Problem 42415. Divisible by 13

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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>Write a function to determine if a number is divisible by 13. Similar to the number seven, this can be done by a few different methods:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>Form the alternating sum of blocks of three (separated at the comma locations). Apply this recursively until a three-digit number remains. If this number is divisible by 13, then so is the original number. This three-digit number can also be further reduced using one of the other methods below.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>Add four times the last digit to the remaining number. Apply recursively until a two-digit number remains. As before, if this number is divisible by 13, then so is the original number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>Similar to the previous method, multiply the last digit by nine and subtract it from the remaining number. Apply recursion, etc.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Some of the function restrictions have been lifted.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Previous problem:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42414-divisible-by-12\"><w:r><w:t>divisible by 12</w:t></w:r></w:hyperlink><w:r><w:t>. Next problem:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42416-divisible-by-14\"><w:r><w:t>divisible by 14</w:t></w:r></w:hyperlink><w:r><w:t>.</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>"}]}

Write a function to determine if a number is divisible by 13. Similar to the number seven, this can be done by a few different methods:<ol><li>Form the alternating sum of blocks of three (separated at the comma locations). Apply this recursively until a three-digit number remains. If this number is divisible by 13, then so is the original number. This three-digit number can also be further reduced using one of the other methods below.</li><li>Add four times the last digit to the remaining number. Apply recursively until a two-digit number remains. As before, if this number is divisible by 13, then so is the original number.</li><li>Similar to the previous method, multiply the last digit by nine and subtract it from the remaining number. Apply recursion, etc.</li></ol>Some of the function restrictions have been lifted.Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42414-divisible-by-12">divisible by 12</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42416-divisible-by-14">divisible by 14</a>.

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Problem 42415. Divisible by 13

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