2019 AMC 8 Problems/Problem 13
Contents
Problem 13
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321 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 ?
Solution 1
Note that the only positive 2-digit palindromes are multiples of 11, namely . Since is the sum of 2-digit palindromes, is necessarily a multiple of 11. The smallest 3-digit multiple of 11 which is not a palindrome is 110, so is a candidate solution. We must check that 110 can be written as the sum of three distinct 2-digit palindromes; this suffices as . Then , and the sum of the digits of is .
Solution 2
Associated video - https://www.youtube.com/watch?v=bOnNFeZs7S8
Video Solution - https://youtu.be/Lw8fSbX_8FU (Also explains problems 11-20)
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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