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 $N$?

A. 2

B. 3

C. 4

D. 5

E. 6

1. 2019 AMC 8 官方解析

回文数．设$N$是最小的这种三位数：不是回文数且是三个不同的两位回文数之和．问$N$的数位之和是多少？
Two-digit palindromes must be of the form $\overline{aa}$. Thus immediately $11|N$ as a sum of three multiplies of 11. Smallest three-digit multiple is 110. Good news is that it is not a palindrome. We can easily rewrite as, for example, $22 + 33 + 55$.