mathschallenge.net

Problem

By adding the different 2-digit numbers 12 and 32 we get 44. If the digits in each number are reversed we get two different 2-digit numbers, and 21 + 23 also equals 44.
The same is true of 42 + 35 = 24 + 53 = 77.

Prove that the sum of two 2-digit numbers with this property will always be divisible by 11.