Ok! Nice question, by the way!
11 + 11 = 4
What is the sum of the digits of 11? 1 + 1 = 2.
Now square that. You get 2^2 = 4.
12 + 12 = 9
What is the sum of the digits 12? 1 + 2 = 3.
Now square that. You get 3^2 = 9.
Now, 13 + 13 = ?
What is the sum of the digit 13? 1 + 3 = 4
Now square that. You get 4^2 = 16.
13 + 13 = 16.
