What's So Special About Eleven?
The above are some examples of palindromes with an even number of digits, and they so happen to be all divisible by 11. Is it true that all palindromes with an even number of digits are all divisible by 11?
Assume all palindromes are whole numbers.
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1 solution
Relevant wiki: Divisibility Rules (2,3,5,7,11,13,17,19,...)
A number is divisible by 11 if the sum of the digits in the odd places minus the sum of the digits in the even places is divisible by 11.
For palindromes, the sum of the digits in the odd places is equal to the sum of the digits in the even places.
Hence all palindromes with an even number of digits are divisible by 11.