px; text-align: left; transform-origin: 444.5px 256.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"685\" height=\"507\" style=\"vertical-align: baseline;width: 685px;height: 507px\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Vs, Vc] = sweptClearanceVolume(V_BDC, V_TDC)\r\nVs = 0;\r\nVc = 0;\r\nend","test_suite":"%%Test 1\r\nV_BDC=550e-6; V_TDC=50e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 500e-6) \u003c 1e-9)\r\nassert(abs(Vc - 50e-6) \u003c 1e-9)\r\n%%Test 2\r\nV_BDC=750e-6; V_TDC=62.5e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 687.5e-6) \u003c 1e-9)\r\nassert(abs(Vc - 62.5e-6) \u003c 1e-9)\r\n%%Test 3\r\nV_BDC=400e-6; V_TDC=36.36e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - (V_BDC-V_TDC)) \u003c 1e-9)\r\nassert(abs(Vc - V_TDC) \u003c 1e-9)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:17:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:13:10.000Z","updated_at":"2026-06-09T14:03:37.000Z","published_at":"2026-05-21T10:13:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"507\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"685\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61341,"title":"Specific Fuel Consumption","description":"Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \r\nModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\r\n\r\nGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 55.5px; transform-origin: 468.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBrake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bsfc = calcBSFC(m_dot, P)\r\nbsfc = 0;\r\nend","test_suite":"%%Test 1\r\nm_dot=0.0070; P=100000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)\r\n%%Test 2\r\nm_dot=0.0105; P=150000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)\r\n%%Test 3\r\nm_dot=0.0040; P=60000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:12:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:05:55.000Z","updated_at":"2026-06-09T14:04:53.000Z","published_at":"2026-05-21T10:05:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBrake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61338,"title":"Fuel-Air Equivalence Ratio (Lambda)","description":"Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \r\nλ = 1 is perfect stoichiometry, \r\nλ \u003c 1 is rich, \r\nλ \u003e 1 is lean. \r\nEngine management systems constantly target λ = 1 for optimal catalyst performance.\r\n\r\nGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 286px; transform-origin: 468.5px 286px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ = 1 is perfect stoichiometry, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026lt; 1 is rich, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026gt; 1 is lean. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 392px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 196px; text-align: left; transform-origin: 444.5px 196px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026amp;rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function lam = calcLambda(AFR, AFR_s)\r\nlam = 0;\r\nend","test_suite":"%%Test 1\r\nassert(abs(calcLambda(14.7, 14.7) - 1.0) \u003c 1e-6)\r\n%%Test 2\r\nassert(abs(calcLambda(12.5, 14.7) - 12.5/14.7) \u003c 1e-6)\r\n%%Test 3\r\nassert(abs(calcLambda(16.2, 14.7) - 16.2/14.7) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-27T03:46:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:51:05.000Z","updated_at":"2026-06-09T14:07:15.000Z","published_at":"2026-05-21T09:51:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ = 1 is perfect stoichiometry, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026lt; 1 is rich, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026gt; 1 is lean. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"386\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"686\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpg\",\"contentType\":\"image/jpg\",\"content\":\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":738,"title":"Criss_Cross_010 : Unique elements, Square array, Words in one array","description":"Criss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\r\n\r\nArrange the \"words\" into a solid square such that all words are used.\r\n\r\nGiven an array of words make the original Square or Square Transpose.\r\n\r\nWords are left to Right or Top to Bottom. No fliplr or flipud.\r\n\r\n*Example:*\r\n\r\nM_orig = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nvr = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nvc = [1 2 3; 4 5 6; 7 8 9]\r\n\r\n*Inputs:*\r\n\r\nw = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\r\n\r\nsorted w gives\r\n\r\nw = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\r\n\r\n\r\n*Output:*\r\n\r\nM_out = [1 2 3; 4 5 6; 7 8 9] or\r\n\r\nM_out=[1 4 7; 2 5 8; 3 6 9]\r\n\r\n\r\nMax size : 256\r\n\r\nThis is the second in the Criss Cross puzzles series.\r\n\r\nFollow up puzzles will have non-unique values and quite a few other variations.\r\n","description_html":"\u003cp\u003eCriss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\u003c/p\u003e\u003cp\u003eArrange the \"words\" into a solid square such that all words are used.\u003c/p\u003e\u003cp\u003eGiven an array of words make the original Square or Square Transpose.\u003c/p\u003e\u003cp\u003eWords are left to Right or Top to Bottom. No fliplr or flipud.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_orig = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003evc = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003ew = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\u003c/p\u003e\u003cp\u003esorted w gives\u003c/p\u003e\u003cp\u003ew = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_out = [1 2 3; 4 5 6; 7 8 9] or\u003c/p\u003e\u003cp\u003eM_out=[1 4 7; 2 5 8; 3 6 9]\u003c/p\u003e\u003cp\u003eMax size : 256\u003c/p\u003e\u003cp\u003eThis is the second in the Criss Cross puzzles series.\u003c/p\u003e\u003cp\u003eFollow up puzzles will have non-unique values and quite a few other variations.\u003c/p\u003e","function_template":"function M_out = Criss_Cross(w)\r\n\r\n M_out=zeros(size(w,2));\r\n \r\nend","test_suite":"%%\r\nformat long\r\nformat compact\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=4;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\nM_out=Criss_Cross(w)\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=8;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\nM_out=Criss_Cross(w)\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=16;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=16;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nn=256;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-03T20:11:23.000Z","updated_at":"2026-06-10T04:21:55.000Z","published_at":"2012-06-03T21:38:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCriss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the \\\"words\\\" into a solid square such that all words are used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of words make the original Square or Square Transpose.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWords are left to Right or Top to Bottom. No fliplr or flipud.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_orig = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evc = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esorted w gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out = [1 2 3; 4 5 6; 7 8 9] or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out=[1 4 7; 2 5 8; 3 6 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMax size : 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second in the Criss Cross puzzles series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow up puzzles will have non-unique values and quite a few other variations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":737,"title":"Criss_Cross_000 : Unique elements in a Square array","description":"Criss Cross matrix puzzle - Easy: Square matrix, Unique elements\r\n\r\nArrange the \"words\" into a solid square such that all words are used.\r\n\r\nGiven an array of row words and an array of column words make the unique Square.\r\n\r\nThere is no flipping or rotating in this simplest case.\r\n\r\nexample:\r\n\r\nM_orig =[1 2 3; 4 5 6; 7 8 9]\r\n\r\n*Inputs:*\r\n\r\nvr = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nscramled gives vr =[7 8 9; 1 2 3; 4 5 6]\r\n\r\nvc =[1 2 3; 4 5 6; 7 8 9]\r\n\r\nscrambled gives vc =[3 1 2;6 4 5; 9 7 8]\r\n\r\n*Output:*\r\n\r\nM_out=[1 2 3; 4 5 6; 7 8 9]\r\n\r\nMax size : 4096\r\n\r\n\r\nThis is the first in a series of Criss Cross puzzles.\r\n\r\nFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.","description_html":"\u003cp\u003eCriss Cross matrix puzzle - Easy: Square matrix, Unique elements\u003c/p\u003e\u003cp\u003eArrange the \"words\" into a solid square such that all words are used.\u003c/p\u003e\u003cp\u003eGiven an array of row words and an array of column words make the unique Square.\u003c/p\u003e\u003cp\u003eThere is no flipping or rotating in this simplest case.\u003c/p\u003e\u003cp\u003eexample:\u003c/p\u003e\u003cp\u003eM_orig =[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003escramled gives vr =[7 8 9; 1 2 3; 4 5 6]\u003c/p\u003e\u003cp\u003evc =[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003escrambled gives vc =[3 1 2;6 4 5; 9 7 8]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_out=[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003eMax size : 4096\u003c/p\u003e\u003cp\u003eThis is the first in a series of Criss Cross puzzles.\u003c/p\u003e\u003cp\u003eFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.\u003c/p\u003e","function_template":"function M_out = Criss_Cross(vr,vc)\r\n\r\n M_out=vr*0;\r\n \r\nend","test_suite":"%%\r\nformat long\r\nformat compact\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=4;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\nM_out\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=8;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\nM_out\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=128;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=1024;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=4096;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2012-06-03T20:42:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-03T18:05:05.000Z","updated_at":"2026-06-11T08:59:30.000Z","published_at":"2012-06-03T19:37:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCriss Cross matrix puzzle - Easy: Square matrix, Unique elements\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the \\\"words\\\" into a solid square such that all words are used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of row words and an array of column words make the unique Square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is no flipping or rotating in this simplest case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_orig =[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003escramled gives vr =[7 8 9; 1 2 3; 4 5 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evc =[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003escrambled gives vc =[3 1 2;6 4 5; 9 7 8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out=[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMax size : 4096\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the first in a series of Criss Cross puzzles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61387,"title":"Multiply the Diagonals of Two Vectors","description":"Find the diagonals of vectors a and b and multiply them.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the diagonals of vectors a and b and multiply them.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = diagonalsProduct(a,b)\r\n  s = \r\nend","test_suite":"%%\r\na = [0 1 2; 3 4 5; 6 7 8]\r\nb = [9 10 11; 12 13 14; 15 16 17]\r\ns = diag(a).*diag(b);\r\nassert(isequal(diagonalsProduct(a,b),s))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-05T15:39:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2026-06-05T15:39:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-05T15:37:19.000Z","updated_at":"2026-06-11T21:01:31.000Z","published_at":"2026-06-05T15:37:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the diagonals of vectors a and b and multiply them.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61346,"title":"Find The Area Of Triangle Using Base \u0026 Height","description":"You should find the area of the Triangle using base and height.\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should find the area of the Triangle using base and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangleArea(base, height)\r\n  area = ;\r\nend","test_suite":"%%\r\nbase = 1;\r\nheight = 1;\r\narea = 0.5;\r\nassert(isequal(triangleArea(base, height),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-23T16:51:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:46:19.000Z","updated_at":"2026-06-11T21:04:01.000Z","published_at":"2026-05-23T16:49:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should find the area of the Triangle using base and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61353,"title":"Basic Algebra II","description":"You have the equation X^2 = n you should find the value of X.\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX^2 = n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyou should find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation(n)\r\n  X = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nX = sqrt(n);\r\nassert(isequal(equation(n),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:23:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2026-05-24T13:23:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:20:58.000Z","updated_at":"2026-06-11T21:07:51.000Z","published_at":"2026-05-24T13:23:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX^2 = n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eyou should find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61345,"title":"Get The Opposite Of The Number Without Negative (-) On It","description":"You must get the opposite of the number X without making -X.\r\nHint: You can make it by Subtraction and Multiplication.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou must get the opposite of the number X without making -X.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eHint: You can make it by Subtraction and Multiplication.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = getOpposite(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = -1;\r\nassert(isequal(getOpposite(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-05-23T14:51:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T14:48:38.000Z","updated_at":"2026-06-11T21:13:11.000Z","published_at":"2026-05-23T14:48:38.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou must get the opposite of the number X without making -X.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint: You can make it by Subtraction and Multiplication.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61358,"title":"Basic Physics IV","description":"Calculate the Mechanical Energy (ME).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the Mechanical Energy (ME).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ME = ME(PE,KE)\r\n  ME = ;\r\nend","test_suite":"%%\r\nPE = 1;\r\nKE = 1;\r\nME = PE+KE;\r\nassert(isequal(ME(PE,KE),ME))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T14:58:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-26T14:58:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T14:56:53.000Z","updated_at":"2026-06-11T21:13:44.000Z","published_at":"2026-05-26T14:56:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the Mechanical Energy (ME).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61347,"title":"Find The Area Of The Circle","description":"Find the area of the Circle using PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the area of the Circle using PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = circleArea(r)\r\n  area = ;\r\nend","test_suite":"%%\r\nr = 1;\r\narea = pi * r^2;\r\nassert(isequal(circleArea(r),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:33:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-23T17:01:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:57:42.000Z","updated_at":"2026-06-11T21:15:54.000Z","published_at":"2026-05-23T16:59:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the area of the Circle using PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61351,"title":"Get The Square Root Of Number Power (^) Three","description":"Get the Square Root of number Power (^) Three.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Square Root of number Power (^) Three.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function num = calc(n)\r\n  num = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nnum = sqrt(n^3);\r\nassert(isequal(calc(n),num))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T12:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2026-05-24T12:06:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:57:15.000Z","updated_at":"2026-06-11T21:42:04.000Z","published_at":"2026-05-24T11:59:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Square Root of number Power (^) Three.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61385,"title":"Watermelon [MATLAB Cody Edition]","description":" YOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \r\nhttps://codeforces.com/problemset/problem/4/A\r\nNOW INSTEAD OF DISPLAYING \"YES\" OR \"NO\" YOU SHOULD RETURN.\r\nEX:\r\ncorrect =  \"YES\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201.009px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 100.497px; transform-origin: 400.994px 100.504px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ehttps://codeforces.com/problemset/problem/4/A\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOW INSTEAD OF DISPLAYING \"YES\" OR \"NO\" YOU SHOULD RETURN.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eEX:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003ecorrect =  \"YES\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function correct = watermelon(w)\r\n  \r\nend","test_suite":"%%\r\nw = 1;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 2;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 3;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 4;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 5;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 6;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 7;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 8;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 9;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 10;\r\ncorrect = \"YES\"\r\nassert(isequal(watermelon(w),correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-02T13:18:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-06-02T13:18:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-02T13:00:13.000Z","updated_at":"2026-06-11T21:48:26.000Z","published_at":"2026-06-02T13:11:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://codeforces.com/problemset/problem/4/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOW INSTEAD OF DISPLAYING \\\"YES\\\" OR \\\"NO\\\" YOU SHOULD RETURN.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEX:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecorrect =  \\\"YES\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61388,"title":"Draw '\\'","description":"Can you draw the sign '\\' by zeros and ones?\r\nNOTICE: Be x-by-x matrix.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 50.9722px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.49px 25.4861px; transform-origin: 468.498px 25.4861px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.497px 10.4861px; text-align: left; transform-origin: 444.505px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCan you draw the sign '\\' by zeros and ones?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.497px 10.4861px; text-align: left; transform-origin: 444.505px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eNOTICE: Be x-by-x matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = drawSign(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny = eye(x);\r\nassert(isequal(drawSign(x),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-08T17:24:05.000Z","updated_at":"2026-06-11T21:49:11.000Z","published_at":"2026-06-08T17:24:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCan you draw the sign '\\\\' by zeros and ones?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTICE: Be x-by-x matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61354,"title":"Rhombus","description":"Get the area of the Rhombus using it's Diagonals.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the area of the Rhombus using it's Diagonals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = area(d1,d2)\r\n  area = ;\r\nend","test_suite":"%%\r\nd1 = 1;\r\nd2 = 1;\r\narea = 0.5*(d1*d2);\r\nassert(isequal(area(d1,d2),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:30:18.000Z","updated_at":"2026-06-11T21:34:59.000Z","published_at":"2026-05-24T13:30:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the area of the Rhombus using it's Diagonals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61386,"title":"Prime or No","description":"If the number is prime, make theCase = \"YES\", else, make it \"NO\".","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf the number is prime, make theCase = \"YES\", else, make it \"NO\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theCase = primeOrNo(n)\r\n  \r\nend","test_suite":"%%\r\nn = randi(100);\r\nif isprime(n)\r\n    theCase = \"YES\"\r\nelse\r\n    theCase = \"NO\"\r\nend\r\nassert(isequal(primeOrNo(n),theCase))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-03T15:27:06.000Z","updated_at":"2026-06-11T21:26:49.000Z","published_at":"2026-06-03T15:27:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf the number is prime, make theCase = \\\"YES\\\", else, make it \\\"NO\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61349,"title":"Trapezium","description":"Calculate the area of the Trapezium using it's bases and height.