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2023 AMC 8 Question 23

AMC8 · 2023 AMC 8

Question 23

Each square in a $3 \times 3$ grid is randomly filled with one of the $4$ shaded-and-unshaded tiles shown below on the right.

Question illustration

What is the probability that the tiling will contain a large shaded diamond in one of the smaller $2 \times 2$ grids? Below is an example of such a tiling.

Question illustration
  1. $\dfrac{1}{1024}$
  2. $\dfrac{1}{256}$
  3. $\dfrac{1}{64}$
  4. $\dfrac{1}{16}$
  5. $\dfrac{1}{4}$