Problem 43584. Find Pseudo-Cyclic Number

Created by Jaeho Seol

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>A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Cyclic_number\"><w:r><w:t>https://en.wikipedia.org/wiki/Cyclic_number</w:t></w:r></w:hyperlink><w:r><w:t>&gt;). The most widely known is 142857:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[    142857 × 1 = 142857\n    142857 × 2 = 285714\n    142857 × 3 = 428571\n    142857 × 4 = 571428\n    142857 × 5 = 714285\n    142857 × 6 = 857142]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In fact, 142857 is the only cyclic number in decimal, if leading zeros are not permitted on numerals.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Therefore, instead of the pure cyclic number, we will find the integer in which</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>any</w:t></w:r><w:r><w:t> cyclic permutations of the digits are</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>any</w:t></w:r><w:r><w:t> multiples of the number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example, 230769 is the one, because 23076</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>9</w:t></w:r><w:r><w:t> x 4 =</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>9</w:t></w:r><w:r><w:t> 23076.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given an integer x, return whether x is a pesudo-cyclic number.</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

58 Solutions
30 Solvers

Last Solution submitted on Sep 02, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Peng Liu on 22 Oct 2016

A fantastic problem compared to those JUNK problems recently added to Cody.

Solution Comments

Show comments

Problem Recent Solvers30

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 43584. Find Pseudo-Cyclic Number

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author1

Problem Tags

Community Treasure Hunt

Problem 43584. Find Pseudo-Cyclic Number

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author1

Problem Tags

Community Treasure Hunt

Players