2009
Problem - 1539
What is the sum of the digits of the square of $111,111,111$?
Answer
E
The answer is $81$ by noticing that
- $1^2 = 1 \implies 1$
- $11^2 = 121 \implies 4 = 2^2$
- $111^2 = 12321 \implies 9 = 3^2$
- $\cdots$
The pattern is obvious.