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Why is it that when you subtract a number by its palindrome you always get you result as a multiple of 9?

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If you take a number and you transpose the digits e.g. the number $1234$ and move the digits around to give something like $4321$, the difference between these two numbers is a multiple of $9$.

So palindromes, being numbers that have their digits transposed will always obey this rule. Remember a difference of $0$ can also be written as $0 \times 9$.
ago by Diamond (61,634 points)

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