Problem:
Find the arithmetic mean of all the three-digit palindromes. (Recall that a palindrome is a number that reads the same forward and backward, such as or .)
Solution:
We start by listing out the first few and last few palindromes next to each other:
It is apparent that each of these pairs sum to . As the average of all three-digit palindromes will be the average of the first and last three-digit palindromes, the requested mean is .