Problem 273. Recurring Cycle Length (Inspired by Project Euler Problem 26)

Created by @bmtran (Bryant Tran)

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<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>Preface: This problem is inspired by</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://projecteuler.net/problem=26\"><w:r><w:t>Project Euler Problem 26</w:t></w:r></w:hyperlink><w:r><w:t> and uses text from that question to explain what a recurring cycle is.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Description</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[1/2  =   0.5\n1/3  =  0.(3)\n1/4  =   0.25\n1/5  =   0.2\n1/6  =   0.1(6)\n1/7  =   0.(142857)\n1/8  =   0.125\n1/9  =   0.(1)\n1/10 =   0.1]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Create a function that can determine the length of the recurring cycle of 1/d given d.</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

292 Solutions
68 Solvers

Last Solution submitted on Jan 17, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

@bmtran (Bryant Tran) on 23 Feb 2012

sorry everyone, there was an issue in my reference solution used to generate the test suite. I have corrected this now.

Solution Comments

Solution 339591

1 Comment

1 Comment

J.R.! Menzinger on 25 Oct 2013

Java + Signal processing aproach.

Solution 58781

1 Comment

1 Comment

Venu Lolla on 9 Mar 2012

Ah feeling a little guilty :| ...

Solution 33957

4 Comments

4 Comments

Show 1 older comment

Igor on 8 Feb 2012

Unless my math (or counting) is wrong, the result of 1/17 by long division has a 16-digit (not 15) recurring cycle. I cannot find an error in my code or hand calculations. Any help?

Alfonso Nieto-Castanon on 10 Feb 2012

I believe you are right, the current test results seem to use something similar to the current leading method which disregards the effect of 0's so it typically underestimates the cycle length when d>10...
I believe in the test problems the cycle lengths of 17,19,197,1977,12345 should be 16,18,98,658,822 instead...

Igor on 10 Feb 2012

And those are precisely the numbers I am getting.

Alan Chalker on 12 Feb 2012

Wikipedia agrees with you: http://en.wikipedia.org/wiki/Repeating_decimal#Cyclic_numbers

Problem Recent Solvers68

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 273. Recurring Cycle Length (Inspired by Project Euler Problem 26)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers68

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Problem 273. Recurring Cycle Length (Inspired by Project Euler Problem 26)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers68

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Players