2020 AMC 8 第 9 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
9.
阿卡什的生日蛋糕是一个 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 个 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 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 smaller cubes, each measuring inch, as shown below. How many small pieces will have icing on exactly two sides?
小提示：
把顶层和下面三层分开数
Separate the top layer from the other layers
大提示：
顶层边上非角块和下面各层角块恰好有两个糖霜面
Top edge pieces and lower corner pieces are the exactly-two-sided pieces
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 条边，每条边有 个这样的块，共 块。
在下面 层中，恰好有两个糖霜面的只有每层的 个角块，共 块。
总数为 。
正确答案是 D。
In the top layer, the non-corner edge pieces have icing on exactly two sides. There are edges with such pieces each, for pieces.
In each of the other layers, the only pieces with exactly two iced sides are the corner pieces. This adds pieces.
The total is
Thus, the correct answer is D.
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