Problem 42413. Divisible by 11

Created by goc3

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>Pursuant to the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2\"><w:r><w:t>first problem</w:t></w:r></w:hyperlink><w:r><w:t> in this series, this one involves checking for divisibility by 11.</w:t></w:r></w:p><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 11. Like the number seven, this can be done by a variety of methods. Some are:</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 the digits (e.g., positive even digits and negative odd digits). Apply recursively until a two-digit number results. If that result is divisible by 11, 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>Add the digits of the number in blocks of two from right to left. Apply recursively, as needed, and check for divisibility as stated in the previous method.</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>Subtract the last digit from the remaining number (e.g., 649: 64 - 9 = 55). Apply recursion, as needed.</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 ten times the last digit to the remaining number. Apply recursion, as needed. For example: 737: 73 + 70 = 143: 14 + 30 = 44.</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>Etc.</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/42412-divisible-by-10\"><w:r><w:t>divisible by 10</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/42414-divisible-by-12\"><w:r><w:t>divisible by 12</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>"}]}

Pursuant to the <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2">first problem</a> in this series, this one involves checking for divisibility by 11.Write a function to determine if a number is divisible by 11. Like the number seven, this can be done by a variety of methods. Some are:<ol><li>Form the alternating sum of the digits (e.g., positive even digits and negative odd digits). Apply recursively until a two-digit number results. If that result is divisible by 11, then so is the original number.</li><li>Add the digits of the number in blocks of two from right to left. Apply recursively, as needed, and check for divisibility as stated in the previous method.</li><li>Subtract the last digit from the remaining number (e.g., 649: 64 - 9 = 55). Apply recursion, as needed.</li><li>Add ten times the last digit to the remaining number. Apply recursion, as needed. For example: 737: 73 + 70 = 143: 14 + 30 = 44.</li><li>Etc.</li></ol>Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42412-divisible-by-10">divisible by 10</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42414-divisible-by-12">divisible by 12</a>.

Pursuant to the <http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2 first problem> in this series, this one involves checking for divisibility by 11.

Write a function to determine if a number is divisible by 11. Like the number seven, this can be done by a variety of methods. Some are:

# Form the alternating sum of the digits (e.g., positive even digits and negative odd digits). Apply recursively until a two-digit number results. If that result is divisible by 11, then so is the original number.
# Add the digits of the number in blocks of two from right to left. Apply recursively, as needed, and check for divisibility as stated in the previous method.
# Subtract the last digit from the remaining number (e.g., 649: 64 - 9 = 55). Apply recursion, as needed.
# Add ten times the last digit to the remaining number. Apply recursion, as needed. For example: 737: 73 + 70 = 143: 14 + 30 = 44.
# Etc.

Previous problem: <http://www.mathworks.com/matlabcentral/cody/problems/42412-divisible-by-10 divisible by 10>. Next problem: <http://www.mathworks.com/matlabcentral/cody/problems/42414-divisible-by-12 divisible by 12>.

Solve

Solution Stats

331 Solutions
79 Solvers

Last Solution submitted on Jun 23, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Jean-Marie Sainthillier on 16 Aug 2015

Grant, your divisible series should become a challenge by its own right.

goc3 on 18 Aug 2015

Thanks for the vote. We'll see if the Cody team agrees. I just added a few more problems to the series today to round it out.

ME on 11 Dec 2017

Nice problem - deceptively tricky.

Solution Comments

Solution 1705821

2 Comments

2 Comments

Chris Breshike on 10 Jan 2019

my solution is failing because when the numbers are very large it gets confused by the "eXX" where XX is the exponent associated with the test number.

Can i get help on how to avoid this?

goc3 on 11 Jan 2019

You need to find a way to operate on the string, which may involve mathematical operations on small portions of the string, bit by bit, converting small portions of the string to a number, in an iterative fashion, etc., based on the method you choose. str2num() is subject to loss of precision for very large numbers and will not work for at least one test case in essentially all of these problems (by design).

Problem Recent Solvers79

Problem Tags

Community Treasure Hunt

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

Start Hunting!