Difference between revisions of "2010 AMC 12A Problems/Problem 6"
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Revision as of 17:34, 10 February 2010
Problem 6
A $\texti{palindrome}$ (Error compiling LaTeX. Unknown error_msg), such as 83438, is a number that remains the same when its digits are reversed. The numbers and are three-digit and four-digit palindromes, respectively. What is the sum of the digits of ?
Solution
is at most , so is at most . The minimum value of is . However, the only palindrome between and is , which means that must be .
It follows that is , so the sum of the digits is .