# Sum of Palindromes a Palindrome?

Algebra Level 3

Let $$A$$ and $$B$$ be four-digit palindromes, and let $$C$$ be a five-digit palindrome. If $$A+B=C$$, determine the sum of all possible values of $$C$$.

Note: A palindrome is a number that reads the same forwards or backwards, such as 7227 or 52325.

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