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Question

A palindrome, such as 83438, is a number that remains the same when its digits are reversed. The numbers x and x+32 are three-digit and four-digit palindromes, respectively. What is the sum of the digits of x?

Accepted Answer

x is at most 999, so x+32 is at most 1031. The minimum value of x+32 is 1000. However, the only palindrome between 1000 and 1032 is 1001, which means that x+32 must be 1001. It follows that x is 969, so the sum of the digits is 24.