Difference between revisions of "2014 AMC 12A Problems/Problem 15"
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Revision as of 20:35, 7 February 2014
Problem
A five-digit palindrome is a positive integer with respective digits , where is non-zero. Let be the sum of all five-digit palindromes. What is the sum of the digits of ?
Solution
For each digit there are (ways of choosing and ) palindromes. So the s contribute to the sum. For each digit there are (since ) palindromes. So the s contribute to the sum. Similarly, for each there are palindromes, so the contributes to the sum.
It just so happens that so the sum of the digits of the sum is , or .
(Solution by AwesomeToad)