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the area of the Trapezium using it's bases and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function trapeziumArea = trapeziumArea(base1, base2, height)\r\n  base3 = ;\r\n  trapeziumArea = ;\r\nend","test_suite":"%%\r\nbase1 = 1;\r\nbase2 = 1;\r\nheight = 1;\r\ntrapeziumArea = 0.5*(base1+base2)*height;\r\nassert(isequal(trapeziumArea(base1, base2, height),trapeziumArea))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T18:08:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-23T18:08:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T17:59:40.000Z","updated_at":"2026-06-11T21:30:15.000Z","published_at":"2026-05-23T18:03:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the area of the Trapezium using it's bases and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61350,"title":"Circle Perimeter","description":"Get the perimeter of the Circle by PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the perimeter of the Circle by PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = circleP(r)\r\n  p = ;\r\nend","test_suite":"%%\r\nr = 1;\r\np = 2*pi*r;\r\nassert(isequal(circleP(r),p))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T11:52:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-24T11:52:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:50:23.000Z","updated_at":"2026-06-11T21:28:08.000Z","published_at":"2026-05-24T11:52:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the perimeter of the Circle by PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61355,"title":"Basic Algebra III","description":"Get the Cube Root of the number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Cube Root of the number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = cbRt(n)\r\n  ans = ;\r\nend","test_suite":"%%\r\nn = 8;\r\nans = nthroot(n,3);\r\nassert(isequal(cbRt(n),ans))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T12:25:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2026-05-26T12:25:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T12:24:06.000Z","updated_at":"2026-06-11T21:38:22.000Z","published_at":"2026-05-26T12:24:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Cube Root of the number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61352,"title":"Basic Algebra I","description":"You should solve the problem 3X - 2 = 7 by finding the value of X.\r\nYou must use this array/vector [2 3 7].\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should solve the problem \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e3X - 2 = 7 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eby finding the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou must use this array/vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e[2 3 7].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation()\r\n  nums = [2 3 7];\r\n  X = ;\r\nend","test_suite":"%%\r\nnums = [2 3 7]\r\nX = (nums(3)+nums(1))/nums(2);\r\nassert(isequal(equation(),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:26:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-24T13:13:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:07:29.000Z","updated_at":"2026-06-12T07:25:30.000Z","published_at":"2026-05-24T13:11:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should solve the problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3X - 2 = 7 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eby finding the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must use this array/vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2 3 7].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61362,"title":"Calculate the h-index (revisited)","description":"H-index is a powerful tool for quantifying the scientific contribution of a researcher. The \r\nH-index is defined as follows (from source - wikipedia):\r\n\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\r\nIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\r\nExample:\r\nInput = [4 4 4 4]; Output = 4\r\nCalculate the h-index score \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 157.5px; transform-origin: 243.5px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is defined as follows (from source - wikipedia):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 31.5px; text-align: left; transform-origin: 219.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput = [4 4 4 4]; Output = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the h-index score \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [5 2 10 11 2 7 9 10 7];\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 4*ones(1,4);\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = zeros(1,1000);\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [3 2 0 0 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-27T22:40:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2026-05-27T22:40:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-27T18:21:09.000Z","updated_at":"2026-06-12T13:23:54.000Z","published_at":"2026-05-27T18:21:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is defined as follows (from source - wikipedia):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput = [4 4 4 4]; Output = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the h-index score \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61384,"title":"varargin","description":"Write a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\r\nExample:\r\nf(a,b) = a+b,    f(1,...,n) = 1+...+n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401.5px 55.5px; transform-origin: 401.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summ(va )\r\ny = ;\r\nend","test_suite":"%%\r\ny_correct = 6;\r\nassert(isequal(summ(1,2,3),y_correct))\r\n%%\r\ny_correct = sum(1:200:10^10);\r\nassert(isequal(summ(1:200:10^10),y_correct))\r\n%%\r\ny_correct = sum(-5:3.2:200);\r\nassert(isequal(summ(-5:3.2:200),y_correct))\r\n%%\r\nfor k = 1:100\r\n    x = num2cell(randi(100,1,randi(10)));\r\n\r\n    erwartet = sum([x{:}]);\r\n    erhalten = summ(x{:});\r\n\r\n    assert(isequal(erhalten, erwartet))\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5124132,"edited_by":5124132,"edited_at":"2026-06-01T17:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2026-06-01T17:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-01T16:52:16.000Z","updated_at":"2026-06-12T12:59:31.000Z","published_at":"2026-06-01T17:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":8,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2026-06-12T23:22:27.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61375,"title":"If-Elseif-Else","description":"If a more than zero, b = true, if a = zero , b = zero, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a more than zero, b = true, if a = zero , b = zero, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = 0;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-30T17:31:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-30T17:23:40.000Z","updated_at":"2026-06-13T11:58:13.000Z","published_at":"2026-05-30T17:23:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a more than zero, b = true, if a = zero , b = zero, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61380,"title":"NOT","description":"If a not equal to zero, b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a not equal to zero, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = false;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:12:13.000Z","updated_at":"2026-06-13T12:09:31.000Z","published_at":"2026-05-31T07:12:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a not equal to zero, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61378,"title":"AND","description":"If a greater than 0 and n less than 10, b = true, else, b = false.\r\n(Checking a should be in one line by AND special sign in MATLAB)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than 0 and n less than 10, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(Checking a should be in one line by AND special sign in MATLAB)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a,n)\r\n  \r\nend","test_suite":"%%\r\na = 9;\r\nn = 4;\r\nb = true;\r\nassert(isequal(IF(a,n),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-31T06:59:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2026-05-31T06:54:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T06:50:30.000Z","updated_at":"2026-06-13T12:05:15.000Z","published_at":"2026-05-31T06:50:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than 0 and n less than 10, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(Checking a should be in one line by AND special sign in MATLAB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61381,"title":"Switch-Case-Otherwise","description":"You should make random numbers to 10, by 3 rows and 3 columns.\r\nCases from 1 to 3, b = true.\r\nOtherwise, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCases from 1 to 3, b = true.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eOtherwise, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = CASE(a)\r\n  \r\nend","test_suite":"%%\r\na = 6;\r\nb = false;\r\nassert(isequal(CASE(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:39:29.000Z","updated_at":"2026-06-13T12:13:00.000Z","published_at":"2026-05-31T07:39:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCases from 1 to 3, b = true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOtherwise, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61377,"title":"Nested If(s)","description":"If a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 2;\r\nb = true;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T06:43:15.000Z","updated_at":"2026-06-13T12:03:11.000Z","published_at":"2026-05-31T06:43:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61379,"title":"OR","description":"If a greater than zero or c less than 10, b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than zero or c less than 10, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a,c)\r\n  \r\nend","test_suite":"%%\r\na = 1;\r\nc = 11;\r\nb = true;\r\nassert(isequal(IF(a,c),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:02:58.000Z","updated_at":"2026-06-13T12:07:30.000Z","published_at":"2026-05-31T07:02:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than zero or c less than 10, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61406,"title":"MATLAB 101: Scalar-Vector Multiplication","description":"Write a MATLAB function that takes a numeric array (vector or matrix) v and a scalar multiplier s. The function should return a new array where every element in v is multiplied by s.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a scalar multiplier \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return a new array where every element in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is multiplied by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = multiply_vector(v, s)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard positive vector and scalar\r\nassert(isequal(multiply_vector([1, 2, 3], 2), [2, 4, 6]));\r\n\r\n%% Test 2: Negative scalar\r\nassert(isequal(multiply_vector([5, 10], -1), [-5, -10]));\r\n\r\n%% Test 3: Zero scalar\r\nassert(isequal(multiply_vector([7, 8, 9], 0), [0, 0, 0]));\r\n\r\n%% Test 4: Empty vector\r\nassert(isempty(multiply_vector([], 5)));\r\n\r\n%% Test 5: Single element vector\r\nassert(isequal(multiply_vector(42, 2), 84));\r\n\r\n%% Test 6: Decimal/Fractional scalar\r\nassert(isequal(multiply_vector([10, 20], 0.5), [5, 10]));\r\n\r\n%% Test 7: Negative elements in vector\r\nassert(isequal(multiply_vector([-2, -4, 6], 3), [-6, -12, 18]));\r\n\r\n%% Test 8: Matrix input\r\nassert(isequal(multiply_vector([1, 2; 3, 4], 10), [10, 20; 30, 40]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:38:47.000Z","updated_at":"2026-06-14T22:40:00.000Z","published_at":"2026-06-14T18:38:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a scalar multiplier \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return a new array where every element in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is multiplied by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61405,"title":"MATLAB 101: Tribonacci Sequence","description":"Each number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_tribonacci(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_tribonacci(6), [0, 0, 1, 1, 2, 4]));\r\n%%\r\nassert(isequal(get_tribonacci(-6), []));\r\n%%\r\nassert(isequal(get_tribonacci(0), []));\r\n%%\r\nassert(isequal(get_tribonacci(16), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504,927,1705]));\r\n%%\r\nassert(isequal(get_tribonacci(14), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504]));\r\n%%\r\nassert(isequal(get_tribonacci(10), [0, 0, 1, 1, 2, 4,7,13,24,44]));\r\n%%\r\nassert(isequal(get_tribonacci(15), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504,927]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:12:19.000Z","updated_at":"2026-06-14T22:39:59.000Z","published_at":"2026-06-14T18:12:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61410,"title":"MATLAB 101: Rectangle Properties","description":"Write a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [area, perimeter] = rectangle_properties(L, W)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard scalar inputs\r\n[a, p] = rectangle_properties(5, 10);\r\nassert(a == 50 \u0026\u0026 p == 30);\r\n\r\n%% Test 2: Identical values (Square)\r\n[a, p] = rectangle_properties(4, 4);\r\nassert(a == 16 \u0026\u0026 p == 16);\r\n\r\n%% Test 3: Zero width\r\n[a, p] = rectangle_properties(10, 0);\r\nassert(a == 0 \u0026\u0026 p == 20);\r\n\r\n%% Test 4: Decimal values\r\n[a, p] = rectangle_properties(2.5, 4);\r\nassert(a == 10 \u0026\u0026 p == 13);\r\n\r\n%% Test 5: Row vector inputs (Multiple rectangles)\r\n[a, p] = rectangle_properties([2, 3], [4, 5]);\r\nassert(isequal(a, [8, 15]) \u0026\u0026 isequal(p, [12, 16]));\r\n\r\n%% Test 6: Column vector inputs\r\n[a, p] = rectangle_properties([10; 20], [10; 20]);\r\nassert(isequal(a, [100; 400]) \u0026\u0026 isequal(p, [40; 80]));\r\n\r\n%% Test 7: Matrix inputs\r\nL_mat = [1, 2; 3, 4];\r\nW_mat = [2, 2; 2, 2];\r\n[a, p] = rectangle_properties(L_mat, W_mat);\r\nassert(isequal(a, [2, 4; 6, 8]) \u0026\u0026 isequal(p, [6, 8; 10, 12]));\r\n\r\n%% Test 8: Large numbers\r\n[a, p] = rectangle_properties(1000, 2000);\r\nassert(a == 2000000 \u0026\u0026 p == 6000);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T19:08:37.000Z","updated_at":"2026-06-14T22:56:25.000Z","published_at":"2026-06-14T19:08:37.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61411,"title":"MATLAB 101: Hypotenuse Calculator","description":"Write a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function hyp = calculate_hypotenuse(base, height)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Pythagorean triple (3, 4, 5)\r\nassert(calculate_hypotenuse(3, 4) == 5);\r\n\r\n%% Test 2: Pythagorean triple (5, 12, 13)\r\nassert(calculate_hypotenuse(5, 12) == 13);\r\n\r\n%% Test 3: Zero base\r\nassert(calculate_hypotenuse(0, 10) == 10);\r\n\r\n%% Test 4: Zero height\r\nassert(calculate_hypotenuse(7, 0) == 7);\r\n\r\n%% Test 5: Vector inputs\r\nassert(isequal(calculate_hypotenuse([3, 5], [4, 12]), [5, 13]));\r\n\r\n%% Test 6: Matrix inputs\r\nb_mat = [3, 0; 0, 5];\r\nh_mat = [4, 10; 7, 12];\r\nexpected = [5, 10; 7, 13];\r\nassert(isequal(calculate_hypotenuse(b_mat, h_mat), expected));\r\n\r\n%% Test 7: Decimal values (floating point comparison)\r\nassert(abs(calculate_hypotenuse(1.5, 2.0) - 2.5) \u003c 1e-10);\r\n\r\n%% Test 8: Same base and height (Isosceles right triangle)\r\nassert(abs(calculate_hypotenuse(100, 100) - 141.421356237) \u003c 1e-5);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T19:11:20.000Z","updated_at":"2026-06-14T22:56:27.000Z","published_at":"2026-06-14T19:11:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61408,"title":"MATLAB 101: Replace Negatives with Zero","description":"Write a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function clean_arr = replace_negatives(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Mix of positive and negative numbers\r\nassert(isequal(replace_negatives([1, -2, 3, -4]), [1, 0, 3, 0]));\r\n\r\n%% Test 2: All positive numbers\r\nassert(isequal(replace_negatives([5, 10, 15]), [5, 10, 15]));\r\n\r\n%% Test 3: All negative numbers\r\nassert(isequal(replace_negatives([-1, -2, -3]), [0, 0, 0]));\r\n\r\n%% Test 4: Array containing zeros\r\nassert(isequal(replace_negatives([0, -5, 0, 5]), [0, 0, 0, 5]));\r\n\r\n%% Test 5: Empty array\r\nassert(isempty(replace_negatives([])));\r\n\r\n%% Test 6: Single negative element\r\nassert(isequal(replace_negatives(-42), 0));\r\n\r\n%% Test 7: Single positive element\r\nassert(isequal(replace_negatives(42), 42));\r\n\r\n%% Test 8: Matrix input\r\ninput_matrix = [1, -2; -3, 4];\r\nexpected_matrix = [1, 0; 0, 4];\r\nassert(isequal(replace_negatives(input_matrix), expected_matrix));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":2294940,"edited_at":"2026-06-14T18:48:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:44:40.000Z","updated_at":"2026-06-14T22:56:22.000Z","published_at":"2026-06-14T18:44:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61409,"title":"MATLAB 101: Reverse a Vector","description":"Write a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function rev_arr = reverse_vector(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard row vector\r\nassert(isequal(reverse_vector([1, 2, 3, 4]), [4, 3, 2, 1]));\r\n\r\n%% Test 2: Standard column vector\r\nassert(isequal(reverse_vector([10; 20; 30]), [30; 20; 10]));\r\n\r\n%% Test 3: Vector with negative numbers\r\nassert(isequal(reverse_vector([-5, 0, 5]), [5, 0, -5]));\r\n\r\n%% Test 4: Single element vector\r\nassert(isequal(reverse_vector([42]), [42]));\r\n\r\n%% Test 5: Empty vector\r\nassert(isempty(reverse_vector([])));\r\n\r\n%% Test 6: Vector with duplicate elements\r\nassert(isequal(reverse_vector([7, 7, 8, 7]), [7, 8, 7, 7]));\r\n\r\n%% Test 7: Floating point numbers\r\nassert(isequal(reverse_vector([1.5, 2.5, 3.5]), [3.5, 2.5, 1.5]));\r\n\r\n%% Test 8: Two-element vector\r\nassert(isequal(reverse_vector([99, 100]), [100, 99]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:52:14.000Z","updated_at":"2026-06-14T22:56:24.000Z","published_at":"2026-06-14T18:52:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61407,"title":"MATLAB 101: Count the Evens","description":"Write a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function count = count_even_numbers(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Mix of even and odd numbers\r\nassert(count_even_numbers([1, 2, 3, 4, 5, 6]) == 3);\r\n\r\n%% Test 2: All even numbers\r\nassert(count_even_numbers([2, 8, 14, 20]) == 4);\r\n\r\n%% Test 3: All odd numbers\r\nassert(count_even_numbers([1, 3, 5, 7, 9]) == 0);\r\n\r\n%% Test 4: Empty array\r\nassert(count_even_numbers([]) == 0);\r\n\r\n%% Test 5: Array containing zero\r\nassert(count_even_numbers([0, 1, 3]) == 1);\r\n\r\n%% Test 6: Array with negative even numbers\r\nassert(count_even_numbers([-2, -4, -5, 7]) == 2);\r\n\r\n%% Test 7: Single even number\r\nassert(count_even_numbers(42) == 1);\r\n\r\n%% Test 8: Matrix input (should count all evens across rows/cols)\r\nassert(count_even_numbers([1, 2; 3, 4]) == 2);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:41:02.000Z","updated_at":"2026-06-14T22:40:02.000Z","published_at":"2026-06-14T18:41:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61401,"title":"MATLAB 101: Factorial Finder","description":"The factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\r\nWrite a MATLAB function that calculates the factorial of a given number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 36px; transform-origin: 468.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that calculates the factorial of a given number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = find_factorial(n)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard Positive Integer\r\nassert(find_factorial(5) == 120);\r\n\r\n%% Test 2: Base Case (0!)\r\nassert(find_factorial(0) == 1);\r\n\r\n%% Test 3: Smallest Positive Factorial (1!)\r\nassert(find_factorial(1) == 1);\r\n\r\n%% Test 4: Larger Integer\r\nassert(find_factorial(7) == 5040);\r\n\r\n%% Test 5: Input Validation (Ensure it handles non-negative)\r\n% If n \u003c 0, this test assumes function returns NaN\r\nassert(isnan(find_factorial(-1)));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:22:54.000Z","updated_at":"2026-06-14T21:10:18.000Z","published_at":"2026-06-14T17:22:54.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that calculates the factorial of a given number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61402,"title":"MATLAB 101: Fibonacci Sequence","description":"The Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \r\nWrite a function that returns the first n numbers of the Fibonacci sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 36px; transform-origin: 468.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the first n numbers of the Fibonacci sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_fibonacci(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_fibonacci(5), [0, 1, 1, 2, 3]));\r\n%%\r\nassert(isequal(get_fibonacci(1), [0]));\r\n%%\r\nassert(isequal(get_fibonacci(15), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34,55, 89,144, 233,377]));\r\n%%\r\nassert(isequal(get_fibonacci(10), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]));\r\n%%\r\nassert(isequal(get_fibonacci(7), [0, 1, 1, 2, 3, 5, 8]));\r\n%%\r\nassert(isequal(get_fibonacci(13), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34,55, 89,144]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:35:57.000Z","updated_at":"2026-06-14T21:11:20.000Z","published_at":"2026-06-14T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the first n numbers of the Fibonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61403,"title":"MATLAB 101: Lucas Sequence","description":"The Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \r\nWrite a function that returns the first n numbers of the Lucas sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 25.5px; transform-origin: 468.5px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the first n numbers of the Lucas sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_lucas(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_lucas(5), [2, 1, 3, 4, 7]));\r\n%%\r\nassert(isequal(get_lucas(1), [2]));\r\n%%\r\nassert(isequal(get_lucas(15), [2, 1, 3, 4, 7,11,18,29,47,76,123,199,322,521,843]));\r\n%%\r\nassert(isequal(get_lucas(12), [2, 1, 3, 4, 7,11,18,29,47,76,123,199]));\r\n%%\r\nassert(isequal(get_lucas(-15), []));","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:42:51.000Z","updated_at":"2026-06-14T21:12:39.000Z","published_at":"2026-06-14T17:42:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the first n numbers of the Lucas sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":1942,"title":"GJam 2014 China Rd B: Party","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/2929486/dashboard#s=p1 GJam 2014 China Party\u003e. Small Case.