AMC 8 2023 Problem 23

AMC8 2023 年第 23 题

概率★★★★☆

Each square in a $3×3$ grid is randomly filled with one of the 4 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 $2×2$ grids? Below is an example of such a tiling.

将3×3方格表中的每个小方格随机的用如下图左侧所示的4个灰白双色方块之一嵌入，有一个大灰色菱形将出现在某个2×2子方格表中的概率是多少？一个这样的镶嵌方案的例子如下图右侧所示，

A. $\displaystyle \frac{1}{1024}$
B. $\displaystyle \frac{1}{256}$
C. $\displaystyle \frac{1}{64}$
D. $\displaystyle \frac{1}{16}$
E. $\displaystyle \frac{1}{4}$

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