Problem:
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, is a palindrome.) Let be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of
Answer Choices:
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Solution:
Note that -digit palindromes have the tens and units digits the same. This means that they are all multiples of . If a -digit number is the sum of -digit palindromes, then it itself must also be a multiple of . The smallest -digit multiple of that is not a palindrome is . This can be achieved by adding .
Therefore, . The sum of its digits is .
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions