Problem 44309. Pi Digit Probability

Created by Mehmet OZC

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Assume that the next digit of pi constant is determined by the historical digit distribution. What is the probability of next digit (N) being (n).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example if we consider the first 100 digits of pi, we will see that the digit '3' is occured 12 times. So the probability of the being '3' the 101th digit will be 12/100 = 0.12.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Round the results to four decimals.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

3560 Solutions
440 Solvers

Last Solution submitted on Oct 01, 2022

Last 200 Solutions

Problem Comments

18 Comments

18 Comments

Show 15 older comments

Alfonso Nieto-Castanon on 16 Oct 2017

testsuite not working, please change "assert(isequal(pidigit(N,n)-y_correct<0.0001))" to "assert(abs(pidigit(N,n)-y_correct)<0.0001)"

Mehmet OZC on 16 Oct 2017

Thanks, I have made the change

Peng Liu on 16 Oct 2017

Still missing a ")" in your assert statement

Mehmet OZC on 16 Oct 2017

Thanks, I have add ')'

David Verrelli on 19 Oct 2017

In Solution 1301292 I am finding the same thing as Yona reported (see comment below). "Digits" should mean all digits, including the leading 3. That is the definition required to pass Test 1. But to pass Test 2 and Test 5, it is required to ignore the leading 3. Or else some people have misread the problem statement, which says that the number of digits to inspect is not N, but rather N–1. (Because we're trying to predict the N'th digit.) I count only 15 occurrences of "6" in the first 200 digits, when the leading "3" is included (as it should be).

Angelo Gelmini on 20 Oct 2017

I can not find a solution without using the symbolic math toolbox ;(

Mehmet OZC on 21 Oct 2017

David, Maurício, Yona and mhartma3 check your solutions. They should pass all the test suit now.

David Verrelli on 23 Oct 2017

Thanks, Mehmet OZC. I suppose that numerically my Solution 1301292 should now pass, but it seems it is failing the new assertion that uses regex to parse the M-file. I guess it is looking for hard-coded solutions that might characteristically contain any of the numbers [101,201,202,203,1001], which are important parameters in your Test Suite. However, inspection of pi reveals that the sequence "101" appears at the 852nd decimal place, "201" appears at the 244th decimal place, etc. So the new assertion might be creating unexpected side-effects.

Alfonso Nieto-Castanon on 23 Oct 2017

@David it is somewhat funny but that solution is not failing because of those partial matches in the pi sequence (the regexp command used will disregard partial matches) but rather because of the explicit 1001 value in your commented line (reading "First 1001 digits of pi")

David Verrelli on 27 Oct 2017

Ah, thanks for the clarification, Alfonso. So it was an unintended side-effect, but not the one I had supposed. That also explains why it didn't disrupt most other solutions.

Adam on 12 Aug 2019

It is a shame vpa does not work, this could lead to some more interesting challenges

Hau Van on 11 Oct 2019

......

Jonas on 20 Jun 2020

You have to provide the number pi as a string as input. This is horrible, however, this is needed, because the symbolic toolbox is not working. Therefore, here is the number:
initPI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989';

Igor Kheyfets on 5 Oct 2020

I think the answers to the second and the last tests are wrong, they should be 0.08 and .105 respectively

Hao Ting on 25 Nov 2020

The question is boring

Adrian Scott on 18 Dec 2020

Pretty sure that there is an error in the test bench or the internet has the PI digits wrong on some sites

Ozer Eroglu on 3 Jan 2021

- result for the last case must be 0.106.
- if vpa is not accepted this is a silly question.

A C on 10 Jan 2021

% I used Machin's Formula: pi = 4[4arctan(1/5) - arctan(1/239)] because it was used for speed. But it will not go no more than 16 digits. How can I go beyond 16 digits?
function [PI] = pidigit(N,n)
A = 0;
F = 10^300;
% Machin's Formula: pi = 4[4arctan(1/5) - arctan(1/239)]
x1 = 1/5;
x2 = 1/239;
for K = 0:1000000000
A1 = 4*((-1)^K*x1^(2*K+1)/(2*K+1));
A2 = (-1)^K*x2^(2*K+1)/(2*K+1);
A = A + 4*(A1 - A2)*F;
end
E = abs(pi*F-A)/(pi*F);
PI = sprintf('%.f',A) -'0';
sum(PI(1:N-1) == n)
sum(PI(1:N-1) == n)/(N-1)
end

Solution Comments

Solution 3840823

2 Comments

2 Comments

Tadesse Hadush Negash on 25 Nov 2020

What is the error with code as a solution?
m = 'n';
Pi='3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983052358089330657574067954571637752542021149557615814002501262285941302164715509792592309907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111790429782856475032031986915140287080859904801094121472213179476477726224142548545403321571853061422881375850430633217518297986622371721591607716692547487389866549494501146540628433663937900397692656721463853067360965712091807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862947265473642523081770367515906735023507283540567040386743513622224771589150495309844489333096340878076932599397805419341447377441842631298608099888687413260472';
b = Pi(1:N);
x = length(strfind(b, m));
y=round(x/(N-1),4);

Jiang Senmiao on 14 Feb 2021

Not m = 'n', but:
m = num2str(n);

Solution 3826418

1 Comment

1 Comment

Tadesse Hadush Negash on 24 Nov 2020

It does not accept VPA and digits function? Something wrong with online debugging?

Solution 3786713

1 Comment

1 Comment

mahesh kumar on 22 Nov 2020

at least the first 20 SOL are fun ;P

Solution 2571678

1 Comment

1 Comment

Li Kehan Li on 17 Jun 2020

quite silly as we cannot use the vpa function.

Solution 1392794

1 Comment

1 Comment

Kodavati Mahendra on 25 Dec 2017

how do I solve this without using either the Pi value string or symbolic toolbox?

Solution 1327517

2 Comments

2 Comments

Gökhan Ayar on 4 Nov 2017

why do I always get this error message:
Undefined function 'vpa' for input arguments of type 'double'.

When running the code in my Matlab version, it works fine

Mehmet OZC on 6 Nov 2017

to use vpa function you must have symbolic math toolbox. We cannot use the toolbox on cody.

Solution 1324652

3 Comments

3 Comments

Kyle Chappell on 2 Nov 2017

I think the answer to test suite 3 should be 0.0746 rather than 0.0796.

Mehmet OZC on 3 Nov 2017

Kyle, test suite is correct. your code includes decimal point. check your solution

Kyle Chappell on 4 Nov 2017

Ah, you're correct. Thanks!

Solution 1302748

1 Comment

1 Comment

Maurício Girardi-Schappo on 19 Oct 2017

My code passes all tests but the last... I'm getting 0.1050 as a result instead of 0.1060.

Solution 1292887

1 Comment

1 Comment

YIMIN ZHONG on 17 Oct 2017

can we just do not paste pi and truncate? try something different.

Solution 1290282

4 Comments

4 Comments

Show 1 older comment

@bmtran (Bryant Tran) on 16 Oct 2017

Shouldn't the correct answer for test 2 be 0.08? There are be 16 occurrences of the digit 6 in the first 200 digits. 16/200 = 0.08.

Mehmet OZC on 17 Oct 2017

Sorry for that, I have corrected the mistake.

Yona on 17 Oct 2017

I think this correction is not good. the 201th digit is 6 so only 15 until 200 (when the first digit is 3 and not only the decimal part)

same problem in test 5. need to be 105. (see solution 1292755 and 1292769)

mhartma3 on 19 Oct 2017

I agree with Yona that the "corrected" solution is now wrong. There are only 15 occurrences of the digit 6 in the first 200 digits. 15/200 = 0.0750. Similarly, the solution to test 5 should be 105/1000 = 0.1050.

Solution 1288492

1 Comment

1 Comment

Gergely Patay on 16 Oct 2017

Not a particularly cool solution to be proud of, but a string literal would be neither too elegant...

Problem Recent Solvers440

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44309. Pi Digit Probability

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers440

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Problem 44309. Pi Digit Probability

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers440

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Players