Problem:
Each square in a grid is randomly filled with one of the four gray-and-white tiles shown below on the right.
What is the probability that the tiling will contain a large gray diamond in one of the smaller grids? Below is an example of such tiling.
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are a total of configurations. The square that contains the large gray diamond can occur in spots (as there are four squares in the big square). The four tiles in the square have a fixed tile. The other squares can be any tiles, which allows for configurations for the other tiles. The total number of configurations that include the large gray diamond is therefore . The desired probability is then .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions