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
All the two digit palindromes are multiples of . The least digit integer that is the sum of two digit palindromes is a multiple of . The least digit multiple of is . The sum of the digits of is .
~heeeeeeheeeee
Solution 2
We let the two digit palindromes be , , and , which sum to . Now, we can let . This means we are looking for the smallest such that and is not a palindrome. Thus, we test for , which works so , meaning that the sum requested is . ~smartninja2000
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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