Question

Akash 的生日蛋糕是一个 $4 \times 4 \times 4$ 英寸的立方体。蛋糕的顶面和四个侧面有糖霜，底面没有糖霜。若把蛋糕切成 $64$ 个 $1 \times 1 \times 1$ 英寸的小立方体，如下图所示，有多少小块恰好有两个面带糖霜？

Akash's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many small pieces will have icing on exactly two sides?

$12$

$16$

$18$

$20$

$24$

答案：D

知识点：正方体分类讨论

难度评级：1100

视频讲解：

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文字解答：

顶层中，每条边上非角的小块恰好有两个糖霜面。共有 $4$ 条边，每条边有 $2$ 个这样的块，共 $8$ 块。

在下面 $3$ 层中，恰好有两个糖霜面的只有每层的 $4$ 个角块，共 $3\cdot4=12$ 块。

总数为 $8+12=20$ 。

正确答案是 D。

In the top layer, the non-corner edge pieces have icing on exactly two sides. There are $4$ edges with $2$ such pieces each, for $8$ pieces.

In each of the other $3$ layers, the only pieces with exactly two iced sides are the $4$ corner pieces. This adds $3\cdot4=12$ pieces.

The total is $8+12=20.$

Thus, the correct answer is D.

2020 AMC 8 第 9 题

答案：D

难度评级：1100

视频讲解：

文字解答：

其他年份的第 9 题