\r\n\r\nThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\r\n\r\nThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\r\n\r\n\r\n*Input:* [M], Bx4 matrix (B\u003c=100). Total B area of \u003c=1000\r\n\r\n*Output:* [x,y,d] where [x,y] is Party House and d is everyone's total distance\r\n\r\n*Examples:*\r\n\r\n  M   [x y d]\r\n  [0 0 2 2] [1 1 12]\r\n  [-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]\r\n\r\n \r\n*Contest Performance:* Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\r\n\r\n\r\n*Commentary:*\r\n\r\n  1) The small can be solved by brute force since fewer than 1000 points require evaluation.\r\n  2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\r\n  3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/2929486/dashboard#s=p1\"\u003eGJam 2014 China Party\u003c/a\u003e. Small Case.\u003c/p\u003e\u003cp\u003eThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\u003c/p\u003e\u003cp\u003eThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [M], Bx4 matrix (B\u0026lt;=100). Total B area of \u0026lt;=1000\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [x,y,d] where [x,y] is Party House and d is everyone's total distance\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM   [x y d]\r\n[0 0 2 2] [1 1 12]\r\n[-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eContest Performance:\u003c/b\u003e Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\u003c/p\u003e\u003cp\u003e\u003cb\u003eCommentary:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) The small can be solved by brute force since fewer than 1000 points require evaluation.\r\n2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\r\n3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.\r\n\u003c/pre\u003e","function_template":"function [x,y,d]=Party_CH(p)\r\n x=0;\r\n y=0;\r\n d=0;\r\nend","test_suite":"%%\r\ntic\r\nzm=[0 0 30 30 ];\r\nvexp=[15 15 14880];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[0 0 29 29 ];\r\nvexp=[14 14 13500];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[0 1 0 100 ;0 -100 0 -1 ;-100 0 -1 0 ;1 0 100 0 ];\r\nvexp=[-1 0 20400];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[616 34 616 34 ;78 -828 78 -828 ;-762 -671 -762 -671 ;-199 -960 -199 -960 ;427 -575 427 -575 ;448 798 448 798 ;-819 -939 -819 -939 ;852 -564 852 -564 ;-145 281 -145 281 ;694 828 694 828 ;-278 963 -278 963 ;47 813 47 813 ;-393 24 -393 24 ;198 -257 198 -257 ;-393 -177 -393 -177 ;596 237 596 237 ;-678 760 -678 760 ;-180 92 -180 92 ;-590 995 -590 995 ;27 -946 27 -946 ;459 799 459 799 ;-491 -739 -491 -739 ;-691 -922 -691 -922 ;-38 185 -38 185 ;495 -471 495 -471 ;-850 532 -850 532 ;-360 798 -360 798 ;589 -104 589 -104 ;-492 -364 -492 -364 ;-797 415 -797 415 ;105 319 105 319 ;-879 -347 -879 -347 ;-795 172 -795 172 ;529 831 529 831 ;357 -199 357 -199 ;621 959 621 959 ;-475 125 -475 125 ;769 884 769 884 ;172 -706 172 -706 ;618 222 618 222 ;989 734 989 734 ;-273 478 -273 478 ;-548 930 -548 930 ;-634 889 -634 889 ;599 879 599 879 ;836 834 836 834 ;463 901 463 901 ;972 -903 972 -903 ;-319 495 -319 495 ;-727 -368 -727 -368 ;-685 -487 -685 -487 ;834 902 834 902 ;-114 -961 -114 -961 ;-984 193 -984 193 ;-388 867 -388 867 ;712 232 712 232 ;-750 19 -750 19 ;855 -455 855 -455 ;857 996 857 996 ;493 -722 493 -722 ;-582 426 -582 426 ;-824 848 -824 848 ;479 -993 479 -993 ;-976 -820 -976 -820 ;208 443 208 443 ;919 745 919 745 ;-460 -548 -460 -548 ;375 556 375 556 ;-572 980 -572 980 ;345 -411 345 -411 ;-275 613 -275 613 ;718 -895 718 -895 ;-838 -892 -838 -892 ;-241 836 -241 836 ;336 -878 336 -878 ;891 -355 891 -355 ;-986 989 -986 989 ;629 856 629 856 ;-779 787 -779 787 ;970 711 970 711 ;-578 -163 -578 -163 ;779 735 779 735 ;572 -203 572 -203 ;237 192 237 192 ;-427 -213 -427 -213 ;-338 9 -338 9 ;-905 45 -905 45 ;64 -35 64 -35 ;476 -560 476 -560 ;-370 24 -370 24 ;-836 487 -836 487 ;53 50 53 50 ;540 -897 540 -897 ;-179 -8 -179 -8 ;-979 227 -979 227 ;528 257 528 257 ;-876 615 -876 615 ;-342 -895 -342 -895 ;802 -744 802 -744 ;-458 -395 -458 -395 ];\r\nvexp=[-38 185 110298];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[241 -635 241 -635 ;75 -432 75 -432 ;-522 -517 -522 -517 ;-589 -931 -589 -931 ;-903 447 -903 447 ;-555 757 -555 757 ;-584 19 -584 19 ;420 -458 420 -458 ;-127 517 -127 517 ;-417 158 -417 158 ;542 703 542 703 ;865 -531 865 -531 ;-592 -191 -591 -190 ;570 467 570 467 ;-326 -668 -325 -668 ;197 516 197 516 ;238 -442 239 -441 ;-339 -71 -338 -70 ;255 -450 256 -450 ;408 -232 409 -231 ;302 -765 303 -764 ;-575 687 -575 688 ;-352 -651 -351 -650 ;-483 -96 -483 -95 ;285 170 286 170 ;-349 -660 -348 -659 ;518 -419 518 -418 ;555 -506 556 -506 ;900 97 901 98 ;-969 -258 -969 -257 ;-514 -199 -513 -198 ;-422 -197 -422 -197 ;-852 -115 -852 -114 ;166 -651 166 -650 ;628 -930 629 -930 ;-53 853 -52 853 ;484 503 484 504 ;-912 -976 -911 -975 ;-386 -562 -386 -561 ;521 946 521 947 ;717 -799 718 -797 ;-463 -348 -461 -348 ;-14 167 -13 169 ;-346 -677 -344 -675 ;-675 176 -673 179 ;894 807 896 811 ];\r\nvexp=[-338 -71 136630];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[468 377 468 377 ;839 -105 839 -105 ;-871 487 -871 487 ;-307 651 -307 651 ;135 -929 135 -929 ;-411 -829 -411 -829 ;745 -64 745 -64 ;336 784 336 784 ;-875 -84 -875 -84 ;-723 -736 -723 -736 ;701 -818 701 -818 ;-239 210 -239 210 ;-15 614 -15 614 ;362 225 362 225 ;894 443 894 443 ;-352 -303 -352 -303 ;-287 254 -287 255 ;-739 -960 -739 -960 ;110 28 110 28 ;540 434 541 435 ;-103 -962 -102 -962 ;913 -274 913 -273 ;835 -730 836 -730 ;544 866 545 867 ;-97 -358 -96 -358 ;-490 -319 -490 -319 ;-122 700 -122 702 ;37 902 39 902 ;103 266 104 266 ;-581 -714 -579 -710 ];\r\nvexp=[-97 -358 62565];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[28 122 30 124 ;-85 -609 -83 -607 ;763 19 764 20 ;612 -204 613 -203 ;-521 792 -520 794 ;-782 193 -781 195 ;-662 149 -661 151 ;-561 -568 -559 -567 ;-190 -897 -189 -896 ;-725 -317 -723 -315 ;704 -957 706 -956 ;-329 -967 -328 -966 ;-564 -639 -563 -637 ;-603 -86 -601 -84 ;-165 548 -164 550 ;-197 -150 -195 -148 ;-379 -581 -377 -579 ;401 -684 403 -683 ;546 -194 548 -192 ;267 573 268 574 ;-634 288 -632 290 ;593 857 595 858 ;78 -240 80 -238 ;800 981 801 982 ;473 472 474 473 ;-894 469 -893 471 ;582 347 583 349 ;516 189 518 190 ;333 -865 335 -864 ;-192 507 -191 508 ;-310 534 -309 536 ;-783 -487 -781 -486 ;-915 -696 -914 -695 ;-57 872 -56 874 ;717 -423 718 -422 ;509 -810 510 -809 ;-186 -335 -184 -333 ;-403 629 -401 631 ;-598 104 -596 106 ;-149 -210 -147 -208 ;920 911 922 913 ;819 -934 821 -932 ;518 -328 520 -326 ;-630 429 -628 431 ;348 -766 350 -764 ;242 -300 244 -298 ;387 -191 389 -189 ;-19 -871 -17 -869 ;383 723 385 725 ;-742 -327 -740 -325 ;-181 -43 -179 -41 ;799 -46 801 -44 ;729 -373 731 -371 ;-863 -16 -861 -14 ;998 -444 1000 -442 ;242 962 244 964 ;-249 -412 -247 -410 ;116 -14 118 -12 ;871 -455 873 -453 ;669 492 671 494 ;877 -447 879 -445 ;990 -938 992 -936 ;43 522 45 524 ;-70 45 -68 47 ;808 8 810 10 ;-879 -310 -877 -308 ;979 79 981 81 ;-695 202 -693 204 ;-650 469 -648 471 ;690 -624 692 -622 ;-169 -43 -167 -41 ;-81 723 -78 726 ;-789 968 -787 970 ;-913 698 -912 701 ;-597 -970 -595 -968 ;693 -79 694 -77 ;41 847 43 849 ;39 -728 41 -725 ;422 470 425 473 ;-518 -883 -517 -880 ;-858 784 -855 786 ;-246 311 -245 312 ;194 -715 197 -712 ;-370 -868 -369 -865 ;377 174 380 176 ;-697 223 -694 225 ;-489 -957 -486 -955 ;-585 -164 -583 -162 ;-283 -880 -281 -878 ;-141 -729 -140 -728 ;835 447 838 450 ;-424 -612 -423 -610 ;-280 376 -276 377 ;-351 -393 -350 -392 ;-793 -436 -788 -434 ;-548 -180 -547 -175 ;826 775 831 778 ;-664 -604 -658 -602 ;987 -65 988 -57 ;-540 -796 -533 -795 ];\r\nvexp=[-167 -43 874364];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-291 955 -289 956 ;276 -710 278 -708 ;-724 283 -722 285 ;-850 588 -848 589 ;625 -511 627 -509 ;-530 -994 -529 -993 ;-312 -655 -311 -654 ;86 -269 87 -267 ;565 -521 566 -520 ;438 320 440 321 ;-330 985 -328 986 ;-408 -942 -407 -940 ;755 792 756 794 ;847 -794 848 -793 ;436 -1 438 0 ;206 -637 208 -635 ;516 544 518 546 ;77 -200 78 -199 ;-618 276 -616 277 ;380 868 382 870 ;-664 284 -663 286 ;-526 929 -524 931 ;743 -555 745 -553 ;331 145 333 146 ;98 124 99 126 ;220 -661 222 -660 ;-92 498 -90 500 ;646 -552 647 -550 ;-531 -850 -529 -849 ;573 -80 574 -79 ;-317 299 -315 300 ;-963 713 -962 714 ;411 818 412 819 ;-99 -503 -97 -501 ;279 599 280 601 ;793 -237 794 -235 ;-41 -876 -39 -875 ;-550 -478 -549 -477 ;-107 820 -105 822 ;657 886 659 888 ;-460 684 -458 686 ;-80 455 -78 457 ;-779 -528 -777 -526 ;-829 719 -827 721 ;-760 -716 -758 -714 ;39 342 41 344 ;254 447 256 449 ;-272 -705 -270 -703 ;-900 507 -898 509 ;498 327 500 329 ;-669 168 -667 170 ;519 -367 521 -365 ;-674 323 -672 325 ;-724 519 -722 521 ;52 -596 54 -594 ;897 -724 899 -722 ;6 -387 8 -385 ;62 808 64 810 ;-84 -749 -82 -747 ;-475 -379 -473 -377 ;-467 -819 -465 -817 ;-130 232 -128 234 ;218 862 220 864 ;-206 339 -204 341 ;821 658 823 660 ;261 61 263 63 ;-704 869 -702 871 ;788 -490 790 -488 ;482 67 484 69 ;-328 -781 -326 -779 ;150 -117 152 -115 ;946 -90 948 -88 ;-68 477 -65 479 ;-704 915 -701 918 ;979 -761 980 -759 ;328 705 331 708 ;969 951 971 953 ;-638 991 -637 993 ;-621 120 -619 121 ;-546 651 -545 654 ;217 550 218 551 ;-743 196 -740 199 ;-591 847 -588 849 ;-48 -769 -46 -766 ;678 424 680 425 ;-250 268 -248 270 ;964 -389 966 -386 ;193 -818 195 -815 ;-803 107 -801 109 ;16 -725 19 -722 ;-721 -274 -720 -273 ;14 666 17 668 ;-822 933 -820 936 ;-895 -416 -894 -412 ;821 -329 824 -326 ;382 68 387 68 ;590 282 595 284 ;97 -310 103 -307 ;147 933 150 933 ;-772 -42 -765 -33 ];\r\nvexp=[-128 232 914624];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-987 -105 -985 -103 ;-22 -655 -20 -653 ;-622 412 -621 414 ;-526 641 -524 642 ;-694 573 -692 575 ;268 -697 269 -695 ;366 544 368 545 ;648 218 649 220 ;314 443 316 445 ;-589 354 -588 355 ;60 544 62 546 ;21 -444 23 -442 ;175 -224 176 -223 ;-915 -696 -914 -695 ;-417 766 -415 767 ;-874 -599 -873 -598 ;606 921 607 922 ;-672 562 -671 564 ;-17 39 -16 40 ;-708 632 -707 633 ;823 -170 825 -168 ;996 -372 997 -371 ;961 -169 962 -167 ;572 577 573 579 ;53 345 55 347 ;569 453 570 454 ;716 753 718 754 ;-803 -873 -802 -872 ;-110 940 -108 942 ;-943 841 -941 842 ;186 997 187 999 ;-107 388 -105 390 ;193 -54 195 -52 ;-231 -916 -230 -914 ;-962 749 -960 750 ;794 -458 796 -457 ;259 -909 261 -908 ;-719 65 -718 67 ;242 -481 244 -479 ;-528 -223 -526 -221 ;283 955 285 957 ;-888 946 -886 948 ;847 -707 849 -705 ;757 -814 759 -812 ;-940 -941 -938 -939 ;2 -176 4 -174 ;665 -708 667 -706 ;656 170 658 172 ;494 949 496 951 ;994 802 996 804 ;-65 785 -63 787 ;147 684 149 686 ;-488 807 -486 809 ;-875 462 -873 464 ;-152 253 -150 255 ;114 247 116 249 ;760 -206 762 -204 ;-204 569 -202 571 ;89 -752 91 -750 ;-464 -975 -462 -973 ;-783 -545 -781 -543 ;75 -251 77 -249 ;471 -462 473 -460 ;-126 -169 -124 -167 ;-311 615 -309 617 ;-398 -727 -396 -725 ;834 -915 836 -913 ;-87 -21 -85 -19 ;-301 918 -299 920 ;-740 -366 -738 -364 ;24 47 26 49 ;-929 -761 -927 -759 ;-863 -36 -861 -33 ;541 604 543 606 ;-279 -423 -276 -422 ;-620 -116 -619 -114 ;-145 571 -143 573 ;-638 133 -636 136 ;-885 546 -882 549 ;-625 -11 -622 -8 ;-610 -369 -609 -367 ;80 -655 83 -652 ;-398 -183 -395 -182 ;-71 -953 -69 -951 ;-767 939 -766 942 ;-763 -362 -760 -360 ;46 -897 47 -895 ;23 -437 25 -436 ;550 -440 553 -439 ;-660 178 -658 182 ;851 -919 853 -917 ;124 437 125 438 ;-414 -524 -411 -520 ;881 797 884 799 ;-73 -303 -68 -301 ;-373 -585 -369 -584 ;-239 963 -237 968 ;453 965 456 968 ;-742 875 -738 877 ;-894 -954 -884 -944 ];\r\nvexp=[-126 -168 1055075];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\n%%\r\nzm=[-648 -872 -646 -871 ;739 270 741 272 ;-847 -333 -845 -331 ;-510 -174 -508 -173 ;182 -353 183 -352 ;-573 277 -571 278 ;297 245 299 247 ;-223 818 -221 819 ;886 57 887 58 ;888 -773 889 -772 ;-593 513 -591 514 ;-587 -107 -585 -106 ;-564 40 -563 41 ;234 -624 236 -622 ;-82 902 -81 903 ;222 851 223 852 ;-726 476 -724 478 ;-392 -160 -390 -158 ;-153 -484 -152 -483 ;-522 -962 -520 -960 ;66 -926 68 -925 ;-535 28 -534 29 ;-603 -292 -602 -291 ;-981 -471 -980 -469 ;-367 865 -365 867 ;-445 -75 -443 -73 ;300 -40 301 -38 ;-329 -287 -328 -286 ;554 935 556 936 ;593 -932 594 -930 ;206 873 208 875 ;335 574 336 575 ;296 154 298 155 ;323 -423 325 -422 ;-144 472 -143 474 ;-284 211 -282 213 ;-289 -996 -287 -994 ;167 574 168 575 ;65 803 67 805 ;264 173 266 175 ;-820 -637 -818 -635 ;-897 813 -895 815 ;60 -524 62 -522 ;652 850 654 852 ;-837 57 -835 59 ;31 -96 33 -94 ;-607 540 -605 542 ;-240 794 -238 796 ;386 453 388 455 ;-421 -468 -419 -466 ;-838 -196 -836 -194 ;248 -366 250 -364 ;7 -933 9 -931 ;578 742 580 744 ;-634 -828 -632 -826 ;678 16 680 18 ;706 -163 708 -161 ;228 771 230 773 ;-440 -564 -438 -562 ;228 -606 230 -604 ;-361 652 -359 654 ;-608 -741 -606 -739 ;-926 42 -924 44 ;984 147 986 149 ;-132 -334 -130 -332 ;492 870 494 872 ;-470 523 -468 525 ;440 983 442 985 ;-68 -14 -66 -12 ;652 970 654 972 ;-591 -410 -589 -408 ;-252 -573 -250 -571 ;-639 -424 -637 -421 ;-306 -234 -303 -231 ;-720 81 -718 83 ;-645 845 -642 846 ;-938 507 -936 508 ;646 122 648 125 ;-76 864 -73 867 ;777 -142 778 -141 ;267 -756 269 -755 ;-151 -11 -150 -10 ;-568 -929 -567 -926 ;753 -830 756 -828 ;-205 -663 -202 -661 ;329 368 330 369 ;-402 -682 -399 -679 ;-649 463 -647 465 ;995 538 999 539 ;107 817 111 818 ;-546 -441 -544 -437 ;-856 920 -854 921 ;-587 -483 -584 -479 ;717 -641 719 -639 ;-892 -134 -890 -132 ;-300 -887 -296 -883 ;605 -228 607 -224 ;-93 -994 -90 -994 ;-421 -56 -414 -50 ;76 -592 80 -583 ];\r\nvexp=[-303 -231 855861];\r\n[x y d]=Party_CH(zm);\r\nv=[x y d];\r\nassert(isequal(v,vexp))\r\ntoc\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-18T01:44:26.000Z","updated_at":"2026-05-27T13:44:32.000Z","published_at":"2013-10-18T02:33:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is derived from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://code.google.com/codejam/contest/2929486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2014 China Party\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Small Case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Goal is determine the optimal Party House. Given a set of people to attend a party, select the home from this set that minimizes the total travel of people. People travel only NSEW, no diagonals, to reach the host's home. If multiple homes have equal distance then select the home with minimum X. If there are more than one with Min distance and equal Min X then choose the house with Min Y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input is an array that defines rectangles of partiers. One line of the array is [xmin,ymin,xmax,ymax]. Blocks do not overlap.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [M], Bx4 matrix (B\u0026lt;=100). Total B area of \u0026lt;=1000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [x,y,d] where [x,y] is Party House and d is everyone's total distance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M   [x y d]\\n[0 0 2 2] [1 1 12]\\n[-1 2 -1 2;0 0 0 0;1 3 1 3] [-1 2 6]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eContest Performance:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Delta Time of 16 minutes with 496 of 2010 able to process the small data set. The large data set was only achieved by 47 in the 3 hrs of contest duration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCommentary:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1) The small can be solved by brute force since fewer than 1000 points require evaluation.\\n2) The large case, which is giving me fits, has up to 1,000,000 points to evaluate.\\n3) Graphing the small case with surf gives some unexpected asymmetric results relative to the simple centroid.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2737,"title":"Prouhet–Tarry–Escott (basic)","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves problem 660.\u003e\r\n\r\nGiven n return two disjoint sets of integers _A_ and _B_ with same cardinality having following property:\r\n\r\n\u003c\u003chttps://i.imgur.com/gSW7nWy.png\u003e\u003e\r\n\r\nfor i = 1:n\r\n\r\nTry to minimize sets cardinality. ","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves\"\u003eproblem 660.\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven n return two disjoint sets of integers \u003ci\u003eA\u003c/i\u003e and \u003ci\u003eB\u003c/i\u003e with same cardinality having following property:\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/gSW7nWy.png\"\u003e\u003cp\u003efor i = 1:n\u003c/p\u003e\u003cp\u003eTry to minimize sets cardinality.\u003c/p\u003e","function_template":"function [A, B] = prouhet(n)\r\n  A = 1:n;\r\n  B = -A;\r\nend","test_suite":"%%\r\nn = 1;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 2;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 5;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\nn = 7;\r\n[A, B] = prouhet(n);\r\nassert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\nassert(isempty(intersect(A, B)));\r\nassert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\nassert(isequal(sum(A(:).^(1:n),1), sum(B(:).^(1:n),1)));\r\ndisp(sprintf('Each set has %i elements.', numel(A)))\r\n%%\r\n%n = 9;\r\n%[A, B] = prouhet(n);\r\n%assert(isequal(A, round(A)) \u0026\u0026 isequal(B, round(B)))\r\n%assert(isempty(intersect(A, B)));\r\n%assert(isequal(numel(A), numel(B), numel(unique(A)), numel(unique(B))));\r\n%assert(isequal(sum(uint64(A(:)).^uint64(1:n)), sum(uint64(A(:)).^uint64(1:n))));\r\n%disp(sprintf('Each set has %i elements.', numel(A)))\r\n%if numel(A) \u003c=20\r\n%    disp('A:')\r\n%    disp(A)\r\n%    disp('B:')\r\n%    disp(B)\r\n%end\r\n%%\r\n% test info\r\n%\r\n% larger n will be added later\r\n%\r\n% scoring function will be added later as well\r\n% scoring will be entirely based on size of output: smaller output == better score\r\n% something like this:\r\n%\r\n% score = 0;\r\n% for n = 1:25\r\n%   [A, B] = prouhet(n)\r\n%   assert(...);\r\n%   score = score + numel(A);\r\n% end\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2016-10-08T00:11:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-08T09:56:20.000Z","updated_at":"2026-06-08T14:44:05.000Z","published_at":"2016-10-07T08:07:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/660-find-a-subset-that-divides-the-vector-into-equal-halves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 660.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n return two disjoint sets of integers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with same cardinality having following property:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efor i = 1:n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTry to minimize sets cardinality.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.JPEG\",\"contentType\":\"image/JPEG\",\"content\":\"data:image/JPEG;base64,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\"}]}"},{"id":61269,"title":"Precise Almost Pythagorean Triples ","description":"This  is essentially the same as:  Problem 52834. Easy Sequences 32: Almost Pythagorean Triples; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\r\nRepeating the original problem description:\t\t\t\t\r\nAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is 1 less than the sum of square of the smaller elements (shorter sides). This means that if c is the hypotenuse and a and b are the shorter sides, , satisfies the following equation: \r\n        \r\n        where:  \r\nThe smallest  is the triple , with  and perimeter (the sum of the 3 elements)  of . Some researchers consider  as the smallest , but here, we will only look at 's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of 's are , and . \r\nUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible 's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with 's with a known ratio between the hypotenuse and the shortest side: . \r\nGiven the value of r, find the perimeter of the  with the r-th smallest perimeter. For example for , that is , the smallest perimeter is  for  , while the second (r-th) smallest perimeter is , for the  with dimensions . For , the third smallest perimeter is  for  . \r\nThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\r\nFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 334px 334.917px; transform-origin: 334px 334.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 42px; text-align: left; transform-origin: 310px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.675px 7.91667px; transform-origin: 102.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis  is essentially the same as:  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52834\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 10.5px; text-align: left; transform-origin: 310px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.933px 7.91667px; transform-origin: 201.933px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepeating the original problem description:\t\t\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 86.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 43.4583px; text-align: left; transform-origin: 310px 43.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303.05px 7.91667px; transform-origin: 303.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.45px 7.91667px; transform-origin: 12.