Problem 42413. Divisible by 11

Created by goc3

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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>.

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Last Solution submitted on Sep 08, 2023

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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.

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Problem 42413. Divisible by 11

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Problem 42413. Divisible by 11

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