2003 AMC 8 第 15 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。
15.
一个图形由单位立方体构成。每个立方体至少与另一个立方体共享一个面。若要得到图中所示的正视图和侧视图，最少需要多少个立方体？
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
答案：B
解答：
正视图需要一个有三个可见位置的 L 形，所以至少需要三个立方体。
若只有三个立方体，它们都必须占据这三个正视图位置。这样侧视图只会有一个深度列，而不是所需的 L 形。
图中的四立方体构造具有两个所需视图，所以最小值是 。
所以正确答案是 B。
The front view requires an L-shape with three visible positions, so at least three cubes are needed.
Suppose there were exactly three cubes. The two cubes that appear one above the other must share a face, so they have the same depth. The third cube appears beside the lower one. To share a face with either of the first two cubes, it must share the lower cube's depth as well; otherwise it would be disconnected from both. Thus all three cubes would occupy one depth column, giving a one-column side view instead of the required L-shape.
The shown four-cube construction has both required views, so the minimum is .
Thus, B is the correct answer.
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