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eless\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.8917px 7.91667px; transform-origin: 94.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 7.91667px; transform-origin: 3.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 7.91667px; transform-origin: 72.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hypotenuse and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 7.91667px; transform-origin: 49.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the shorter sides, \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.692px 7.91667px; transform-origin: 102.692px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, satisfies the following equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 12.4583px; text-align: left; transform-origin: 310px 12.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 7.91667px; transform-origin: 15.5333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"99\" height=\"19\" style=\"vertical-align: baseline;width: 99px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 23.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 11.9583px; text-align: left; transform-origin: 310px 11.9583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.425px 7.91667px; transform-origin: 40.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        where:  \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"62\" height=\"18\" style=\"vertical-align: baseline;width: 62px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 96.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 48.3333px; text-align: left; transform-origin: 310px 48.3333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.725px 7.91667px; transform-origin: 37.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the triple \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 7.91667px; transform-origin: 18.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"100\" height=\"19\" style=\"vertical-align: baseline;width: 100px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.508px 7.91667px; transform-origin: 101.508px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and perimeter (the sum of the 3 elements)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.91667px; transform-origin: 7.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6UlEQVRYhe2WQQ3DMAxFP4cwCIESGIIiKIMxKINSKIZBKIdRKIZR6A6ztWiHxkm+qkjzl6xenOQpL5UMeDyevhIBhEzPAOBmrKEFZAVwGDbZpc9SSylISEC0zoDGApgDn1syZwQwy/dpBNqk4klPkH32EpjfzAagKIfk3tiESl01QBYFD1ToqgGyRHW9kL/JS4BU19oCwwRSXWMPQDRdLCCaLhYQTRcDiKqLAUTVxQDaQNTVChRB1tUKdAdZVyuQTgpTD0CprrORpCg6VijQXLBWdW0skAXfoSutVQ7LRdfT/i6Px+P5u7wB3c96XQFb71kAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.4083px 7.91667px; transform-origin: 91.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Some researchers consider \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 7.91667px; transform-origin: 50.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as the smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7917px 7.91667px; transform-origin: 70.7917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but here, we will only look at \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.942px 7.91667px; transform-origin: 243.942px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.8333px 7.91667px; transform-origin: 18.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's are \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"56\" height=\"18\" style=\"vertical-align: baseline;width: 56px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 35.875px; text-align: left; transform-origin: 310px 35.875px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 269.142px 7.91667px; transform-origin: 269.142px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.9417px 7.91667px; transform-origin: 21.9417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.775px 7.91667px; transform-origin: 6.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"50\" height=\"18\" style=\"vertical-align: baseline;width: 50px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 95.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 47.8333px; text-align: left; transform-origin: 310px 47.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2083px 7.91667px; transform-origin: 62.2083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 7.91667px; transform-origin: 2.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.925px 7.91667px; transform-origin: 85.925px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the perimeter of the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAkCAYAAADWzlesAAACIklEQVRoge2YS5XDMAxFH4cwCIESCIJBEAZlEAalEAyFEA6hUAyh0FlUmr4o/sj5rMb3nCzq2LItS09OgUqlUqlUrqID0Dj7NtI/96TseW3stV9MD+Athj00MmaWcfxM8ujvWfraBd/NuBeNXah9ibS/ineZ2dBLDPeFYzusN8JObLF20oi1I57SPmDrILb5Y96N0v4oXGuSgSYsNfyD9YlZWsQ3tMjcKZtvbB3UBGwdwi5yLhz/oLHPSB+OBnVyl5iLbU6RPiHn7GbCNxU0z0qM8wbviTmso1TYcjZDkQKcmAqazzYaSioEj7tF+rETcou3Nr1CvZsXLYq97801rSg5pWZFzwlvTmNOZZBJ9NRVqVNhbVGVVuUPwWXQU9I8GnMKDT4O4M3uqRC5E+5Mn1i6MKxP3sPYxYitMnMYeirEDevc7fEVux7rKJnhc4DVJs+YXagY2rznTXkqBIf5gk/oTvSM0qdkI16NOcyEz8mE7uElFaJE8b14NOYw6ukp8nD+5irEFWWM9aD0+u5CxTB1at4KYa+1Z2A15tSvQ0XVP2XcWyGuKGOsMaVXdxequrncZWFKLeSKMsZRGLsqnzJBLsRYHGMV4qoyxnp0+lVZN+ZRW5uXbaDPFWUs9+l8iBu+HvY4wS7GhiX/+aJOCDmqhAbbf6eO2vyjw7YEDpEJOnkXKps6psf2QjRJ255y1ibmfMq7y78gK5VKpVKpVP4Nv14fLJbptxZTAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3167px 7.91667px; transform-origin: 30.3167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003er-th smallest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3417px 7.91667px; transform-origin: 37.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e perimeter. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 7.91667px; transform-origin: 12.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.4917px 7.91667px; transform-origin: 24.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"43\" height=\"18\" style=\"vertical-align: baseline;width: 43px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 7.91667px; transform-origin: 81.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABLUlEQVRYhe2WUbHDIBBFjwccYKAGoiAK4qAOcBAL0RAJeKiFaoiFvg+WmX2dPEIC5fWDO7Nfu1lOLiwJdHV1fZcsYE4+M0jcaoMswCuzsQFm4Ak4iafEvQTEKJAYR0AWeMji726u0sPv5A41Et5slAVygWKt28kZYEvks+UygaaMOu34aZfOAsUt2RI1GvqyS7lAcTtSQIPqtX4aKNakgGxmXVWgo/PRDMiruvEbgO4cn4+mW2YIF2LKJT32j08DIXkN5eX5meDIqnJLCyAITk2yoBcIR9iumbxzVhUoBRrvqr1vXXMg3Wcq6FMF6MbxBDYD0tN36dejJpCeurUGjOX3GJ/5QjvCId4o/FOMIDPB4vdY/ljAEEY53jle6opduSorAMN/QnR1dXWV6Ae9sZqCc2SAGwAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.9583px 7.91667px; transform-origin: 57.9583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, while the second (r-th) smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2WUQ2DMBCGfw91UAMYmIIqwMEc4AAL1TAJ9TALaJgF9sBd0i2DXQ9u4+G+5MIDBT74QgBwHOc/dAAuwumE54wAglZoAjALZxSIZForlX8hNcjMWJ7SJ0IlwqMSKjRxY02gC0wr+xOAgbb3PUKRLvKtdQ9ZLpDYLqG1BDU3bOc6TEgC53pA9taYC3GuLFxvLsS50hmEWnOZC7XmMhdqzWUqpMllKqTJZSpU0J7LTChCl8tM6ApdLjMh/mL3ZxCqc239kvxMiHMVxbH8O8NCwxFCI8m0vF2xOu59MpabdBzHcSQ8AUZlel3qgGXQAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6583px 7.91667px; transform-origin: 25.6583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAkCAYAAADWzlesAAACIklEQVRoge2YS5XDMAxFH4cwCIESCIJBEAZlEAalEAyFEA6hUAyh0FlUmr4o/sj5rMb3nCzq2LItS09OgUqlUqlUrqID0Dj7NtI/96TseW3stV9MD+Athj00MmaWcfxM8ujvWfraBd/NuBeNXah9ibS/ineZ2dBLDPeFYzusN8JObLF20oi1I57SPmDrILb5Y96N0v4oXGuSgSYsNfyD9YlZWsQ3tMjcKZtvbB3UBGwdwi5yLhz/oLHPSB+OBnVyl5iLbU6RPiHn7GbCNxU0z0qM8wbviTmso1TYcjZDkQKcmAqazzYaSioEj7tF+rETcou3Nr1CvZsXLYq97801rSg5pWZFzwlvTmNOZZBJ9NRVqVNhbVGVVuUPwWXQU9I8GnMKDT4O4M3uqRC5E+5Mn1i6MKxP3sPYxYitMnMYeirEDevc7fEVux7rKJnhc4DVJs+YXagY2rznTXkqBIf5gk/oTvSM0qdkI16NOcyEz8mE7uElFaJE8b14NOYw6ukp8nD+5irEFWWM9aD0+u5CxTB1at4KYa+1Z2A15tSvQ0XVP2XcWyGuKGOsMaVXdxequrncZWFKLeSKMsZRGLsqnzJBLsRYHGMV4qoyxnp0+lVZN+ZRW5uXbaDPFWUs9+l8iBu+HvY4wS7GhiX/+aJOCDmqhAbbf6eO2vyjw7YEDpEJOnkXKps6psf2QjRJ255y1ibmfMq7y78gK5VKpVKpVP4Nv14fLJbptxZTAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6833px 7.91667px; transform-origin: 53.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with dimensions \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAlCAYAAACUJtElAAAEa0lEQVR4nO1bbZHrMAxcDmFQAiEQBEUQBmVQBqUQDIUQDqVQDKXQ98PRZOvKsp2vJve8M565mUtsWVpLsqICBQUFBQUFh8U1MJpfClWwChqE7Z2NN4AHgN4b7RKSFuwKLb7t/IDjQDbeKN7lf0aDHxGnzni2GtbSxhnAbYYcIcj8OXJqqOFcejeM88z5fLBupkDePU14b1PitACeAO4Z71yH9UJjKc9XwRnXn/8F4JI5zxVun+/h71zDxHDGGC543Ib1LZzg9vnCmKs84UJQ6kHZjDhnjIp8I504FdwGQ6TpM2SwcIqsI0aJoca4zx7LEwZwh0/mvw5ysW4tndRw+3zikyQVzZHiFTchzg3uxF6QTxw5DbFTNBf9sA4n9zW+PZCl1BZ5J38KmkFOTQ6WVbMNk0PzoEKGN+Kybx6qconzwjo5DOM8rBNy0xwqQ3Kz0nusR3QrnJxIBo0Yso8Xwp5QiBWzz66JIyf4gvlJqoU77Bymwme+o/3/hbhR5qJCvNxheUaR8WG8z17LIv+uicNxW4zSYXkSdYgbu0eYOKzstb2jBfE4Wmg/Y5SxM+bgdMIi6W6Jw/mCNjqsn/cwhDh+4sne6I2RgDWmXXPnQEKR5m043FrelUOuRbDdEgdwSm/gNnrHN3nWzCV8hJJKPqFPOAP5t7On8t7SaId1Q8k76y+VOFZI2zVxfJzwTaBJ30smrCsE8D2IL48U+RqMNas1w1jtyRCqOfXIJ44Wlv3nsvEL4gg4jL2wvtcRN68pnItw2v8r75klK8c3jGUE3xv7JGXixHLEP0scwCnGqlksBbkxhYpqrORQPsOJ6VIFSx+aN2aCMHEsfcVukILDEidWs1gKdziPEfJqKUr2n1vTQ/KB4jBeQhVBQsBaxLnguzTvg+s3FnJCxRywx2AdT7lVWTY6NHHEGGv0AEliGzMy13csT7IVcXgt1jHnhanEsZL5QxNHPM7StZJU0gCfocF6PpVgS0DWYoJwaLd0z57JSuQPSxxRhFVrmAL5im+RoMZnoU/2ZHk+ufksLW9oLS1ZF0I9jXfv9MwhPzlI5TUEKfOHvgJf4E5PTliQloPYreOBT6OI5wuRgvMOn1zSz9tiGU8kBtXCDIehkN5SLxy7JI5fjfWNL/E6VPzzWyFSyCOkeSDcmM0NTww2iOZ1xP3773H4SDlM3DOktW3IHqyKuoRWba2QnBo2JQ7HT60K6wvFoxvel4KXFX+1aq4FUbi/Zmhoa7c0B3sPOQR36Ib257byNZ9o0nIirampnzbkYDH5RM7UzzibEKeFU5zfKS8dbJpHOGGsjPKzKTcoKcP3GL+oWwjJpg2NAAIJkTxf7CdDchhSE/1m2A/Lc0V+RbrBp35vmXP8rFl9KxzlJzvS2XcU/GniSP/vlu0XUxFrJtsb/ixxajj3v3axbQl0+G0D2BTMIs4F379z2rJxKYQKzhB7kCWGFvsPpdIXxUOS6WyEbhxb9McUbAvrd20FBQUFBQUFBQUFBRb+AeqNb10z+oPdAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.325px 7.91667px; transform-origin: 16.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 7.91667px; transform-origin: 31.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the third smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"33\" height=\"18\" style=\"vertical-align: baseline;width: 33px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"101\" height=\"18\" style=\"vertical-align: baseline;width: 101px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 305.717px 7.91667px; transform-origin: 305.717px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 282.908px 7.91667px; transform-origin: 282.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function function perimeter = rthPerAPTdbl(r)\r\n  perimeter = r^2;\r\nend","test_suite":"%% Test Case 1\r\nr = 2;\r\np_correct = 71;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 2\r\nr = 3;\r\np_correct = 1393;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 3\r\nr = 5;\r\np_correct = 1046629;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 4\r\nr = 10;\r\np_correct = 737287485879;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 5\r\nr = 100;\r\np_correct = 16183149010201;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 6\r\nrs = 101:150;\r\nps = arrayfun(@(r) rthPerAPTdbl(r),rs);\r\nps = mod([sum(ps) ps(5:5:end) floor(std(double(ps)))],1e6);\r\nps_correct = [12636 824229 203679 227761 926641 15749 664839 210241 515881 139269 477199 789840];\r\nassert(isequal(ps,ps_correct))\r\n%% Test Case 7\r\nr = 1000;\r\np_correct = 499499001002001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 8\r\nr = 10000;\r\np_correct = 100020001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 9\r\nr = 123456;\r\np_correct = uint64(76696064606196865);\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 10: Forbid java and BigInteger\r\nfiletext = fileread('rthPerAPTdbl.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":2404920,"edited_by":2404920,"edited_at":"2026-03-04T15:24:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-04T14:14:29.000Z","updated_at":"2026-06-06T17:53:55.000Z","published_at":"2026-03-04T15:24:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis  is essentially the same as:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52834\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e; it even presents the same set of test problems.  The difference is that the \\\"correct\\\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepeating the original problem description:\\t\\t\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn Almost Pythagorean Triple (abbreviated as \\\"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eless\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the hypotenuse and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are the shorter sides, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, satisfies the following equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"99\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"62\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the triple \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"100\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and perimeter (the sum of the 3 elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Some researchers consider \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but here, we will only look at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's where the hypotenuse is \\\"strictly\\\" greater than the other shorter sides. Other examples of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"56\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId9\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"50\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the perimeter of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er-th smallest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e perimeter. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"43\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId12\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId13\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId14\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while the second (r-th) smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId15\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId17\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the third smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"33\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId18\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"101\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId19\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not 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Power Steering (EPS) Motor Torque with Efficiency","description":"In EPS systems, the motor must generate additional torque to compensate for system losses.\r\nGiven Required assist torque at rack Ta and Mechanical efficiency η (0 \u003c η ≤ 1)\r\nCompute required motor torque Tm.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Required assist torque at rack \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMechanical efficiency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eη (0 \u0026lt; η ≤ 1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute required motor torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Tm = epsMotorTorque(Ta,eta)\r\nTm = 0;\r\nend","test_suite":"%%\r\nTa = 10; eta = 0.9;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 15; eta = 0.85;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 8; eta = 0.8;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:46:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:46:15.000Z","updated_at":"2026-06-09T08:08:23.000Z","published_at":"2026-04-28T09:46:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Required assist torque at rack \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eMechanical efficiency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eη (0 \u0026lt; η ≤ 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute required motor torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1440,"title":"USC Spring 2013 ACM: Snow Cones","description":"This Challenge is to solve the \u003chttp://contest.usc.edu/index.php/Spring13/Home USC Spring 2013 ACM Contest\u003e Problem F, Snow Cones.\r\n\r\nSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O.\r\nInput is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child. \r\n\r\nDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\r\n\r\n\r\n*Input:* From XXO to  OXX   *Output:* 2\r\n\r\n*Input:* From OXOX to XOXO  *Output:* 1\r\n\r\nOnly two competitors solved this challenge.\r\n\r\nA little complex requiring a Matlab 3-Liner solution versus \u003chttp://contest.usc.edu/index.php/Spring13/Home?action=download\u0026upname=cones.zhengcao.cpp.txt Cao's C solution\u003e ","description_html":"\u003cp\u003eThis Challenge is to solve the \u003ca href = \"http://contest.usc.edu/index.php/Spring13/Home\"\u003eUSC Spring 2013 ACM Contest\u003c/a\u003e Problem F, Snow Cones.\u003c/p\u003e\u003cp\u003eSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O.\r\nInput is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child.\u003c/p\u003e\u003cp\u003eDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e From XXO to  OXX   \u003cb\u003eOutput:\u003c/b\u003e 2\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e From OXOX to XOXO  \u003cb\u003eOutput:\u003c/b\u003e 1\u003c/p\u003e\u003cp\u003eOnly two competitors solved this challenge.\u003c/p\u003e\u003cp\u003eA little complex requiring a Matlab 3-Liner solution versus \u003ca href = \"http://contest.usc.edu/index.php/Spring13/Home?action=download\u0026upname=cones.zhengcao.cpp.txt\"\u003eCao's C solution\u003c/a\u003e\u003c/p\u003e","function_template":"function swaps=snowcones(v1,v2)\r\n% v1 is a string of Xs and Os (not zeros)\r\n% v2 is string of desired sequence\r\n swaps=0;\r\nend","test_suite":"i='X'; %1\r\nd='X';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XO'; %2\r\nd='XO';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XO'; %3\r\nd='OX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XX'; %4\r\nd='XX';\r\ne=0;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXO'; %5\r\nd='XOX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXO'; %6\r\nd='OXX';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XOX'; %7\r\nd='OXX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXXXOOOO'; %8\r\nd='OOOOXXXX';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XOXOXOXO'; %9\r\nd='OXOXOXOX';\r\ne=1;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOXXO'; %10\r\nd='XXOXXOO';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOOOOXX'; %11\r\nd='OOXXXXOO';\r\ne=3;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOXOXOXOXOX'; %12\r\nd='XXOOXXOXXOXOO';\r\ne=2;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXXOOXOXOXXXO'; %13\r\nd='OXOOXXOXXOXXX';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOOXXOXXOXXX'; %14\r\nd='XXXOOXOXOXXXO';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOOOOOXOXOXXXXXOOXX'; %15\r\nd='OXOOXXOXXOOXOXOOXOXX';\r\ne=5;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOXXXXOXXOXXXXXXXXX'; %16\r\nd='XXXXXXXOOXXXXXOXXXXX';\r\ne=5;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXOXOOXXOOXOXXOXOXOO'; %17\r\nd='XOXOXXOXOXOOOXOXOOOX';\r\ne=3;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OXXOOXXXOOXXXXXXOXXX'; %18\r\nd='OXOOXOXXXXXXXXXXOOXX';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='XXOXXXXXXXOXXXOOXXOO'; %19\r\nd='XXOXXOXOXXXXOOXXXXXO';\r\ne=7;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%20\r\ni='XOOXXXXXOXXOXOXXXOOOXXOOXXOOOXXXXOXXXXOOOOXOXXXXXOXOOOOXXOOOXOXOOXOXOOOOOOXOOOXOOXXXXXXXOXXOXXXOXXOXOOOOXOOXXXXOXXXXXXXXOOOOOXOXOXXXOXXOOOXOXXOOOOOXOXXXOXXOXOXOOOOXXOOXXOXOOOOXOOXOOXXOOXXOOOXOXOXXXXOOXXXXXOOXOOXOXXXXXXOOOOOXOXXXOOOXOOOOOOXXOXOOXXOOOOXXXOXOXOXXXOXOOXXOXXOXOXOXXOXOXOOOOXXOXXOXXXXOXOXXOXOOOOOXOXXOOXOOXXXOXOXXOXXOXXXXXOXXOOOOOOXOOOOXOOOOXOXOXXOXOXXXOXOOOOXXOXXXOXXXOXXOOXXXOOXOXXOOXOOXOXOOOOXOOOOXXOXXOOXXXOXXOOXXOXOXXXOXOOOXXOXOOXXOOXOOOXXOOXXOXOXOXOOOOOOXXXXOXXOXOOXOXXOOOOXXXOOOOOOOOXOOOOOOXXOXXOXOOOOOOXOOOOOXOOXXOOXXOXXXOXOXOXXXOOOOOOXXOOOOXOXOXOOXXOOXOXXXOXOOXXOXOXOOXOXOXOXOXOOOXOOXXXOOOXXXOXOOOXOXXOXXOXXOXXXXOXOOXXOXOXXOOOXXXXXOXXXXOOOOOOOOXXOOXOOOXXXXXOOOXOOXOOOOOXXOOXXOOXXOXXXOXOXOXOOOXOXXOXXOOOOOXOOOOXXXOOXXXOOXOXOXXXXXOOXXOXOOOXOOOXXXOXXOXOXXOXOXOOXOOXXXOOXOOXOXOOXOOOOOOOXXOOOOOOXOOOOOOXOXXXXOOXOXOOXXXOXOXXOXOOOXOOOOOOXOOXOXOOXXOOXOOXXOXOXOOOOOOOOXOXXOXXXXOXXXOOXXOXOOXXXOXOXOOOOXXOXXOXOXXOXOXOOXXXOXXXOOXOOOXOOOXXOXXOOXXXXOXOOXOXOXXOOXXOXXXXXXXXXXOXXOOOOXXXOOXXOOXOOX';\r\nd='OXXXXOOOOXXOOOOXOXXOXOXXXOXXOOOXXOOOXXOXOOXXXOOOOOXOOXOOXXOOXOOOXXOXOOXXXOXOXOXOOOOOOOXOXXXOOXOOXOXXOXXXOXXXXOXXXOOXXXXOXXXOOXOXXXOOXOXXOXXOXOOOXXOOXXXOOXXXXXXOOXXXOXOXXOOOOOXOXOOXOOOOXXXOOOXXXXXOOXOXXXOOOOOXOOOOXXXOOOXXOOOOOOOXOOXXOOOOXOXXXXXOOXOXOXOXOOOXOXOOXOOXOOXXXOOXXXXOOOXXOXXOOXOOOOXOOOXOXOOXOXOXOXXOXXOOOOOOOXOXXOXXOOXOXOXOXXOXXOOOXOOOOOOOOOXOOXXOXOXXOOOOOOXOXOOOOOXXOXOXOXXOXOXXXOOOXXOOXXOXXOXOXXOXXXOOOOOXOOOOOXXXXXOXXOXOOXXOXXXXXOOOOOXOXOXOOXXOXOOXXOXOXXOOXOOXOXOXXOXOOOXXXOXXOXXOOXXXXXXOXOXOXOXXXOXXXOOOOOXXXXOXXXOXOXOOXOXOOXOOOXOOOOXOOOXXOXXXXOXXXXOOOOOXOOOOOOXXOOXOOXXXOXOXOXOXOXOOOOOXOOXXXXOOXOXXOXOOXOOXOXXXXOOOOXXOOXOXOOXOOXOOOOXXXOOOOOOOOXOOXXOOXXOOOXOOXXXXXXOOOOXOOOOXXOXXXXXXOXXXOXOXXXOXXXOXOOOXXOOXOOOOXOOOXOXOXOOOXXXOXOOXOXOOOXXXOOOXXXOXXOOOOOOXOXXOXXOOXXOOXOXOOOXXXOOOOOXXOOXXOXOXXXOXXOXOOXXOXOOOXXXOXXOOXOXXXOXXOXXOXXOOXXXXXOXXOXOOOOOXOXXOOOXOXOOOOXXXXXOOXOOXXOXXXXOXOOXXOXXXOOXXOXOXXOOXOXOOOOXXXXXXXOXOXXOXXXXXOOOOXOOXOXOXOOOXXOXOXOOOOXOXOOOXXOOOXXXOXXOXOXXXXXXOXOXOOOOXOOXX';\r\ne=47;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%21\r\ni='XOXXOXXXOXOOXXOOOXXXOOXXOOOXXOOXXOOXXOXOXXOOXOXXXOOOXOXXXXOOOXXOOXOXOXXOOOOXXOOOOXOXXOXOXOXOXXOXXXOXXXOOXOOOXXXOXOXXOOOOOXOXXOXXXXXOXOXXXXXOXXOOXXOXXXOOOOXOOOOOOXXXXXXXXOXXXOOXXOOOXXXXXOOXXXOXXOOXXXXXOXOXOOXOXOOXOOOOXOOXXOXXOOXXOOXXOXXXXXXOOXOOXOXOOOXXOOXXOOOOOOXXXXOOXOXXOXOOXXOOXXXOXXXOOOXXOOXOXXXOOXXOOOOOOXOXXXOXOOOXOOXOOXOXOXXOXOOXXOOXXOXXXOXOOXOXXOOOXXXXOXXOOXOOXXXOXXXXXOXOOOXOOOXXOXOXXXXOOOXXXXOXOOXOXOOXOXOXXXOXXXXXXOXOOXOOXOOXXXOXOOOOXXXXXOXXXXOXOXXOOOXOOOOOOOOXXXOXXOOXXXXOXXOOXOXXXOOOXOOXOXXXOXOXXXXXXXOOOXOOXOXXXXOXXOOOOOXOOXOXOOXXXOXXOXXOXXXXXOOXOOOOOXOOOXXOXOXXOOOOXXOXXXXOOOOXOOXOXOOOOXXXOXXXXXXXOXOOXOXOOXOOXOOXXXXOXOOOXXXOXXXXOOOOOOXXOXOXXOXOXXXXOXXOXXXOXOOXXOXXXXOXXXOXOOOXOOOXXOXOXOOOXXOOOOOOXOXOXOXXXXOXOOOXXOOXOOXXXOXXOXXXOXOXXOOOXXXOOXOOXXOOOOOOOOOXXOOXOXXOOOXOXOXOXXXOXXXOOOXOXOOXOOXOXXXOOOOOXOOOXXXOXOXOXOOOOOXXOXXXXXOXXOXXXXXXXOOOOOXXXOXXOOXOXOXXOXOXOOXOOXXXOOXXXXOOOOXXOOOOOOXOOOXXOOXOXOOOOOOXXXOXXOXXOOXXOXXXXXOOOOXOXOOXOOXXOOXXXOXXXXXOXOXOXOOOOOXXOXXXOOOOOOXXXOXOXXOOXXOO';\r\nd='XXXXOXOXOOXXXOOOXXXOXXXOXXXXXOOOXOOOXXOOOOXOOOOOOOOOXXXOOXOOXXXXOXXOXOXXXOXOXOXOOXOOOXXOXXOXOXOXXXXOOOOXXOXXXOOOXOXXXOXOOOOXOXOOOXOOOOXXXOOOOXOOOOXOOXOXXOXXOOXXOXOXXXOOXOXOOOOXOOXXXOXOOOOOOXOXOXXXXOOXXXOXXOXOXXOXOOOXOXXOOXXOXXOXXOXXXXOOOXXXXXOOOOXOXXXXOOOOOXOOOXOOXXXOOOOOOOOOOOXOOOOOOOXOXXOXOOXOOXXXOXXOXXOOOOOXOOOXXOXXXOXOOXOOOOOOOXXOXXOXOXOOXXXOOOXOOXXOOXXXXXOOOOOXXOOOOOXXOXXOXXXXOXXXXXOXXXXOOXXXOXXXXXOXOOXOOOOXXXOOOOXXXOXOOOXOXOXOXOOXOXXXXXOXXXOXOOXOXOXXXXOXOOXOOOXXOOXXOXXXXXXXOXXXXXXXOOXXXXXXOXXOXXXOOXOOOOXXOOOOXOXXXXXOOOXOXXOOXOXOXXXXOOXOOXOOOXXOOOOOXOOXOOXXXXOOXXXOOOXOOXOXXXOXOOXXXXOXXXOXOXXOXXXXOXXXXOOOXXXOOXXXXOOXXOXOOOOXXOXXXXOOXOXXXXXOOXXXXOOXXXXXOXXXOXXOXOOXOXXXOXOXXOOXOXXXOXOOOOXXOXOOXXOOOXOXXOXXOOXXXOOXOOOOXOOOXXOXOXOXOXOXOOXXOOXXXXXXXOOOOOXXXXOOXOXXXXXOXOXOXXXOOXOOXXXXOOXXOXXOXXXXOOXOXXOOXXXXOOXOOXOOXXXOXOOOXOOXOXXXXXOOOOXOOOXOOXOXXOOOXOXOXOOXOXXXOXOOXXXXXXXXXOOXOOXOOOXXOXXOOOXXXOXXOXXOOOXXOXOXOXOXXXOOXOOXXOOXXOOXOXOOOXXXOXOOXOXXOXOOXXOOOOXOXXOXOOOXXOOXOOOOXXXOOXXOXOXOOXOX';\r\ne=60;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%22\r\ni='XXXXOOOXXOXXOXXOOXOXXOXOOOXOXOOXXXOOOOOXXOOXXOXOOOXXOOOOXOOOOXXXXOXOOOOXOXXOOOOXOOXOXXXXOXOXXOXOOOOXXXOXXOOOOXOOXOOXXOOOOOXOXOOXXXXXOXXXOXXXOOXOOOOXOXXOOOXXXXOOXOOOOOXXOXOXOOXOOOXOXOXXXXXOOOXXXOXOOXXOOXXXXXOXXXXOOXOXXXXOXOXXOOOOOXOXXXXXXOXXOOOXOOXXXOOOXXOOXOOXXOOOOXOXOOXOOXXXOXXXXXOOXOXOXXXXXXXXOOXOXXOOOXOXOOXXOOOOXOOOOOXOOXXOOXOOXXXOXXOOXXOXOXOXOXXOXXOXXOOOXXOOOXOXOOOOXOOOOXOXXXOXOOOOXXXXXXXXOOXXOOOXXOOXXXOOXXXXXOXXOXOXXXOOOXOOXXOXXOXOXXOXXOOOXOXXOOOXOXXXOXXXOOXXOXXXXXXOOXXXXXOOOOXOXOXOXOOOXOOOXXXOXOOXXXOOXXXOOOOOXXOXXOXXOOXOXXXOOOXXXOXXXOOOXXXXXXXOOOXOOOXXXXXXOXXOXOXXOOOXXOOXOOOXOXOOOXOXXOXXOXOOXOOXOOOXOOOOXOXOXXOOOXOXOXOXXXOOOXOOOXOOXXXOOXOXOXXOOXXXOOOOOOXXXXXXXOOOXXOXOXXOOOXOXOXXOOOOOOXXXXXXOOXOOXXXXOOOOOOOXOOOOXXXXOXOXOOXOXOOOOXOXXXOOOOXXOXOXOXOOXXOOOOOOXXOOOOOXXXXXXOOXOOOOOOXXXOOXXOXXOXXOOOOOXOXOXXOXXOXOXOOXXXOOOOOXOOXXXOXOXOOOXXOXOOOOOXXOXOOOXOXXOOXOXXXOOXXOXXXXXOXOOOXXOXXOOOOOXXXOXXOOOXOOOXOOXOOXXOXXXOXXXOOXXXXOOXXXOOXXXXOXXXXOXXXOOXXOXOOXXOOXOXOXXOXXOXOOXOOOXOXXOOOOOOOXOOOOXOX';\r\nd='OXOXOXXOXXXXOOXOOXOOXXOXXOOXOXXXXXOOOXXOXOOXOXXOXXOXXOOXXOXXOXOOOXOOOOOOXXOOOOXOXXOOXOXOXXOXXXXOXOXOOXOXXXOXOOOXOXOXOOOOOOXOXOOOOXXOOOOXOXOOOOXXOOOXXOXOXOOXXOOXOOOOXXOOXXOXXOOXXOOOOXOXXXOXXXXOOXXOXXOOOXOXXXOOXXXOOXOXOOOXXOOXOOXXXXOOXXOOOOOXOOXOXXXXXOOOXOOXXOOOOOXXXXOXOXXXXOXXOOXOOOOXOOOOOXXOOXOXOOOOOXOOXXXOOXXOOOOOXXXXOXXXOOXXXXOXOXOOXXXOXOXOXOOXOOXOXXOOXOOOOOOOXXXOOXOXOXOOOOOOXOXXOOXXOXXXXOXOXOOOXOXOXOOOXOXOXOXXXXXOOOXXXOXOXOOXXXOXOXOOOOOOOXOOXXXOOXXXOOOOXOOXXXOXOOOOXOOOXXOXOOXXXXXXOXOOXXOOXXXXXOXXXXXXOOOXOXOOOXOXOXXXXXXXOXOOXXOOXXOXXOXOOXXXXOOXOXOOOOOOXOXXOOOXOXXXXOXOXXOOXOOXXXOOOOXOXOXOXXXOOXOOOXXOOOXXOXXXXXOXOXOOXOXOOOXOXXXOOOXOXOOOXXXOXOXOXOOXOOXOOXXOOXXXOOXOOOOXXOOOXXXXOOXOOXXXXOOXXOOXOOXXOOXXOOXOOXXOXXOXXXOXXOOXXXOOOXXOOOOXOXOXXOXOXOXXXOOXXXXOXOXXXOOOXXXOOXOOXOOXXXXOOOXXOOOOOOXXXOOOXOXXXOOOXOOXXXXOOXOXXOXXOOXOOXXXXXOXXXXXOOXOXXOXXOXOXOXOXXXOOXOXOXXOOOOXXOOOOOOOOOOXOOXOOOXXXOXXXXXOXOXXXOOXOOOOOOXXXXXXXOXOOOXXOOOOXXXXOXOXOXXOOXXOOXXOXXOXOXXOXXXXXOXXOXOXXXOOOOXXXOXOXOXOOOOXXOXOOXXO';\r\ne=47;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%23\r\ni='OXXXXOOXXXOOOOOOXXXOOXXXOOOOOXOOOOXOOXXOXOOXOOXOXOOOOOOXXXOOXOOXXXOOXXOXOOOXXOXOOOOOOOOXXOOXOXOXXXOXOOOOOXOOXXOOOOXXOXOXXOXOXOXXOXXXXOXXXOXOXXXXXXXOXXOXXXOXXXOOOOXOXOXXOOOXXXXXOOOXXXOXXOXOOXXOXXXOXOXOOOOXXXOOXXOOOOOOXOXOOOXXXXOXOXOXXXOOOOXOOOXOXOXOOOXOOXOXOOOXOOOXXXOOOXXXXXXOXXXOXOXOXOOOOXXOXOOOXXOXXOOOXOOOXOOXOOOXXOOXXXXXOOXOXXXOOOXXXOOXXXXXXOXXOOOOXXOOXXXXXOOXXXOXXXXXXXXOOOOOOXOXXOOOOOXXXOXXOOOOXOOOXXOXOXXOXOOOOXXOOXOXOOXXOXOXOXOOXOOXXXXXOOXXOXXXXXOOXXXXOXOOOOXXXXOOXXXXOOOOXOOOOOOOOXXXOXXXXOOXXXOXXXOOXOXXOXOXXXXOXXOOOOOXOOOOXXOOOXOOXXXOXOXXOOXOOXXOOXXOXOXXXXOXOXXXXOXXOXXXOXOOOOOOOOOXOOOOOOXOXXXOXOXOXXXXXOXOXOXOOOXOOXXOXXOXXOXXXOOOXXOOOOXOXOXXOXOOOXXOXXXOOXXOOXOXXXXOXXXOXXXXOXXXXXXOOXOXOXXXOOOXXXOXOOXXOOOOOXOXOOXOXOXXXOOOXXXOXOXXOOOXOOXXOOXOOXOXOXXOXXOOOXXOXOXXXXXXXXOOXXOOOXXOXOOOOXOOOOXOOOXXXXOOOOXOOXXOXXOXOOOXOXXOOOOXXOOOOXOOXXXXXOOXOOXXOXOXOOXXXOOXXOOXXOXXOXXOOOXXXOXOOOXOXOXXOXXXXXXOXOOXXOXXOOXXOOXOXXXOXOOOOXOXOOXXOXXOXXOOXOXXXXOXOXOOOOXOOOOXXXOOOOXXXXXXXXOXXOXXOXXXXXOXXXOXXOOXXXXO';\r\nd='XXOOXXOXOOXOOOOOXOXXXXXXXOOOXXXOOXOXOXOOOXXOOXXXOOXXXXOOOOXOOOOXOOOXOOXOXXOOOOOXXXOXOOXOXOOOOXOOOXXOOXXOXOXOXOXXOOOXXOOXOXOXOXXXOXXXXOOXXXXOXXXOXXOXXXOOXXXOXOXXOOXXOXXOXOOOOOXXXOOOXOXOOXXXXOXXOXXOXOXXOOXXOOXXXXXOXXXOXXXXXXOOXOOOOXOXOOXOOOXOXXXOXOXOOXOOXXXOXXXXXXXXOXXXOOOXXXXXXOXOOXXXOXXXOOXOXXOOXXOOOOXOXXXOOOXOOXOXOOOXXXOOXXXOOOOOXOOXXOXXOOXXXXXXXOOXOOOXXXOXXXOOXOOOOOOXOXXOOXOOOOOXOXXXOXOXOOOOXXOXXXXOOOXOXXOOXXXOXOXXOOOXXXOXXXXOXOOOOXOXXXOXOXOOXOOXOXXXOXOXXOXOXXXXXOXOOOXOXOOXXXXXOOOXOXXOXXXXOOXOXOXOXXOOOXXXXOOOOOOOOOOOXOOXXOOOOOXXOXXOXXOOOOOXXOXXXXOOXOOXXOXOXOXXXXXOOXOOOOOXOXXOXXXXXOXXOXOXXOOXOOXXXXXOOOOOXOOOOXOXOOOXOXXXOOOOXXOOXOOOOOOXXOXXOXOOOOXOOOXXXXOXXXOXOXXOXXOXXOOXOOOXXXXXXXOXOXXXOOOOOXOOOXXOXXOOOXXOOXXXOXXOXOXXXOOOOOOXXOXOOXXOXXXOXOXXOXOOOXOOXXOXXOXXXOXXOOOOOXOOXOXXXXXOXOXOXOOOXXXOXOXOXXOOXOOOXXOOOXXXOOOOOOOOOOOOXXOOOOXXOOXOOOXXOXOXXOXOXXOXXXOOOXXXOXOOXOOOXXOOXXXOOOOOXXXXOXXOXXXOXOXXXOXXXOXOOOOOXOXXXXXXXOXOOXOXOXXXOXXXXOOXOOXOOXOOOXXOOXXOXOXOOXOXXXOOXXOXXXXOXXXOOXXOOXOXXOXOOXOX';\r\ne=42;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%24\r\ni='XOOXXOOXOOOXOOOOOXOOOXXOXXOOOXOXXOOOOXXXOXOOOXXXOXOOXXXOOXOOXOXXXOOOOXOXXOOOXOXXOXXXOXXXXXOOOOXXXOXOOOXOXXXOXOXXOOOOOOOOOOOOOXOXOXXOOXXOXXOXXOOXXOXXXOXOXOXXXXXXOXXOOXXXOXOXXOXXXXOOXXXXOXOXXOOOXOXXOXOOOXXOXOXXXXXOOOOXXOOXOXOOXXXOOOXOOXOOXOXXOOOOOOXXXOOOOOOXXOOXOXXOOXXXXOXXXOOXXOOOOXXOXXXOOXXXOXXOXOOXXXOXXXXOXXXOXXOOXXOXXOXXXXXOXXOXXOOXOXOXXOXOXXOOOXOXXOXXOOOOOOOOOOOXXOOOXOXXOXXXXXOXOOXXXOOOOXOXOXOOXOOOOOOXOXOOOXOXXOXOXXOOXOOOXXOXOOXOXXXXXXOOXOXOOOXXOOOOXOXOXXOXXXOOOXOOXOOXOOXXXXOXOXOOOXXXOOXOOXOXXOOOXXXXXXOXOXOXXOOOXXXOOXXOXOXOOOOOXOOXOXXOXOXXXOXXOXXOXOOOOXOXXOXOXXOOXXXOOXXXXXXOXXXXXXOXOOXXXXOXXOXXXOOOXOXOXXOOOOOOXOOOXXXOOXOOXOOOOOOXXXXXOXXXXXXXXXXXOOOXXOOXXXOOXXOOOXOOXOOXOXOXOOOOXOOXOOXXXXOOOXOXXXOOOOOXXOXXXXOXXOXOOXOXXXXOOXXOXOOOXXOOOOXXOXXXOOOXXOXXXOOOOOOXOOXOOXOXXXOOXXXXOOXXOOXXOOOXOOOOOXOXXOOOXOXXXXXOOOOOXXXXOXOOXXOXOXOOXXXXOOXOXXXXXXXOXXOXOOXXXXXXXOOXXXXOOOXOXOOOXXXXOXXXXXXXOXOXXXXXXOXXXOOXOOXXXOXOXXXXOOXXXXXOXOXXOOOOXXOOOXXOXOOXOXXXOXOOOXXOXXXXOOXXOXOOXOXXXXXOXOXXXXXOXOXOXOXXXOXO';\r\nd='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';\r\ne=64;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%25\r\ni='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';\r\nd='XXOXXXXOXOOOXOOOXOXOOOOXOOOOOXXXXOXXXXOOOXXOOXOXXOOOXOXXOXXOXXXOOXOOXOOOXXXXOOOOOOOOXXXXOOXXXXXXOXOXOOOOOXXXOXOOXXOXXXOXXOXOXOXXOOOXXXXOOXOXXXOXOOXOXOOXOXXOXOOXXOOXXXXOOOXXOXOXOOOOOOXXXXOXXXXXOXXOOOXOXXOOOOOOOOXOOOOOOXXXOXOOOOOOOXOOOXXXXOOXOXXXOOOOOOOOOXXXXOOOOXXOOOOOOXOOOXOXXXOOOXXXOOOXXOOXXOOOOXXXOXOOXOXXOXXOXXOOXXOXOOXOXOXOOXXOOOXXXXOXXOXOXXXOXXOXOOXXXOXOXXOXOXXOXOOOXXXOOOOXXXXOXOOOXOXXOOOOOOOOOOOXOOXOXOOXXOXOXXOOOOOXXXOXOXXXOXXXOOXXOOOOXOOOOOXXXXOOOXXXOXXXOOXOXXXOXOXOXXXXOXXOOXXOXOXOXOXOXXXOOOXXOOOXOOXOOOXXOOOXOOOXXOXXXXOOOXOOXOXXXXXOOOXOOOXOOXXXXXOXXOXOXXOOXOOOOXXOOOXOOOOXOXXXOOXXOXXXOOXOXOOOOOXOXXXXOXOOOOOXXXOOOOOOOXXOXXOXOXOOOXXOXOOXOOOOXXXOOXXXXOXXOOOOOOOXOXOXOXOXXXOXOOOXOXOXXXOXXXXXXXXXOXXOXOOOXXXXOOOOXXOOXXOOXOXXOXOXXXXOXOOXOXOOOXXXOOOXOXOXXXXOOOXXOXXOXXOXXOXXXOXXOXXOXXOXXOOOXOOXXXXOOOOOXOXXXXXOOOOXOXXXOXXOXOXXXOOXXOOXOOXOOXOOXOOOXOOXXOOOXXXXXOOOOXOOXOOXXOOXXXXXXOOXXOXOXOXXXOXOXOOOXOXXXOOXXOXXXOXXXOOOOOOOOXXOXXXOXOOXOOXOXXOXOXOOOOOOXOXOXXOOXOOOOXOOXXOXOOOXXXOOOOXOXXOXXOXOOXO';\r\ne=23;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%26\r\ni='OXXOOOOOOXOOOOOXOOXXXXXOXXOOOXOOXXXOOXOXOOXOXOOOXXXOXOXXOOOOXXXXOOXOOXXXXXXOXXXOXXOOXOOXXOXXOXXOXXOXOOOOXXXXXOOOOXXOXXOOOOOOOXXXOOXXOOOXXOOXXXOXOXOXXXOXOOOOXXOXOXXOXOOOXOXXXOOXXXOXXXOXXOOXOXOOOOXXXOXOOXOXXXXXOXXOOOOOOXXXXOOXOXXXXOXOOOOOXXOXXXXXOOXXXXOXOOXXXOOOXXXXOXOXXXOOXXOXOXOXXOOOXXOOXXXXOOXXOOXOXXXXXXOOXXOXOXOXXOOXOOXXOXOOOXOOXXOOXXOXXOOXOOOOOOOXOXOOXOOOOOOXOXXOXXXXOOOXXXXXXXXOXOOXXXOXOOOOOOXOOOOOOXXOOXOOXXOXXOXXOOXXXOXOOXOOXXXXXOOXXXOXOXOXXOXOXOXXXXOXXOOXOXXXOOXXXXOOOXXOXOXXOOXOXXXOXXXXOOXOXOOOXXXXXXOXOOOXOOXXXOXOOOOXXOOOOOOOXOOOXXOOXXOOXOOOOOXXXOXOXOXOOXOXOOXXOOOOOXOOOOOXOOOOXXOOOOOXXXOXXXXOOXXOXOOOXXOXXXXOOXXOOOOOXOOOXXOXOOOOXOOXOOXXOXOXXXXXXXXOOXXOXXOOOXOXXOOOOXOOXOOXOXOXOOOXXOXXXOOOOOXOXXXOXOOXXOXXXOOOXXXXOXXXOXXOOOOXOXXXOXXOOOOOOOXOXOXXXOOXOXXXOXOOOOXXXXOXXXXXXXOXXXXOXOXOXXOXOXOOXOXXXOXXOXXXOOXXXOXOOOXXXOXOOXXOXOOOOOOXXOXOXXXOXOXOOOOOOXOXXOOXOXXOOOOXOOOOXXOOXOOXXOXXOXOXXOOOOXXOXXOOXXXOOOXXXOOXXOOXXOOOXXOXXOXXXXOOXOOXOOXXOOOXXXOXXOXXOOXOXOOXXOOOOOOXXOXOOXXOOXXXXOOXOXXOXOXXOXX';\r\nd='XOOOOXXOXXXOOXXOOOXOXOXXXXOXOOXXXXXOXOXOXXXXOOOOXOOOOXOOXOXOXXXXOOOXOXXOXOOXXOOXOOXXOOXOXXOXXXOOOOXXXXOOXOXXOOOXXXXXOXXOXXOXOOXOOOXOOOXOOOOOXOXOOOXXOOXXXXXOOOOOOXXXXOOOXXXOOOXXXOXOOXXOXXOOOOOOXOXOOOXXXXOXXXXXXXXXOXXOXOXOXXOOXXXXXOOXOOOOXOOOOOXOOOOOXOXXOOOXXXXOOXXXOXXOOXXOOOOOOOOXXXXOXOOXXOXOXOOXOXOOXXOOOXOXXOXOXXOXOOOXOXOOOOOXOXXOOXXXOOXOXOOOOOXXXOXOXXXOOOOXXXXOXOOXXOXXXOOOXXOXXOOXXOOXOXXOXOXXXXXXOOXOXXOXOXOOOXXOXXOXOXOOOXOOXOOOOOOXOOOOOXXXXXXOOXXXOOXXOXXOOOOXXXOXXOXOXOXOOOOXXXOOXOXXOOOXOOXOXOOOXOXOXXOOXXOOOXOXOXOXXXXOXOXOOXXXXXXOOXOXXOXOXOOOXXXOOOOXXOXXXOXOXXOXXOOOXXXOOXOOXOXXXXOOXOOOOXOOOOOOXXOXXXXOOXOXXXXXXOXXOOXOOOOXXXXOXOOXOOOOOXXXXXOOOXXOXXOXXXXXXXXOOXOOOOOXXXXOOOOOXOXOXOOOXOOOOXOOOOOOXXXXXXOXOXOXXOOXXXOXXOXOOXOXXOOXXXXXOXOXXOXOOXXXXXOOOXOOOXXOOOXOXOXOOOOXOOXXXXOXOXOOXOXXXOOOOXXOXXXXXXOXXOXOXOXXXXXXXXOXOXXXOOXXOXXOOXXXXXXOXXXXXOXOOOOOXXOXOOXOXXXXXXXOXXOXOOOXXOOXXXOOXXOOOXXXXOOOOOOXOOXOOOOXOOOXOXOOXOOOXOXXXOOXOXOXXXXOXOXOOOXOOOXXXOOOXXOXXXXXOXOOOOXOOOOOXXXXOOOXXOXOXXXOOXOOOOXXOOX';\r\ne=38;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%27\r\ni='XOXOXOOXOXXOXXOOXXOOOXOOOXOOXOXXXXXXXXOXXOOOOOXOOXOXXOXOXXOOXXOOOOXXOXOXOOXOXOOXXOOOXOXOOXOOXOOOOOOOOXXXXOOOOXOXXXXXOOXOOOOXXOOOXXXOOOXXXXOOXOXOXXOOOXXOXXXOXOXOOOOXXXXXOXOOOXXXXXXXOOOOXXOXOOXXXOXXXOXXOXOOXXXOXOXXOOXOXXOXOXOXOOXOOOXXOXXXOXXXXOXXOOOOXOOOOXXXXXXXXOXXXOXXXOXOOOXXXXOXXXOXOXXXXOXOOXOOXOXXXXXXOOXOXOXXOOOOOXXOXOOXXOOOOXOXXOOOXOOOOXOXXOXOXOOOXXXOXOXOOXOOXOOXOXXXXXOOOXOOXXOOXOOXOOOXXXOOXXOXOOXXXXXOXXXXOXXOXXOOOOOXXXXOOOXOXXXOOOOXOXOOXXOXOXOXOXXOOXXOOXOXXOXXOXOOXOOXOXOXXOOXXXOXXXXXXXXXXOXOXXXOXOXXXOXXOXXXOOXOXOOXOXOOXXOOOXOXXOXOXXOOXXOXOXXOXXOXXXXOXOXOXXOOXOOOXXOXOOXOOXXXXXOXOOOXXOOOOOXXXXXOXOXXOXOOXOXOXXOXOOXXOOOOOXXOXXXXXOOOXOOXOOOXOXXXXOXXXXOOXXXXOXXOXXXXXOOXOOXOXXOXOOXXOOOOOXOOXOXOXXXOXXXOXOXXXOXOXXOXXOXOXOXXOXXXOXXXXOOXXXOXXOOXOOOXOXOOOXOOXXOXXXXOOOXOOXOOOOOOOOXXOOXXOXOOOOXXOOOXOXOOXOOXXXXOXOOXXXXXXXOXOXOXXOXOXXOOXOXOXOXXXOOXXOOOOXOOXOOXXXOXOXOOOXXOXOOXXXOXXOXOXOXOXXOXOOOOXXOOOOXXXXXOOXXXOOXXOXXXXXOXOOOXXOXOXOOXXOOOXXXOOOOXOXXXOXXXOXOXOXOOOOOXXXOXXXOOXOXOXXOXOOOXXXXOOXXXXOO';\r\nd='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';\r\ne=36;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%28\r\ni='XXXXOXOOXXOOXOXXOXOXOOXXXOXOXOXOOOOOXOOOXXOOXOOXOXOXOOXOOXXXXOOXXOOXXOOOOXOXOXOOOXOXXXOOXXXOXXOOXXXOXOOOOOOOOXXOXOXXOOOXOXOXXOOOXOXXOXXOOOOXOXXXXOXOOOXOXOOOXXOXXXOXXXOXOXOXXOOOOXXXXXXOXOOOOXOXOXXXXOXOXOOOOXOOOOOOOOOOOXOXXXOXOXOXXXOXOOOOOOXXXXOXOOOOOOXXXXOXXXXXOXOOOOOOOXXXOOOOOXOOXOXXOOXXOOOXOXXXOXOOXXOOXXOXXXOOOOXXXXXOOXXOOXOOOXOOOXXXXXOXOOXOOOXOXOOOXXOOOOXXXOXXOXOOOXOXOOOOOOOXXXOXXOXXOXXOXXXOXOXXOXOXOXXOXOOXOXXOXOOOXOOOOXOXOXOXOXXXXXOXXOXOOXXXXOXOOXOOXOOOOOXXXXXXXOXOOOXXOOOOOXXXXXOXXXXXOOOXXOXOXOOXXOOXOXOOXXOXOXOXXXXOXOXXOOOXOXOOOOOOXOXOXXXXOOXXOOOOXOXOXXOOXXXOOOXOXXXOXOXXXOXXOOXOXOOOOOXXXOOXOXOOXXXOOOOXOXXXXOOOXXOXOOXOOXXXXOXOOXXXXOOXOXXOOOXOOXXXOXOXXXXXOOOOOXXXOXOOOOXOXOOOOOXXXXXXOXOXOXXXOOXOOXOXXOXXXOXXOOOOOXXXOXOXOOOOOXXOXXXOOXXXXXOOXOOOOOOXXXOOOXXOXOOOOOXXOXOXOXXXOOXXOXXXOOOOXOOOXOXOXOXOXOXOXXOOOXXXOXOOOXXOOXXXXOOOOXXOOXOOOOXXXOXXXOXOOOOOOXXOOOOOXOXXXXOXOXXXOOXOOOOXXOXOOOOOXOXOXOXXOXXXXOOOXXXXOOOOXOXXXOOOXXXXOOOXOXXXXXOOXXXXOXXXXOXXOOXOXOOOXOOOOXOOXOXOOXXXXOOXOXOXXXXOXOOOXOOOOOO';\r\nd='XOOOXXXOXXOXXOOXOOXOXOXXOOOOOOXOXXXXOOOOXXOOXOOXXOOOOXXXOOOXXXXOOOOOOOOXOXXXOXOXXOXOOOOOXOXXXXXOOOOXXOOXXXXXOXXXXXOXXXOXOOOOOXOOOXOXXXXOXXXXXOOOXOOXOXXOOOXXOXOXOOOXXXOOOXOOXOOOXXOXOXXOOOXOXOXXXOXXXXXOOOOXXOXOOXOOOOXXXXXOOOXXOXXXXOXOXXXXOXOOOOOXOXOXXOXOXOOOXOXOXXOXXXXOOXXOOXOOOOOXOXOXXXOOXOXXOOOOXOXXXXOOXXOXOXOXXXOXOXXOXXXXXXOOXXOOOXXXOOXOXOXOOOOOXOXOXXOOOOXXXOOOXXOOOXOXOOXOOXOXOOXXOOOXXXXOOOOOOOXOOOXOOOOOXXXXOXOXOXXOXOOXXXXOOXOXOXXOXOOXOOOXOXOXOOXXXXXOXXXXXXOXOOOOXXXOOOOOXXOXXXXXOXXOXXXOOOXOOOXOOXOXXXXOOXXOXOOXOOOXOOOOXOXOXXXOXOOXOOXOXXOOXOXXXOXOOOOOOOOOOXOOOXOOXXOOXOOXOXOOOXXXOXXXXOOXOXOXOOXXXXOOOXOXXXOOXOXOXXXOOXXXXOXXXXXOXOXOXOXXOOXOXXOXXOOXXOOOOOXOXXXXXXXXOXXOOXXXOXXOOOXOOOOOOOOOXOXOOOXXXXXOXOOOOOOXOXOXOXOOOOXXOOOXOOOOOXXOXOOOXOOXXOXOXOOOXXXOOOXOOXOOOOXXXXXOOXXOOXXXXXOOOOOXOXOOXOXOOXOOOXOOOXXOOXOOOXOOXXOOXXXXXXOOXOXOOOOXXXOOXXOXOOOXXOXXOXOXXOXOXXXOOXOXXXOOXXXXOXXOOXOOOXXOXOOOXXXXXXOXXOOOXOOXOOOXXXOOOOOXOOXXXXXOOXXXOOXOOXXOOXOXOOOXOXOOOXOXXXOXOOXOOXXOOXOOOOOOXXXOXXOXOXOXOXOXXOXXOXX';\r\ne=32;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%29\r\ni='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';\r\nd='OXXXOXXOXOXXOOOOOXOOXXOXOXOOOOOXOXOOXXXOOXOOOXOXXOXXXOOXOXXXOOXOXXXXXOOOXXXOOOOXOOOOOOOOOXXOXXOXXOOXXOXOXXXOXXOXOOXXXOXXXOXXXXXXOOOOXOXXXXOOOXXOOOOXOOOXXXXOXXXXXXOXXOOOXXOXXXXOXOXXOXXXOOOOOXXXOOXXXXOXOOOXXOXXOOXXOOXOOXOXOOOOXXXOOXOOXOOOXXXXXOXOOXXXOOOXXOOOXXXXOOXOXXXOXOOOXXXXOOOXXOOOOXXXXOXXXXOXXOXOOXOXXOOXXXOOXOXXOXOOOXOXOXXXXOXXOXXXXXOOOXOOOXXOXOXOXOXOXOXXOXOOOOOXOOXXOOOXXXOXXXXOOXOOXOXOOXOXOXOOOOXXXXOXXOXXXXXXXOXXXOOXXOOXOXXXXOXOXOOXOOXOXXOOXXXXXXXXXOOOXOXXOXXOXXXOOOOOOOOOXOOOOOXXXOXXXOXXXOXOOOXXOXXOXOXOXXXXOXOXXXXOXOOOOXOXXOXXXXOXXOXXXXOOXXXXOOXOXOOOXXXXXXXXXOOXXOXOXXOXXXOXOOOXXOOXXXXXOXXOXOOXOXXXXOXOOXOOOOOXOXXXOXXXOXOXXOXXXXOOXXOXOOXXXOOXXOOXOXXOXOOOOXOOOXXXXXOXXXOXXOXXOOOXXOXXXXOXXOOXOXXOOOXOXOXOXOXOXOXOOOXOOXOOXXOOXOXOXXXXOXXOXOOOOOOOOOOOOOXXXOOOXXOXXXXOXXOXOXOOXOOXOOXOXOXXOOXOXXXXXOXXOOXOXXOXOXOXXOXOXOOXOXOXOXOOOOOOXOOXOXXXOOOOOOXXXXXXXXOXXXXOXXXXOXOOXXXOXXXOOOXXOXOXXOOOOOOOXOXXXOXXXXOXXXOOXOXOOOXXOXOXOOOXXXXXXOOOOXXOOXOXXXXXXXXXOOXXOXOOXXXOXOOOXXXOXXOXOOOOXXOOOXOOOOOOXXXXOXO';\r\ne=27;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\n%30\r\ni='XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO';\r\nd='OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX';\r\ne=999;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));\r\n%%\r\ni='OOOOXXOOOO'; %31\r\nd='XOOOOOOOOX';\r\ne=4;\r\nswaps=snowcones(i,d);\r\nassert(isequal(swaps,e));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-21T20:43:53.000Z","updated_at":"2026-06-09T10:32:06.000Z","published_at":"2013-04-21T21:37:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to solve the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://contest.usc.edu/index.php/Spring13/Home\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eUSC Spring 2013 ACM Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e Problem F, Snow Cones.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSummary of Challenge is to Swap the Snow Cones in the minimal number of swaps so the children all have their selected flavor. There are only two flavors, X and O. Input is the string of distributed Cone flavors and a string of desired Cone flavors. Adjacent children may exchange cones but in any one round a child may only swap with one other child.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine minimum number of Swap rounds to convert the Distributed to the Desired Cone flavor sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e From XXO to OXX \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e From OXOX to XOXO \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly two competitors solved this challenge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA little complex requiring a Matlab 3-Liner solution versus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://contest.usc.edu/index.php/Spring13/Home?action=download\u0026amp;upname=cones.zhengcao.cpp.txt\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCao's C solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":988,"title":"Convert a substructure reference string into a valid definition structure for subsref and subsasgn","description":"You have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. \r\nTherefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\r\n\r\nFor example, to reference the value a(12), you would have to convert '(12)' into \r\n\r\n  def = \r\n    type: '()'\r\n    subs: {[12]}\r\n\r\nAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into \r\n\r\n  def(1) = \r\n    type: '()'\r\n    subs: {[12]}\r\n\r\n  def(2) = \r\n    type: '.'\r\n    subs: {'field_b'}\r\n\r\n  def(3) = \r\n    type: '{}'\r\n    subs: {[1]  [3]}\r\n\r\n  def(4) = \r\n    type: '{}'\r\n    subs: {2}\r\n\r\n  def(5) = \r\n    type: '()'\r\n    subs: {[3 4]  ':'}\r\n\r\n  def(6) = \r\n    type: '.'\r\n    subs: {'c'}\r\n\r\nThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\r\n\r\nNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.","description_html":"\u003cp\u003eYou have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. \r\nTherefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\u003c/p\u003e\u003cp\u003eFor example, to reference the value a(12), you would have to convert '(12)' into\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edef = \r\n  type: '()'\r\n  subs: {[12]}\r\n\u003c/pre\u003e\u003cp\u003eAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edef(1) = \r\n  type: '()'\r\n  subs: {[12]}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(2) = \r\n  type: '.'\r\n  subs: {'field_b'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(3) = \r\n  type: '{}'\r\n  subs: {[1]  [3]}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(4) = \r\n  type: '{}'\r\n  subs: {2}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(5) = \r\n  type: '()'\r\n  subs: {[3 4]  ':'}\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edef(6) = \r\n  type: '.'\r\n  subs: {'c'}\r\n\u003c/pre\u003e\u003cp\u003eThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\u003c/p\u003e\u003cp\u003eNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.\u003c/p\u003e","function_template":"function def = subsdef(defstr)\r\n  def = substruct('()',{1});\r\nend","test_suite":"%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = 1i;\r\nb(12) = y_correct;\r\ndefstr = '(12)';\r\nassert(isequal(subsref(b,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = -4i;\r\nc{1,2,3,4,5}.field_b = y_correct;\r\ndefstr = '{1,2,3,4,5}.field_b';\r\nassert(isequal(subsref(c,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = 3i;\r\na(12).field_b{1,3}{2}((3),1).c = y_correct;\r\ndefstr = '(12).field_b{1,3}{2}((3),1).c';\r\nassert(isequal(subsref(a,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n\r\n%%\r\nnocheat = isempty(regexp(evalc('type subsdef'),'(eval|regexprep|inline|str2func)'));\r\ny_correct = repmat(2i,3,1);\r\nd{2}.a(1:3,:) = y_correct;\r\ndefstr = '{2}.a(1:3,:)';\r\nassert(isequal(subsref(d,subsdef(defstr)),y_correct) \u0026\u0026 nocheat)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2012-10-11T14:58:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-11T14:55:15.000Z","updated_at":"2026-06-02T03:44:46.000Z","published_at":"2012-10-11T14:55:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have a reference to an element in a data structure, which you want to pass to a function. Not the value itself, but the reference. And you don't like to use evil eval constructions. Therefore, you convert the reference into a structure, like liked by Matlab's built-in subsref and subsasgn functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, to reference the value a(12), you would have to convert '(12)' into\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[def = \\n  type: '()'\\n  subs: {[12]}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd to reference a(12).field_b{1,3}{2}((3:4),:).c, you would need to convert '(12).field_b{1,3}{2}((3:4),:).c' into\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[def(1) = \\n  type: '()'\\n  subs: {[12]}\\n\\ndef(2) = \\n  type: '.'\\n  subs: {'field_b'}\\n\\ndef(3) = \\n  type: '{}'\\n  subs: {[1]  [3]}\\n\\ndef(4) = \\n  type: '{}'\\n  subs: {2}\\n\\ndef(5) = \\n  type: '()'\\n  subs: {[3 4]  ':'}\\n\\ndef(6) = \\n  type: '.'\\n  subs: {'c'}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe assignment is correct when any sub-structure reference that is accepted by subsref and subsasgn is correctly converted from a string to a valid structure.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: Solutions wrapped in (f)eval(c), inline, str2func, regexprep (dynamic regular expressions), etc, are not appreciated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42685,"title":"Cody meets Xiangqi: foresee the unseen (Part 2)","description":"This is the second part of the Xiangqi series. The first part in this series is: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen Cody meets Xiangqi: foresee the unseen (Part 1)\u003e\r\n\r\nBeing increasingly interested in \u003chttps://en.wikipedia.org/wiki/Xiangqi Xiangqi\u003e (a.k.a., *Chinese Chess*), Mr. Cody has designed a new Xiangqi match for \u003chttps://en.wikipedia.org/wiki/Xiang_Yu Xiang Yu\u003e and \u003chttps://de.wikipedia.org/wiki/Han_Gaozu Liu Bang\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\r\n\r\nOnce\r\n\r\n   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \r\n\r\n*whichever comes first*, Mr. Cody announces the outcome accordingly as follows:\r\n\r\n   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\r\n\r\nAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\r\n\r\n                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n\r\nwhere \r\n\r\n* a: the probability that Xiang Yu wins one individual game\r\n* b: the probability that Liu Bang wins one individual game\r\n* Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n* Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n* Nc: # of consecutive ties required to result in a final draw\r\n* Pa: the probability that Xiang Yu wins the match\r\n* Pb: the probability that Liu Bang wins the match\r\n* Pc: the probability of a final draw\r\n\r\nThe main focus of this problem is on *Monte Carlo simulations*, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\r\n\r\n1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u003c tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected. \r\n\r\n2) Check if your solution is based on *pure Monte Carlo simulations* or *analytical approaches*. