Problem:
In the array shown below, three 3s are surrounded by 2s, which are in turn surrounded by a border of 1s. What is the sum of the numbers in the array?
11111122211232112321123211222111111
Answer Choices:
A. 49
B. 51
C. 53
D. 55
E. 57
Solution:
There are 20 ones, 12 twos, and 3 threes. So the sum of all the numbers in the grid is 20⋅1+12⋅2+3⋅3=(C) 53.
The problems on this page are the property of the MAA's American Mathematics Competitions