2010 AMC 12A Problems/Problem 6
- The following problem is from both the 2010 AMC 12A #6 and 2010 AMC 10A #9, so both problems redirect to this page.
Problem
A , 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
Solution 1
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 .
Solution 2
For to be a four-digit number, is in between and . The palindromes in this range are , , , and , so the sum of digits of can be , , , or . Only is an option, and upon checking, is indeed a palindrome.
Video Solution
https://www.youtube.com/watch?v=P7rGLXp_6es ~IceMatrix
See also
2010 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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All AMC 12 Problems and Solutions |
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