Skip to main content
OlympiadHQ

Browse · harp

Print

jmc

counting and probability junior

Problem

Each square in a grid is randomly filled with one of the gray and white tiles shown below on the right.
problem
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.
problem
(A)
(B)
(C)
(D)
Solution
There are cases that the tiling will contain a large gray diamond in one of the smaller grids, as shown below: There are ways to decide the white squares for each case, and the cases do not have any overlap. So, the requested probability is
Final answer
C