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations. \r\n\r\n3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get. \r\n\r\nIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks. \r\n\r\n ","description_html":"\u003cp\u003eThis is the second part of the Xiangqi series. The first part in this series is: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\"\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eBeing increasingly interested in \u003ca href = \"https://en.wikipedia.org/wiki/Xiangqi\"\u003eXiangqi\u003c/a\u003e (a.k.a., \u003cb\u003eChinese Chess\u003c/b\u003e), Mr. Cody has designed a new Xiangqi match for \u003ca href = \"https://en.wikipedia.org/wiki/Xiang_Yu\"\u003eXiang Yu\u003c/a\u003e and \u003ca href = \"https://de.wikipedia.org/wiki/Han_Gaozu\"\u003eLiu Bang\u003c/a\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/p\u003e\u003cp\u003eOnce\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \u003c/pre\u003e\u003cp\u003e\u003cb\u003ewhichever comes first\u003c/b\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\u003c/pre\u003e\u003cp\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/p\u003e\u003cpre\u003e                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\u003c/pre\u003e\u003cp\u003ewhere\u003c/p\u003e\u003cul\u003e\u003cli\u003ea: the probability that Xiang Yu wins one individual game\u003c/li\u003e\u003cli\u003eb: the probability that Liu Bang wins one individual game\u003c/li\u003e\u003cli\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/li\u003e\u003cli\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/li\u003e\u003cli\u003eNc: # of consecutive ties required to result in a final draw\u003c/li\u003e\u003cli\u003ePa: the probability that Xiang Yu wins the match\u003c/li\u003e\u003cli\u003ePb: the probability that Liu Bang wins the match\u003c/li\u003e\u003cli\u003ePc: the probability of a final draw\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe main focus of this problem is on \u003cb\u003eMonte Carlo simulations\u003c/b\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/p\u003e\u003cp\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/p\u003e\u003cp\u003e2) Check if your solution is based on \u003cb\u003epure Monte Carlo simulations\u003c/b\u003e or \u003cb\u003eanalytical approaches\u003c/b\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/p\u003e\u003cp\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/p\u003e\u003cp\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/p\u003e","function_template":"function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n% a: the probability that Xiang Yu wins one individual game\r\n% b: the probability that Liu Bang wins one individual game\r\n% Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n% Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n% Nc: # of consecutive ties required to result in a final draw\r\n% Pa: the probability that Xiang Yu wins the match\r\n% Pb: the probability that Liu Bang wins the match\r\n% Pc: the probability of a final draw\r\n    Pa = ;\r\n    Pb = ;\r\n    Pc = ;\r\nend","test_suite":"%%\r\n% Thanks to Alfonso Nieto-Castanon\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path;\r\n\r\n%%\r\nfh = fopen('EvaluateSolution.p','wb');\r\nfwrite(fh, hex2dec(reshape('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',2,[]).')); rehash path; fclose(fh);\r\n\r\n%%\r\nfid = fopen('Xiangqi2.m');\r\ndelim = {' ', '\\n', ',', '.', ';', '''', '@', '+', '-', '*', '/', '\\', '^', '\u003e', '\u003c', '=', '\u0026', '|', '~', '{', '}', '[', ']', '(', ')'};\r\nfile = textscan(fid, '%s', 'CommentStyle', '%', 'MultipleDelimsAsOne', 1, 'Delimiter', delim); fclose(fid); \r\nassert(~any(ismember({'rng','RandStream','seed','state','twister','shufle','default'},file{1})));\r\n\r\n%%\r\na = 0; b = 0; Na = 2; Nb = 3; Nc = 2; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0; b = 1; Na = 1; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 1; b = 0; Na = 3; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0.15; b = 0.85; Na = 4; Nb = 2; Nc = 1; tol = 1e-4;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.9; b = 0; Na = 3; Nb = 1; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.65; b = 0.3; Na = 3; Nb = 2; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\nNa = 3; Nb = 2; Nc = 1; tol = 2e-3; \r\np = sort(rand(2,30)); \r\np = sort([p(1,:);diff(p);1-p(2,:)]);\r\nfor k = size(p,2):-1:1\r\n    a = p(3,k); b = p(2,k);\r\n    score(k) = EvaluateSolution(a, b, Na, Nb, Nc, tol);    \r\nend\r\nSetSolutionScore(round(mean(score)));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2015-11-12T00:41:35.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-08T20:51:55.000Z","updated_at":"2026-06-01T20:51:40.000Z","published_at":"2015-11-10T00:22:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second part of the Xiangqi series. The first part in this series is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeing increasingly interested in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiangqi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiangqi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (a.k.a.,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eChinese Chess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), Mr. Cody has designed a new Xiangqi match for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiang_Yu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiang Yu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://de.wikipedia.org/wiki/Han_Gaozu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLiu Bang\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu wins Na games consecutively,\\n   2) Liu Bang wins Nb games consecutively, \\n   3) No ties occur consecutively,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhichever comes first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu is the final winner,\\n   2) Liu Bang is the final winner, \\n   3) They end up with a final draw.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea: the probability that Xiang Yu wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb: the probability that Liu Bang wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNc: # of consecutive ties required to result in a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePa: the probability that Xiang Yu wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePb: the probability that Liu Bang wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePc: the probability of a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe main focus of this problem is on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMonte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Check if your solution is based on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epure Monte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eanalytical approaches\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":811,"title":"Genome Sequence 004: Long 3rd Generation Segment Correction","description":"The Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003chttp://www.pacificbiosciences.com/ PacBio\u003e. The \u003chttp://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar Assemblathon Genome Contest\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003chttp://www.sciencedaily.com/releases/2012/07/120702210229.htm Sequence Parrot DNA\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\r\n\r\nThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u003c1% error rate. Jarvis and his team combined this data to achieve \u003c 0.1% error rate.\r\n\r\nGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\r\n\r\n*Input:* \r\n\r\nCall 1: empty array, segment Width, Flag=0\r\n\r\nCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\r\n\r\n*Output:* \r\n\r\nCall 1: empty vector, Number of Requested Vectors\r\n\r\nCall 2: Corrected DNA vector, Number of Requested Vectors\r\n\r\n*Score:* Number of N vectors used to produce correct vector for w=1024 case\r\n\r\nThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\r\n\r\nThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\r\n\r\nThe response to the second call is the fixed DNA sequence, vector of width w.\r\n\r\n*example:*\r\nFirst call return : N=3\r\n\r\n  01230123111122223333 Truth\r\n  Input example\r\n  01232123112122221332 Injected errors\r\n  01130123111122123323\r\n  11230133121122223333\r\n\r\n  Output: \r\n  01230123111122223333 Truth, hopefully\r\n\r\n\r\nThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned. \r\n\r\nThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\r\n\r\nFollow-Up Challenges: Sample Data from the PacBio site for \u003chttp://www.cbcb.umd.edu/software/PBcR/ Lambda Phage\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\r\n","description_html":"\u003cp\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003ca href=\"http://www.pacificbiosciences.com/\"\u003ePacBio\u003c/a\u003e. The \u003ca href=\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\"\u003eAssemblathon Genome Contest\u003c/a\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003ca href=\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\"\u003eSequence Parrot DNA\u003c/a\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/p\u003e\u003cp\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/p\u003e\u003cp\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty array, segment Width, Flag=0\u003c/p\u003e\u003cp\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003e\u003cb\u003eScore:\u003c/b\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/p\u003e\u003cp\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/p\u003e\u003cp\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/p\u003e\u003cp\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/p\u003e\u003cp\u003e\u003cb\u003eexample:\u003c/b\u003e\r\nFirst call return : N=3\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e01230123111122223333 Truth\r\nInput example\r\n01232123112122221332 Injected errors\r\n01130123111122123323\r\n11230133121122223333\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: \r\n01230123111122223333 Truth, hopefully\r\n\u003c/pre\u003e\u003cp\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/p\u003e\u003cp\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/p\u003e\u003cp\u003eFollow-Up Challenges: Sample Data from the PacBio site for \u003ca href=\"http://www.cbcb.umd.edu/software/PBcR/\"\u003eLambda Phage\u003c/a\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/p\u003e","function_template":"function [M_fix,N]=PacBio_fix(M,w,flag)\r\n% 1st Call\r\n% M is empty\r\n% w is width of segment\r\n% flag is 0\r\n% Ouput is N, the number of segments requested to fix the segment\r\n% 2nd Call\r\n% M is an Nxw array of values [0:3]\r\n\r\n M_fix=[];\r\n N=1; % needed for 2nd call with flag==1\r\n if flag==0 % Requested number of Segments\r\n  N=1;\r\n  return;\r\n end\r\n\r\nM_fix=M(1,:);\r\n\r\n\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',0);\r\n%%\r\nM=[];\r\nflag=0;\r\nw=100;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n%%\r\nM=[];\r\nflag=0;\r\nw=6144;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\n%%\r\n% Size Performance is based on w=1024 case\r\nM=[];\r\nflag=0;\r\nw=1024;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,not_N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\nfeval(@assignin,'caller','score',min(20,N));\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2012-10-08T02:30:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-01T05:26:57.000Z","updated_at":"2026-05-31T11:18:13.000Z","published_at":"2012-10-08T02:29:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.pacificbiosciences.com/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePacBio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAssemblathon Genome Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e led the team of Phillippy, Koren and Jarvis to successfully\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSequence Parrot DNA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty array, segment Width, Flag=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScore:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e First call return : N=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[01230123111122223333 Truth\\nInput example\\n01232123112122221332 Injected errors\\n01130123111122123323\\n11230133121122223333\\n\\nOutput: \\n01230123111122223333 Truth, hopefully]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-Up Challenges: Sample Data from the PacBio site for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.cbcb.umd.edu/software/PBcR/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLambda Phage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61337,"title":"Volumetric efficiency","description":"Volumetric efficiency measures how well an engine breathes.\r\nThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \r\nNaturally aspirated engines typically achieve 80–95%.\r\n\r\nGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 317.18px; transform-origin: 467.496px 317.191px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVolumetric efficiency measures how well an engine breathes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 514.477px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 257.227px; text-align: left; transform-origin: 443.508px 257.238px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function eta_v = volEfficiency(m_actual, rho, Vd)\r\neta_v = 0;\r\nend","test_suite":"%%Test 1\r\nm = 0.00180; rho = 1.2; Vd = 0.002;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 2\r\nm = 0.00252; rho = 1.2; Vd = 0.003;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 3\r\nm = 0.00096; rho = 1.15; Vd = 0.0012;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-21T09:48:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:45:01.000Z","updated_at":"2026-06-09T14:09:19.000Z","published_at":"2026-05-21T09:48:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVolumetric efficiency measures how well an engine breathes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-06-09T14:10:05.000Z","published_at":"2026-05-21T09:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61342,"title":"Swept Volume and Clearance Volume","description":"The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \r\nThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\r\n\r\nGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 312px; transform-origin: 468.5px 312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 513px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 256.5px; text-align: left; transform-origin: 444.5px 256.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"685\" height=\"507\" style=\"vertical-align: baseline;width: 685px;height: 507px\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Vs, Vc] = sweptClearanceVolume(V_BDC, V_TDC)\r\nVs = 0;\r\nVc = 0;\r\nend","test_suite":"%%Test 1\r\nV_BDC=550e-6; V_TDC=50e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 500e-6) \u003c 1e-9)\r\nassert(abs(Vc - 50e-6) \u003c 1e-9)\r\n%%Test 2\r\nV_BDC=750e-6; V_TDC=62.5e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 687.5e-6) \u003c 1e-9)\r\nassert(abs(Vc - 62.5e-6) \u003c 1e-9)\r\n%%Test 3\r\nV_BDC=400e-6; V_TDC=36.36e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - (V_BDC-V_TDC)) \u003c 1e-9)\r\nassert(abs(Vc - V_TDC) \u003c 1e-9)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:17:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:13:10.000Z","updated_at":"2026-06-09T14:03:37.000Z","published_at":"2026-05-21T10:13:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"507\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"685\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61341,"title":"Specific Fuel Consumption","description":"Brake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \r\nModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\r\n\r\nGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 55.5px; transform-origin: 468.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBrake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bsfc = calcBSFC(m_dot, P)\r\nbsfc = 0;\r\nend","test_suite":"%%Test 1\r\nm_dot=0.0070; P=100000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)\r\n%%Test 2\r\nm_dot=0.0105; P=150000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)\r\n%%Test 3\r\nm_dot=0.0040; P=60000;\r\nassert(abs(calcBSFC(m_dot,P) - (m_dot/P)*3.6e6) \u003c 1e-3)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:12:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:05:55.000Z","updated_at":"2026-06-09T14:04:53.000Z","published_at":"2026-05-21T10:05:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBrake-specific fuel consumption (BSFC) measures how efficiently an engine converts fuel mass into useful work. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eModern petrol engines achieve roughly 250–270 g/kWh at their best efficiency point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven fuel mass flow rate m_dot (kg/s) and brake power P (W), compute BSFC in g/kWh.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61338,"title":"Fuel-Air Equivalence Ratio (Lambda)","description":"Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \r\nλ = 1 is perfect stoichiometry, \r\nλ \u003c 1 is rich, \r\nλ \u003e 1 is lean. \r\nEngine management systems constantly target λ = 1 for optimal catalyst performance.\r\n\r\nGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 286px; transform-origin: 468.5px 286px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ = 1 is perfect stoichiometry, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026lt; 1 is rich, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026gt; 1 is lean. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 392px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 196px; text-align: left; transform-origin: 444.5px 196px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026amp;rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function lam = calcLambda(AFR, AFR_s)\r\nlam = 0;\r\nend","test_suite":"%%Test 1\r\nassert(abs(calcLambda(14.7, 14.7) - 1.0) \u003c 1e-6)\r\n%%Test 2\r\nassert(abs(calcLambda(12.5, 14.7) - 12.5/14.7) \u003c 1e-6)\r\n%%Test 3\r\nassert(abs(calcLambda(16.2, 14.7) - 16.2/14.7) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-27T03:46:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:51:05.000Z","updated_at":"2026-06-09T14:07:15.000Z","published_at":"2026-05-21T09:51:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ = 1 is perfect stoichiometry, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026lt; 1 is rich, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026gt; 1 is lean. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"386\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"686\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpg\",\"contentType\":\"image/jpg\",\"content\":\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":738,"title":"Criss_Cross_010 : Unique elements, Square array, Words in one array","description":"Criss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\r\n\r\nArrange the \"words\" into a solid square such that all words are used.\r\n\r\nGiven an array of words make the original Square or Square Transpose.\r\n\r\nWords are left to Right or Top to Bottom. No fliplr or flipud.\r\n\r\n*Example:*\r\n\r\nM_orig = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nvr = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nvc = [1 2 3; 4 5 6; 7 8 9]\r\n\r\n*Inputs:*\r\n\r\nw = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\r\n\r\nsorted w gives\r\n\r\nw = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\r\n\r\n\r\n*Output:*\r\n\r\nM_out = [1 2 3; 4 5 6; 7 8 9] or\r\n\r\nM_out=[1 4 7; 2 5 8; 3 6 9]\r\n\r\n\r\nMax size : 256\r\n\r\nThis is the second in the Criss Cross puzzles series.\r\n\r\nFollow up puzzles will have non-unique values and quite a few other variations.\r\n","description_html":"\u003cp\u003eCriss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\u003c/p\u003e\u003cp\u003eArrange the \"words\" into a solid square such that all words are used.\u003c/p\u003e\u003cp\u003eGiven an array of words make the original Square or Square Transpose.\u003c/p\u003e\u003cp\u003eWords are left to Right or Top to Bottom. No fliplr or flipud.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_orig = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003evc = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003ew = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\u003c/p\u003e\u003cp\u003esorted w gives\u003c/p\u003e\u003cp\u003ew = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_out = [1 2 3; 4 5 6; 7 8 9] or\u003c/p\u003e\u003cp\u003eM_out=[1 4 7; 2 5 8; 3 6 9]\u003c/p\u003e\u003cp\u003eMax size : 256\u003c/p\u003e\u003cp\u003eThis is the second in the Criss Cross puzzles series.\u003c/p\u003e\u003cp\u003eFollow up puzzles will have non-unique values and quite a few other variations.