Tuesday, June 2, 2020

06/02/2020 (2019: AMC 8, Problem 13)

Q: 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 N 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 N?

$\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6$

We list out the smallest two 2-digit palindromes plus another, greater, two digit palindrome:
11 + 22 + 33 = 66
11 + 22 + 44 = 77
11 + 22 + 55 = 88
11 + 22 + 66 = 99
11 + 22 + 77 = 110
The smallest number to satisfy the conditions given above is 110. The sum of its digits is 1 + 1 + 0 = 2. The answer is A.
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