Problem 42409. Divisible by 7

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 7.Write a function to determine if a number is divisible by 7. This can be done by a variety of methods. Some are:<ol><li>Multiply each digit in the candidate number (from right to left) by the digit in the corresponding position in this pattern: 1, 3, 2, -1, -3, -2 (1 applies to the ones digit, 3 to the tens digit, etc.). This pattern should be repeated beyond the hundred-thousands digit. The resulting sum will be a smaller number. This method can be applied recursively to the absolute values of the resulting sum until a single digit results. Then, check that number for divisibility by seven.</li><li>The previous method can also be used applying a slightly different pattern: 1, 3, 2, 6, 4, 5 (1 applies to the ones digit again, etc.). The absolute value of the resulting sum is not necessary as none of the factors are negative.</li><li>Multiply the last (ones) digit by two and subtract the result from the remaining number. Apply recursively, as noted in methods above.</li><li>Similar to the previous method, multiply the last digit by five and add to the remaining number. Apply recursively, as noted in methods above.</li><li>Double the last digit and subtract it from the remaining number (original number except for the ones digit). Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</li><li>Similar to the previous method, multiply the ones digit by five and add it to the remaining number. Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</li><li>Along similar lines, take the last three digits of the number and subtract that number from the remaining number. Once you reach a number less than 1000, another method can be applied to further reduce the number to check for divisibility by seven.</li><li>Etc. (there are others)</li></ol>The restriction for multiplication has been lifted for this specific problem.Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42408-divisible-by-6">divisible by 6</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42410-divisible-by-8">divisible by 8</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 7.

Write a function to determine if a number is divisible by 7. This can be done by a variety of methods. Some are:

# Multiply each digit in the candidate number (from right to left) by the digit in the corresponding position in this pattern: 1, 3, 2, -1, -3, -2 (1 applies to the ones digit, 3 to the tens digit, etc.). This pattern should be repeated beyond the hundred-thousands digit. The resulting sum will be a smaller number. This method can be applied recursively to the absolute values of the resulting sum until a single digit results. Then, check that number for divisibility by seven.
# The previous method can also be used applying a slightly different pattern: 1, 3, 2, 6, 4, 5 (1 applies to the ones digit again, etc.). The absolute value of the resulting sum is not necessary as none of the factors are negative.
# Multiply the last (ones) digit by two and subtract the result from the remaining number. Apply recursively, as noted in methods above.
# Similar to the previous method, multiply the last digit by five and add to the remaining number. Apply recursively, as noted in methods above.
# Double the last digit and subtract it from the remaining number (original number except for the ones digit). Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.
# Similar to the previous method, multiply the ones digit by five and add it to the remaining number. Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.
# Along similar lines, take the last three digits of the number and subtract that number from the remaining number. Once you reach a number less than 1000, another method can be applied to further reduce the number to check for divisibility by seven.
# Etc. (there are others)

The restriction for multiplication has been lifted for this specific problem.

Previous problem: <http://www.mathworks.com/matlabcentral/cody/problems/42408-divisible-by-6 divisible by 6>. Next problem: <http://www.mathworks.com/matlabcentral/cody/problems/42410-divisible-by-8 divisible by 8>.

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Last Solution submitted on Sep 07, 2023

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Brandon on 28 Jun 2023

This one is dumb, as you need to use all the digits in the number. You might as well just use normal long division.

Plus, I have to implement modular arithmetic, which uses mod, which is banned in this problem.

Josh on 18 Jul 2023

i keep struggling with timeout issues or the truncation/rounding of large numbers to scientific notation

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Problem 42409. Divisible by 7

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