\u003c/p\u003e","function_template":"function M_out = Criss_Cross(w)\r\n\r\n M_out=zeros(size(w,2));\r\n \r\nend","test_suite":"%%\r\nformat long\r\nformat compact\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=4;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\nM_out=Criss_Cross(w)\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=8;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\nM_out=Criss_Cross(w)\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=16;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed);\r\n\r\nn=16;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));\r\n%%\r\nn=256;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvc=M(:,1:n);\r\n\r\nw=[vr;vc'];\r\nw=sortrows(w);\r\n\r\ntic\r\nM_out=Criss_Cross(w);\r\ntoc\r\n\r\nassert(isequal(M,M_out)||isequal(M',M_out));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-03T20:11:23.000Z","updated_at":"2026-06-10T04:21:55.000Z","published_at":"2012-06-03T21:38:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCriss Cross matrix puzzle - Square matrix, Unique elements, Single Word List\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the \\\"words\\\" into a solid square such that all words are used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of words make the original Square or Square Transpose.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWords are left to Right or Top to Bottom. No fliplr or flipud.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_orig = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evc = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = [1 2 3; 4 5 6; 7 8 9;1 4 7; 2 5 8; 3 6 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esorted w gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = [1 2 3; 1 4 7; 2 5 8; 3 6 9; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out = [1 2 3; 4 5 6; 7 8 9] or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out=[1 4 7; 2 5 8; 3 6 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMax size : 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second in the Criss Cross puzzles series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow up puzzles will have non-unique values and quite a few other variations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":737,"title":"Criss_Cross_000 : Unique elements in a Square array","description":"Criss Cross matrix puzzle - Easy: Square matrix, Unique elements\r\n\r\nArrange the \"words\" into a solid square such that all words are used.\r\n\r\nGiven an array of row words and an array of column words make the unique Square.\r\n\r\nThere is no flipping or rotating in this simplest case.\r\n\r\nexample:\r\n\r\nM_orig =[1 2 3; 4 5 6; 7 8 9]\r\n\r\n*Inputs:*\r\n\r\nvr = [1 2 3; 4 5 6; 7 8 9]\r\n\r\nscramled gives vr =[7 8 9; 1 2 3; 4 5 6]\r\n\r\nvc =[1 2 3; 4 5 6; 7 8 9]\r\n\r\nscrambled gives vc =[3 1 2;6 4 5; 9 7 8]\r\n\r\n*Output:*\r\n\r\nM_out=[1 2 3; 4 5 6; 7 8 9]\r\n\r\nMax size : 4096\r\n\r\n\r\nThis is the first in a series of Criss Cross puzzles.\r\n\r\nFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.","description_html":"\u003cp\u003eCriss Cross matrix puzzle - Easy: Square matrix, Unique elements\u003c/p\u003e\u003cp\u003eArrange the \"words\" into a solid square such that all words are used.\u003c/p\u003e\u003cp\u003eGiven an array of row words and an array of column words make the unique Square.\u003c/p\u003e\u003cp\u003eThere is no flipping or rotating in this simplest case.\u003c/p\u003e\u003cp\u003eexample:\u003c/p\u003e\u003cp\u003eM_orig =[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003escramled gives vr =[7 8 9; 1 2 3; 4 5 6]\u003c/p\u003e\u003cp\u003evc =[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003escrambled gives vc =[3 1 2;6 4 5; 9 7 8]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eM_out=[1 2 3; 4 5 6; 7 8 9]\u003c/p\u003e\u003cp\u003eMax size : 4096\u003c/p\u003e\u003cp\u003eThis is the first in a series of Criss Cross puzzles.\u003c/p\u003e\u003cp\u003eFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.\u003c/p\u003e","function_template":"function M_out = Criss_Cross(vr,vc)\r\n\r\n M_out=vr*0;\r\n \r\nend","test_suite":"%%\r\nformat long\r\nformat compact\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=4;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\nM_out\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=8;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n)\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\nM_out\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=128;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=1024;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));\r\n%%\r\nseed=clock;\r\nseed=1000*seed(6);\r\nrng(seed)\r\n\r\nn=4096;\r\n% Create a Unique element square array\r\nM=randperm(n*n);\r\nM=reshape(M,n,n);\r\n\r\nvr=M(1:n,:);\r\nvr=sortrows(vr);\r\n\r\nvc=M(:,1:n);\r\nvc=sortrows(vc')';\r\n\r\ntic\r\nM_out=Criss_Cross(vr,vc);\r\ntoc\r\n\r\nassert(isequal(M,M_out));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2012-06-03T20:42:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-03T18:05:05.000Z","updated_at":"2026-06-11T08:59:30.000Z","published_at":"2012-06-03T19:37:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCriss Cross matrix puzzle - Easy: Square matrix, Unique elements\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArrange the \\\"words\\\" into a solid square such that all words are used.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of row words and an array of column words make the unique Square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is no flipping or rotating in this simplest case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_orig =[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evr = [1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003escramled gives vr =[7 8 9; 1 2 3; 4 5 6]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evc =[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003escrambled gives vc =[3 1 2;6 4 5; 9 7 8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM_out=[1 2 3; 4 5 6; 7 8 9]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMax size : 4096\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the first in a series of Criss Cross puzzles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow up puzzles will have non-unique values, non-identified row or col, and there are quite a few other variations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61387,"title":"Multiply the Diagonals of Two Vectors","description":"Find the diagonals of vectors a and b and multiply them.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the diagonals of vectors a and b and multiply them.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = diagonalsProduct(a,b)\r\n  s = \r\nend","test_suite":"%%\r\na = [0 1 2; 3 4 5; 6 7 8]\r\nb = [9 10 11; 12 13 14; 15 16 17]\r\ns = diag(a).*diag(b);\r\nassert(isequal(diagonalsProduct(a,b),s))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-05T15:39:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2026-06-05T15:39:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-05T15:37:19.000Z","updated_at":"2026-06-11T21:01:31.000Z","published_at":"2026-06-05T15:37:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the diagonals of vectors a and b and multiply them.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61346,"title":"Find The Area Of Triangle Using Base \u0026 Height","description":"You should find the area of the Triangle using base and height.\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should find the area of the Triangle using base and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangleArea(base, height)\r\n  area = ;\r\nend","test_suite":"%%\r\nbase = 1;\r\nheight = 1;\r\narea = 0.5;\r\nassert(isequal(triangleArea(base, height),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-23T16:51:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:46:19.000Z","updated_at":"2026-06-11T21:04:01.000Z","published_at":"2026-05-23T16:49:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should find the area of the Triangle using base and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61353,"title":"Basic Algebra II","description":"You have the equation X^2 = n you should find the value of X.\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX^2 = n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyou should find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation(n)\r\n  X = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nX = sqrt(n);\r\nassert(isequal(equation(n),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:23:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2026-05-24T13:23:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:20:58.000Z","updated_at":"2026-06-11T21:07:51.000Z","published_at":"2026-05-24T13:23:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX^2 = n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eyou should find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61345,"title":"Get The Opposite Of The Number Without Negative (-) On It","description":"You must get the opposite of the number X without making -X.\r\nHint: You can make it by Subtraction and Multiplication.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou must get the opposite of the number X without making -X.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eHint: You can make it by Subtraction and Multiplication.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = getOpposite(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = -1;\r\nassert(isequal(getOpposite(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-05-23T14:51:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T14:48:38.000Z","updated_at":"2026-06-11T21:13:11.000Z","published_at":"2026-05-23T14:48:38.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou must get the opposite of the number X without making -X.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint: You can make it by Subtraction and Multiplication.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61358,"title":"Basic Physics IV","description":"Calculate the Mechanical Energy (ME).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the Mechanical Energy (ME).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ME = ME(PE,KE)\r\n  ME = ;\r\nend","test_suite":"%%\r\nPE = 1;\r\nKE = 1;\r\nME = PE+KE;\r\nassert(isequal(ME(PE,KE),ME))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T14:58:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-26T14:58:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T14:56:53.000Z","updated_at":"2026-06-11T21:13:44.000Z","published_at":"2026-05-26T14:56:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the Mechanical Energy (ME).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61347,"title":"Find The Area Of The Circle","description":"Find the area of the Circle using PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the area of the Circle using PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = circleArea(r)\r\n  area = ;\r\nend","test_suite":"%%\r\nr = 1;\r\narea = pi * r^2;\r\nassert(isequal(circleArea(r),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:33:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-23T17:01:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:57:42.000Z","updated_at":"2026-06-11T21:15:54.000Z","published_at":"2026-05-23T16:59:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the area of the Circle using PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61351,"title":"Get The Square Root Of Number Power (^) Three","description":"Get the Square Root of number Power (^) Three.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Square Root of number Power (^) Three.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function num = calc(n)\r\n  num = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nnum = sqrt(n^3);\r\nassert(isequal(calc(n),num))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T12:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2026-05-24T12:06:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:57:15.000Z","updated_at":"2026-06-11T21:42:04.000Z","published_at":"2026-05-24T11:59:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Square Root of number Power (^) Three.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61385,"title":"Watermelon [MATLAB Cody Edition]","description":" YOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \r\nhttps://codeforces.com/problemset/problem/4/A\r\nNOW INSTEAD OF DISPLAYING \"YES\" OR \"NO\" YOU SHOULD RETURN.\r\nEX:\r\ncorrect =  \"YES\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201.009px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 100.497px; transform-origin: 400.994px 100.504px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ehttps://codeforces.com/problemset/problem/4/A\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOW INSTEAD OF DISPLAYING \"YES\" OR \"NO\" YOU SHOULD RETURN.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eEX:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003ecorrect =  \"YES\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function correct = watermelon(w)\r\n  \r\nend","test_suite":"%%\r\nw = 1;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 2;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 3;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 4;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 5;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 6;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 7;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 8;\r\ncorrect = \"YES\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 9;\r\ncorrect = \"NO\";\r\nassert(isequal(watermelon(w),correct))\r\n%%\r\nw = 10;\r\ncorrect = \"YES\"\r\nassert(isequal(watermelon(w),correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-02T13:18:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-06-02T13:18:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-02T13:00:13.000Z","updated_at":"2026-06-11T21:48:26.000Z","published_at":"2026-06-02T13:11:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYOU CAN READ THE REAL CHALLENGE FROM THIS URL AND APPLY IT \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://codeforces.com/problemset/problem/4/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOW INSTEAD OF DISPLAYING \\\"YES\\\" OR \\\"NO\\\" YOU SHOULD RETURN.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEX:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecorrect =  \\\"YES\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61388,"title":"Draw '\\'","description":"Can you draw the sign '\\' by zeros and ones?\r\nNOTICE: Be x-by-x matrix.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 50.9722px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.49px 25.4861px; transform-origin: 468.498px 25.4861px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.497px 10.4861px; text-align: left; transform-origin: 444.505px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCan you draw the sign '\\' by zeros and ones?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.497px 10.4861px; text-align: left; transform-origin: 444.505px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eNOTICE: Be x-by-x matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = drawSign(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\ny = eye(x);\r\nassert(isequal(drawSign(x),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-08T17:24:05.000Z","updated_at":"2026-06-11T21:49:11.000Z","published_at":"2026-06-08T17:24:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCan you draw the sign '\\\\' by zeros and ones?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTICE: Be x-by-x matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61354,"title":"Rhombus","description":"Get the area of the Rhombus using it's Diagonals.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the area of the Rhombus using it's Diagonals.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = area(d1,d2)\r\n  area = ;\r\nend","test_suite":"%%\r\nd1 = 1;\r\nd2 = 1;\r\narea = 0.5*(d1*d2);\r\nassert(isequal(area(d1,d2),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:30:18.000Z","updated_at":"2026-06-11T21:34:59.000Z","published_at":"2026-05-24T13:30:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the area of the Rhombus using it's Diagonals.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61386,"title":"Prime or No","description":"If the number is prime, make theCase = \"YES\", else, make it \"NO\".","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf the number is prime, make theCase = \"YES\", else, make it \"NO\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theCase = primeOrNo(n)\r\n  \r\nend","test_suite":"%%\r\nn = randi(100);\r\nif isprime(n)\r\n    theCase = \"YES\"\r\nelse\r\n    theCase = \"NO\"\r\nend\r\nassert(isequal(primeOrNo(n),theCase))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-03T15:27:06.000Z","updated_at":"2026-06-11T21:26:49.000Z","published_at":"2026-06-03T15:27:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf the number is prime, make theCase = \\\"YES\\\", else, make it \\\"NO\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61349,"title":"Trapezium","description":"Calculate the area of the Trapezium using it's bases and height.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the area of the Trapezium using it's bases and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function trapeziumArea = trapeziumArea(base1, base2, height)\r\n  base3 = ;\r\n  trapeziumArea = ;\r\nend","test_suite":"%%\r\nbase1 = 1;\r\nbase2 = 1;\r\nheight = 1;\r\ntrapeziumArea = 0.5*(base1+base2)*height;\r\nassert(isequal(trapeziumArea(base1, base2, height),trapeziumArea))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T18:08:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-23T18:08:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T17:59:40.000Z","updated_at":"2026-06-11T21:30:15.000Z","published_at":"2026-05-23T18:03:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the area of the Trapezium using it's bases and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61350,"title":"Circle Perimeter","description":"Get the perimeter of the Circle by PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the perimeter of the Circle by PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = circleP(r)\r\n  p = ;\r\nend","test_suite":"%%\r\nr = 1;\r\np = 2*pi*r;\r\nassert(isequal(circleP(r),p))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T11:52:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2026-05-24T11:52:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:50:23.000Z","updated_at":"2026-06-11T21:28:08.000Z","published_at":"2026-05-24T11:52:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the perimeter of the Circle by PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61355,"title":"Basic Algebra III","description":"Get the Cube Root of the number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Cube Root of the number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = cbRt(n)\r\n  ans = ;\r\nend","test_suite":"%%\r\nn = 8;\r\nans = nthroot(n,3);\r\nassert(isequal(cbRt(n),ans))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T12:25:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2026-05-26T12:25:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T12:24:06.000Z","updated_at":"2026-06-11T21:38:22.000Z","published_at":"2026-05-26T12:24:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Cube Root of the number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61352,"title":"Basic Algebra I","description":"You should solve the problem 3X - 2 = 7 by finding the value of X.\r\nYou must use this array/vector [2 3 7].\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should solve the problem \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e3X - 2 = 7 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eby finding the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou must use this array/vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e[2 3 7].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation()\r\n  nums = [2 3 7];\r\n  X = ;\r\nend","test_suite":"%%\r\nnums = [2 3 7]\r\nX = (nums(3)+nums(1))/nums(2);\r\nassert(isequal(equation(),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:26:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-24T13:13:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:07:29.000Z","updated_at":"2026-06-12T07:25:30.000Z","published_at":"2026-05-24T13:11:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should solve the problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3X - 2 = 7 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eby finding the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must use this array/vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[2 3 7].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61362,"title":"Calculate the h-index (revisited)","description":"H-index is a powerful tool for quantifying the scientific contribution of a researcher. The \r\nH-index is defined as follows (from source - wikipedia):\r\n\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\r\nIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\r\nExample:\r\nInput = [4 4 4 4]; Output = 4\r\nCalculate the h-index score \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 157.5px; transform-origin: 243.5px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is defined as follows (from source - wikipedia):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 31.5px; text-align: left; transform-origin: 219.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput = [4 4 4 4]; Output = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the h-index score \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [5 2 10 11 2 7 9 10 7];\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 4*ones(1,4);\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = zeros(1,1000);\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [3 2 0 0 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-27T22:40:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2026-05-27T22:40:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-27T18:21:09.000Z","updated_at":"2026-06-12T13:23:54.000Z","published_at":"2026-05-27T18:21:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is defined as follows (from source - wikipedia):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput = [4 4 4 4]; Output = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the h-index score \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61384,"title":"varargin","description":"Write a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\r\nExample:\r\nf(a,b) = a+b,    f(1,...,n) = 1+...