Problem 43584. Find Pseudo-Cyclic Number

Created by Jaeho Seol

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{"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>"}]}

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Last Solution submitted on Jan 20, 2023

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Peng Liu on 22 Oct 2016

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

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Problem 43584. Find Pseudo-Cyclic Number

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