{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":2008,"title":"Number Persistence","description":"A number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until \r\na one-digit number is obtained. \r\n\r\nFor example, 66 has a persistence of \r\nthree because it requires three steps to reduce it to one digit: 66-36-18-8.\r\n","description_html":"\u003cp\u003eA number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until \r\na one-digit number is obtained.\u003c/p\u003e\u003cp\u003eFor example, 66 has a persistence of \r\nthree because it requires three steps to reduce it to one digit: 66-36-18-8.\u003c/p\u003e","function_template":"function y = persistence(x)\r\n\r\n","test_suite":"%%\r\nx = 77;\r\ny_correct =4\r\nassert(isequal(persistence(x),y_correct ))\r\n%%\r\nx = 976;\r\ny_correct =5\r\nassert(isequal(persistence(x),y_correct ))\r\n\r\n%%\r\nx =88869;\r\ny_correct =7\r\nassert(isequal(persistence(x),y_correct ))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-19T15:32:11.000Z","updated_at":"2026-03-05T12:00:35.000Z","published_at":"2013-11-19T15:32:11.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eA number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained.\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\u003eFor example, 66 has a persistence of three because it requires three steps to reduce it to one digit: 66-36-18-8.\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":2040,"title":"Additive persistence","description":"Inspired by Problem 2008 created by Ziko.\r\n\r\nIn mathematics, the persistence of a number is the *number of times* one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (Wikipedia).\r\n\r\nProblem 2008 is an example of multiplicative persistence.\r\nCan you code an additive persistence ?\r\n\r\n2718-\u003e2+7+1+8=18-\u003e1+8=9. So the persistence of 2718 is 2.\r\n\r\nYou can use the tips : num2str(666)-'0'=[6 6 6].\r\n\r\n","description_html":"\u003cp\u003eInspired by Problem 2008 created by Ziko.\u003c/p\u003e\u003cp\u003eIn mathematics, the persistence of a number is the \u003cb\u003enumber of times\u003c/b\u003e one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (Wikipedia).\u003c/p\u003e\u003cp\u003eProblem 2008 is an example of multiplicative persistence.\r\nCan you code an additive persistence ?\u003c/p\u003e\u003cp\u003e2718-\u0026gt;2+7+1+8=18-\u0026gt;1+8=9. So the persistence of 2718 is 2.\u003c/p\u003e\u003cp\u003eYou can use the tips : num2str(666)-'0'=[6 6 6].\u003c/p\u003e","function_template":"function y = add_persistence(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=18;\r\ny_correct = 1;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=2718;\r\ny_correct = 2;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=199;\r\ny_correct = 3;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=100;\r\ny_correct = 1;\r\nassert(isequal(add_persistence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":38,"created_at":"2013-12-11T08:33:55.000Z","updated_at":"2026-05-20T03:55:54.000Z","published_at":"2013-12-11T08:33:55.000Z","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\u003eInspired by Problem 2008 created by Ziko.\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\u003eIn mathematics, the persistence of a number is the\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\u003enumber of times\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2008 is an example of multiplicative persistence. Can you code an additive persistence ?\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\u003e2718-\u0026gt;2+7+1+8=18-\u0026gt;1+8=9. So the persistence of 2718 is 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:t\u003eYou can use the tips : num2str(666)-'0'=[6 6 6].\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\"}]}"}],"problem_search":{"problems":[{"id":2008,"title":"Number Persistence","description":"A number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until \r\na one-digit number is obtained. \r\n\r\nFor example, 66 has a persistence of \r\nthree because it requires three steps to reduce it to one digit: 66-36-18-8.\r\n","description_html":"\u003cp\u003eA number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until \r\na one-digit number is obtained.\u003c/p\u003e\u003cp\u003eFor example, 66 has a persistence of \r\nthree because it requires three steps to reduce it to one digit: 66-36-18-8.\u003c/p\u003e","function_template":"function y = persistence(x)\r\n\r\n","test_suite":"%%\r\nx = 77;\r\ny_correct =4\r\nassert(isequal(persistence(x),y_correct ))\r\n%%\r\nx = 976;\r\ny_correct =5\r\nassert(isequal(persistence(x),y_correct ))\r\n\r\n%%\r\nx =88869;\r\ny_correct =7\r\nassert(isequal(persistence(x),y_correct ))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-19T15:32:11.000Z","updated_at":"2026-03-05T12:00:35.000Z","published_at":"2013-11-19T15:32:11.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eA number's persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained.\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\u003eFor example, 66 has a persistence of three because it requires three steps to reduce it to one digit: 66-36-18-8.\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":2040,"title":"Additive persistence","description":"Inspired by Problem 2008 created by Ziko.\r\n\r\nIn mathematics, the persistence of a number is the *number of times* one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (Wikipedia).\r\n\r\nProblem 2008 is an example of multiplicative persistence.\r\nCan you code an additive persistence ?\r\n\r\n2718-\u003e2+7+1+8=18-\u003e1+8=9. So the persistence of 2718 is 2.\r\n\r\nYou can use the tips : num2str(666)-'0'=[6 6 6].\r\n\r\n","description_html":"\u003cp\u003eInspired by Problem 2008 created by Ziko.\u003c/p\u003e\u003cp\u003eIn mathematics, the persistence of a number is the \u003cb\u003enumber of times\u003c/b\u003e one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (Wikipedia).\u003c/p\u003e\u003cp\u003eProblem 2008 is an example of multiplicative persistence.\r\nCan you code an additive persistence ?\u003c/p\u003e\u003cp\u003e2718-\u0026gt;2+7+1+8=18-\u0026gt;1+8=9. So the persistence of 2718 is 2.\u003c/p\u003e\u003cp\u003eYou can use the tips : num2str(666)-'0'=[6 6 6].\u003c/p\u003e","function_template":"function y = add_persistence(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=18;\r\ny_correct = 1;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=2718;\r\ny_correct = 2;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=199;\r\ny_correct = 3;\r\nassert(isequal(add_persistence(x),y_correct))\r\n%%\r\nx=100;\r\ny_correct = 1;\r\nassert(isequal(add_persistence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":186,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":38,"created_at":"2013-12-11T08:33:55.000Z","updated_at":"2026-05-20T03:55:54.000Z","published_at":"2013-12-11T08:33:55.000Z","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\u003eInspired by Problem 2008 created by Ziko.\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\u003eIn mathematics, the persistence of a number is the\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\u003enumber of times\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e one must apply a given operation to an integer before reaching a fixed point; where further application does not change the number any more (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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2008 is an example of multiplicative persistence. Can you code an additive persistence ?\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\u003e2718-\u0026gt;2+7+1+8=18-\u0026gt;1+8=9. So the persistence of 2718 is 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:t\u003eYou can use the tips : num2str(666)-'0'=[6 6 6].\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\"}]}"}],"errors":[],"facets":[[{"value":"Number Manipulation I","count":1,"selected":false}],[{"value":"easy","count":1,"selected":false},{"value":"medium","count":1,"selected":false}]],"term":"tag:\"persistence\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}