+n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401.5px 55.5px; transform-origin: 401.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summ(va )\r\ny = ;\r\nend","test_suite":"%%\r\ny_correct = 6;\r\nassert(isequal(summ(1,2,3),y_correct))\r\n%%\r\ny_correct = sum(1:200:10^10);\r\nassert(isequal(summ(1:200:10^10),y_correct))\r\n%%\r\ny_correct = sum(-5:3.2:200);\r\nassert(isequal(summ(-5:3.2:200),y_correct))\r\n%%\r\nfor k = 1:100\r\n    x = num2cell(randi(100,1,randi(10)));\r\n\r\n    erwartet = sum([x{:}]);\r\n    erhalten = summ(x{:});\r\n\r\n    assert(isequal(erhalten, erwartet))\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5124132,"edited_by":5124132,"edited_at":"2026-06-01T17:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2026-06-01T17:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-01T16:52:16.000Z","updated_at":"2026-06-12T12:59:31.000Z","published_at":"2026-06-01T17:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":8,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2026-06-12T23:22:27.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61375,"title":"If-Elseif-Else","description":"If a more than zero, b = true, if a = zero , b = zero, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a more than zero, b = true, if a = zero , b = zero, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = 0;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-30T17:31:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-30T17:23:40.000Z","updated_at":"2026-06-13T11:58:13.000Z","published_at":"2026-05-30T17:23:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a more than zero, b = true, if a = zero , b = zero, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61380,"title":"NOT","description":"If a not equal to zero, b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a not equal to zero, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = false;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:12:13.000Z","updated_at":"2026-06-13T12:09:31.000Z","published_at":"2026-05-31T07:12:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a not equal to zero, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61378,"title":"AND","description":"If a greater than 0 and n less than 10, b = true, else, b = false.\r\n(Checking a should be in one line by AND special sign in MATLAB)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than 0 and n less than 10, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(Checking a should be in one line by AND special sign in MATLAB)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a,n)\r\n  \r\nend","test_suite":"%%\r\na = 9;\r\nn = 4;\r\nb = true;\r\nassert(isequal(IF(a,n),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-31T06:59:50.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2026-05-31T06:54:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T06:50:30.000Z","updated_at":"2026-06-13T12:05:15.000Z","published_at":"2026-05-31T06:50:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than 0 and n less than 10, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(Checking a should be in one line by AND special sign in MATLAB)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61381,"title":"Switch-Case-Otherwise","description":"You should make random numbers to 10, by 3 rows and 3 columns.\r\nCases from 1 to 3, b = true.\r\nOtherwise, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 40.5px; transform-origin: 401px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCases from 1 to 3, b = true.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eOtherwise, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = CASE(a)\r\n  \r\nend","test_suite":"%%\r\na = 6;\r\nb = false;\r\nassert(isequal(CASE(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:39:29.000Z","updated_at":"2026-06-13T12:13:00.000Z","published_at":"2026-05-31T07:39:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should make random numbers to 10, by 3 rows and 3 columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCases from 1 to 3, b = true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOtherwise, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61377,"title":"Nested If(s)","description":"If a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a)\r\n  \r\nend","test_suite":"%%\r\na = 2;\r\nb = true;\r\nassert(isequal(IF(a),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T06:43:15.000Z","updated_at":"2026-06-13T12:03:11.000Z","published_at":"2026-05-31T06:43:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than zero, then check, if a = greater that 1 and less than 10, then b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61379,"title":"OR","description":"If a greater than zero or c less than 10, b = true, else, b = false.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eIf a greater than zero or c less than 10, b = true, else, b = false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function b = IF(a,c)\r\n  \r\nend","test_suite":"%%\r\na = 1;\r\nc = 11;\r\nb = true;\r\nassert(isequal(IF(a,c),b))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-31T07:02:58.000Z","updated_at":"2026-06-13T12:07:30.000Z","published_at":"2026-05-31T07:02:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf a greater than zero or c less than 10, b = true, else, b = false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61406,"title":"MATLAB 101: Scalar-Vector Multiplication","description":"Write a MATLAB function that takes a numeric array (vector or matrix) v and a scalar multiplier s. The function should return a new array where every element in v is multiplied by s.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a scalar multiplier \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should return a new array where every element in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is multiplied by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = multiply_vector(v, s)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard positive vector and scalar\r\nassert(isequal(multiply_vector([1, 2, 3], 2), [2, 4, 6]));\r\n\r\n%% Test 2: Negative scalar\r\nassert(isequal(multiply_vector([5, 10], -1), [-5, -10]));\r\n\r\n%% Test 3: Zero scalar\r\nassert(isequal(multiply_vector([7, 8, 9], 0), [0, 0, 0]));\r\n\r\n%% Test 4: Empty vector\r\nassert(isempty(multiply_vector([], 5)));\r\n\r\n%% Test 5: Single element vector\r\nassert(isequal(multiply_vector(42, 2), 84));\r\n\r\n%% Test 6: Decimal/Fractional scalar\r\nassert(isequal(multiply_vector([10, 20], 0.5), [5, 10]));\r\n\r\n%% Test 7: Negative elements in vector\r\nassert(isequal(multiply_vector([-2, -4, 6], 3), [-6, -12, 18]));\r\n\r\n%% Test 8: Matrix input\r\nassert(isequal(multiply_vector([1, 2; 3, 4], 10), [10, 20; 30, 40]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:38:47.000Z","updated_at":"2026-06-14T22:40:00.000Z","published_at":"2026-06-14T18:38:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a scalar multiplier \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should return a new array where every element in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is multiplied by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61405,"title":"MATLAB 101: Tribonacci Sequence","description":"Each number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_tribonacci(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_tribonacci(6), [0, 0, 1, 1, 2, 4]));\r\n%%\r\nassert(isequal(get_tribonacci(-6), []));\r\n%%\r\nassert(isequal(get_tribonacci(0), []));\r\n%%\r\nassert(isequal(get_tribonacci(16), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504,927,1705]));\r\n%%\r\nassert(isequal(get_tribonacci(14), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504]));\r\n%%\r\nassert(isequal(get_tribonacci(10), [0, 0, 1, 1, 2, 4,7,13,24,44]));\r\n%%\r\nassert(isequal(get_tribonacci(15), [0, 0, 1, 1, 2, 4,7,13,24,44,81,149,274,504,927]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:12:19.000Z","updated_at":"2026-06-14T22:39:59.000Z","published_at":"2026-06-14T18:12:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach number in the Tribonacci series is the sum of the three preceding ones. Sequence: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, ... Write a function that returns the first n numbers of the Tribonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61410,"title":"MATLAB 101: Rectangle Properties","description":"Write a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [area, perimeter] = rectangle_properties(L, W)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard scalar inputs\r\n[a, p] = rectangle_properties(5, 10);\r\nassert(a == 50 \u0026\u0026 p == 30);\r\n\r\n%% Test 2: Identical values (Square)\r\n[a, p] = rectangle_properties(4, 4);\r\nassert(a == 16 \u0026\u0026 p == 16);\r\n\r\n%% Test 3: Zero width\r\n[a, p] = rectangle_properties(10, 0);\r\nassert(a == 0 \u0026\u0026 p == 20);\r\n\r\n%% Test 4: Decimal values\r\n[a, p] = rectangle_properties(2.5, 4);\r\nassert(a == 10 \u0026\u0026 p == 13);\r\n\r\n%% Test 5: Row vector inputs (Multiple rectangles)\r\n[a, p] = rectangle_properties([2, 3], [4, 5]);\r\nassert(isequal(a, [8, 15]) \u0026\u0026 isequal(p, [12, 16]));\r\n\r\n%% Test 6: Column vector inputs\r\n[a, p] = rectangle_properties([10; 20], [10; 20]);\r\nassert(isequal(a, [100; 400]) \u0026\u0026 isequal(p, [40; 80]));\r\n\r\n%% Test 7: Matrix inputs\r\nL_mat = [1, 2; 3, 4];\r\nW_mat = [2, 2; 2, 2];\r\n[a, p] = rectangle_properties(L_mat, W_mat);\r\nassert(isequal(a, [2, 4; 6, 8]) \u0026\u0026 isequal(p, [6, 8; 10, 12]));\r\n\r\n%% Test 8: Large numbers\r\n[a, p] = rectangle_properties(1000, 2000);\r\nassert(a == 2000000 \u0026\u0026 p == 6000);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T19:08:37.000Z","updated_at":"2026-06-14T22:56:25.000Z","published_at":"2026-06-14T19:08:37.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts the length (L) and width (W) of a rectangle and returns two outputs: its area and its perimeter. The function must be able to handle scalar numbers as well as arrays (calculating the properties for multiple rectangles at once).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61411,"title":"MATLAB 101: Hypotenuse Calculator","description":"Write a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function hyp = calculate_hypotenuse(base, height)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Pythagorean triple (3, 4, 5)\r\nassert(calculate_hypotenuse(3, 4) == 5);\r\n\r\n%% Test 2: Pythagorean triple (5, 12, 13)\r\nassert(calculate_hypotenuse(5, 12) == 13);\r\n\r\n%% Test 3: Zero base\r\nassert(calculate_hypotenuse(0, 10) == 10);\r\n\r\n%% Test 4: Zero height\r\nassert(calculate_hypotenuse(7, 0) == 7);\r\n\r\n%% Test 5: Vector inputs\r\nassert(isequal(calculate_hypotenuse([3, 5], [4, 12]), [5, 13]));\r\n\r\n%% Test 6: Matrix inputs\r\nb_mat = [3, 0; 0, 5];\r\nh_mat = [4, 10; 7, 12];\r\nexpected = [5, 10; 7, 13];\r\nassert(isequal(calculate_hypotenuse(b_mat, h_mat), expected));\r\n\r\n%% Test 7: Decimal values (floating point comparison)\r\nassert(abs(calculate_hypotenuse(1.5, 2.0) - 2.5) \u003c 1e-10);\r\n\r\n%% Test 8: Same base and height (Isosceles right triangle)\r\nassert(abs(calculate_hypotenuse(100, 100) - 141.421356237) \u003c 1e-5);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T19:11:20.000Z","updated_at":"2026-06-14T22:56:27.000Z","published_at":"2026-06-14T19:11:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts the base and height of a right-angled triangle (or arrays of bases and heights) and returns the length of the hypotenuse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61408,"title":"MATLAB 101: Replace Negatives with Zero","description":"Write a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function clean_arr = replace_negatives(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Mix of positive and negative numbers\r\nassert(isequal(replace_negatives([1, -2, 3, -4]), [1, 0, 3, 0]));\r\n\r\n%% Test 2: All positive numbers\r\nassert(isequal(replace_negatives([5, 10, 15]), [5, 10, 15]));\r\n\r\n%% Test 3: All negative numbers\r\nassert(isequal(replace_negatives([-1, -2, -3]), [0, 0, 0]));\r\n\r\n%% Test 4: Array containing zeros\r\nassert(isequal(replace_negatives([0, -5, 0, 5]), [0, 0, 0, 5]));\r\n\r\n%% Test 5: Empty array\r\nassert(isempty(replace_negatives([])));\r\n\r\n%% Test 6: Single negative element\r\nassert(isequal(replace_negatives(-42), 0));\r\n\r\n%% Test 7: Single positive element\r\nassert(isequal(replace_negatives(42), 42));\r\n\r\n%% Test 8: Matrix input\r\ninput_matrix = [1, -2; -3, 4];\r\nexpected_matrix = [1, 0; 0, 4];\r\nassert(isequal(replace_negatives(input_matrix), expected_matrix));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":2294940,"edited_at":"2026-06-14T18:48:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:44:40.000Z","updated_at":"2026-06-14T22:56:22.000Z","published_at":"2026-06-14T18:44:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a numeric array (vector or matrix) of numbers and replaces all negative numbers with zero. Positive numbers and zeros should remain completely unchanged.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61409,"title":"MATLAB 101: Reverse a Vector","description":"Write a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function rev_arr = reverse_vector(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard row vector\r\nassert(isequal(reverse_vector([1, 2, 3, 4]), [4, 3, 2, 1]));\r\n\r\n%% Test 2: Standard column vector\r\nassert(isequal(reverse_vector([10; 20; 30]), [30; 20; 10]));\r\n\r\n%% Test 3: Vector with negative numbers\r\nassert(isequal(reverse_vector([-5, 0, 5]), [5, 0, -5]));\r\n\r\n%% Test 4: Single element vector\r\nassert(isequal(reverse_vector([42]), [42]));\r\n\r\n%% Test 5: Empty vector\r\nassert(isempty(reverse_vector([])));\r\n\r\n%% Test 6: Vector with duplicate elements\r\nassert(isequal(reverse_vector([7, 7, 8, 7]), [7, 8, 7, 7]));\r\n\r\n%% Test 7: Floating point numbers\r\nassert(isequal(reverse_vector([1.5, 2.5, 3.5]), [3.5, 2.5, 1.5]));\r\n\r\n%% Test 8: Two-element vector\r\nassert(isequal(reverse_vector([99, 100]), [100, 99]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:52:14.000Z","updated_at":"2026-06-14T22:56:24.000Z","published_at":"2026-06-14T18:52:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that takes a 1D vector (either a row or a column vector) and returns the vector with its elements in exact reverse order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61407,"title":"MATLAB 101: Count the Evens","description":"Write a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function count = count_even_numbers(arr)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Mix of even and odd numbers\r\nassert(count_even_numbers([1, 2, 3, 4, 5, 6]) == 3);\r\n\r\n%% Test 2: All even numbers\r\nassert(count_even_numbers([2, 8, 14, 20]) == 4);\r\n\r\n%% Test 3: All odd numbers\r\nassert(count_even_numbers([1, 3, 5, 7, 9]) == 0);\r\n\r\n%% Test 4: Empty array\r\nassert(count_even_numbers([]) == 0);\r\n\r\n%% Test 5: Array containing zero\r\nassert(count_even_numbers([0, 1, 3]) == 1);\r\n\r\n%% Test 6: Array with negative even numbers\r\nassert(count_even_numbers([-2, -4, -5, 7]) == 2);\r\n\r\n%% Test 7: Single even number\r\nassert(count_even_numbers(42) == 1);\r\n\r\n%% Test 8: Matrix input (should count all evens across rows/cols)\r\nassert(count_even_numbers([1, 2; 3, 4]) == 2);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T18:41:02.000Z","updated_at":"2026-06-14T22:40:02.000Z","published_at":"2026-06-14T18:41:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts an array of integers and returns the total count of even numbers present in the array. Note: 0 is considered an even number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61401,"title":"MATLAB 101: Factorial Finder","description":"The factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\r\nWrite a MATLAB function that calculates the factorial of a given number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 36px; transform-origin: 468.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that calculates the factorial of a given number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = find_factorial(n)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: Standard Positive Integer\r\nassert(find_factorial(5) == 120);\r\n\r\n%% Test 2: Base Case (0!)\r\nassert(find_factorial(0) == 1);\r\n\r\n%% Test 3: Smallest Positive Factorial (1!)\r\nassert(find_factorial(1) == 1);\r\n\r\n%% Test 4: Larger Integer\r\nassert(find_factorial(7) == 5040);\r\n\r\n%% Test 5: Input Validation (Ensure it handles non-negative)\r\n% If n \u003c 0, this test assumes function returns NaN\r\nassert(isnan(find_factorial(-1)));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:22:54.000Z","updated_at":"2026-06-14T21:10:18.000Z","published_at":"2026-06-14T17:22:54.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe factorial of a non-negative integer n (denoted as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 * 4 * 3 * 2 * 1 = 120 By definition, 0! = 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that calculates the factorial of a given number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61402,"title":"MATLAB 101: Fibonacci Sequence","description":"The Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \r\nWrite a function that returns the first n numbers of the Fibonacci sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 36px; transform-origin: 468.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the first n numbers of the Fibonacci sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_fibonacci(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_fibonacci(5), [0, 1, 1, 2, 3]));\r\n%%\r\nassert(isequal(get_fibonacci(1), [0]));\r\n%%\r\nassert(isequal(get_fibonacci(15), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34,55, 89,144, 233,377]));\r\n%%\r\nassert(isequal(get_fibonacci(10), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]));\r\n%%\r\nassert(isequal(get_fibonacci(7), [0, 1, 1, 2, 3, 5, 8]));\r\n%%\r\nassert(isequal(get_fibonacci(13), [0, 1, 1, 2, 3, 5, 8, 13, 21, 34,55, 89,144]));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:35:57.000Z","updated_at":"2026-06-14T21:11:20.000Z","published_at":"2026-06-14T17:35:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the first n numbers of the Fibonacci sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61403,"title":"MATLAB 101: Lucas Sequence","description":"The Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \r\nWrite a function that returns the first n numbers of the Lucas sequence.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 25.5px; transform-origin: 468.5px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the first n numbers of the Lucas sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = get_lucas(n)\r\n    % Write your code here\r\nend","test_suite":"%%\r\nassert(isequal(get_lucas(5), [2, 1, 3, 4, 7]));\r\n%%\r\nassert(isequal(get_lucas(1), [2]));\r\n%%\r\nassert(isequal(get_lucas(15), [2, 1, 3, 4, 7,11,18,29,47,76,123,199,322,521,843]));\r\n%%\r\nassert(isequal(get_lucas(12), [2, 1, 3, 4, 7,11,18,29,47,76,123,199]));\r\n%%\r\nassert(isequal(get_lucas(-15), []));","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-14T17:42:51.000Z","updated_at":"2026-06-14T21:12:39.000Z","published_at":"2026-06-14T17:42:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Lucas sequence follows the same additive rule as Fibonacci, but starts with 2 and 1. Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, ... \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the first n numbers of the Lucas sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[{"value":"Cody Challenge","count":94,"selected":false},{"value":"High School Challenge","count":57,"selected":false},{"value":"Number theory","count":45,"selected":false},{"value":"Algorithm I","count":37,"selected":false},{"value":"Operations","count":32,"selected":false},{"value":"Cody5:Easy","count":31,"selected":false},{"value":"MATLAB 101","count":30,"selected":false},{"value":"Strings I","count":30,"selected":false},{"value":"Probability \u0026 Stats","count":29,"selected":false},{"value":"Indexing I","count":27,"selected":false},{"value":"Advent of Code","count":25,"selected":false},{"value":"Introduction to MATLAB","count":24,"selected":false},{"value":"Polynomials","count":24,"selected":false},{"value":"Cody5:Hard","count":23,"selected":false},{"value":"Indexing III","count":23,"selected":false},{"value":"Strings III","count":23,"selected":false},{"value":"Combinatorics III","count":22,"selected":false},{"value":"Indexing II","count":22,"selected":false},{"value":"Advanced Cryptography Algorithms and Mathematics","count":21,"selected":false},{"value":"Computer Games II","count":21,"selected":false},{"value":"Divisible by x","count":21,"selected":false},{"value":"Strings II","count":21,"selected":false},{"value":"Tough Stuff","count":21,"selected":false},{"value":"Board Games I","count":20,"selected":false},{"value":"Computational Geometry I","count":20,"selected":false},{"value":"Computational Geometry II","count":20,"selected":false},{"value":"Computational Geometry IV","count":20,"selected":false},{"value":"M3 Challenge Problem Group","count":20,"selected":false},{"value":"Magic Numbers IV","count":20,"selected":false},{"value":"Matrix Manipulation III","count":20,"selected":false},{"value":"Prime Numbers I","count":20,"selected":false},{"value":"The Prime Directive","count":20,"selected":false},{"value":"Chess","count":19,"selected":false},{"value":"Computational Geometry III","count":19,"selected":false},{"value":"Groundwater","count":19,"selected":false},{"value":"Magic Numbers","count":19,"selected":false},{"value":"Matrix Manipulation II","count":19,"selected":false},{"value":"Prime Numbers II","count":19,"selected":false},{"value":"Prime Numbers III","count":19,"selected":false},{"value":"Basics - 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