1995 AMC 8 第 21 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。
21.
一个塑料拼接立方体的一面有一个凸出的连接扣，另外五面有接受连接扣的孔。最少需要多少个这样的立方体拼接在一起，才能使外面只露出孔？
A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?
答案：B
解答：
每个立方体唯一的凸扣都必须插入另一个立方体的孔中才能被隐藏。用一个、两个或三个立方体时，总会至少有一个凸扣露在外面。
四个立方体可以排成一个方形环，每个凸扣插入相邻立方体的孔中，从而外面只露出孔。因此最少需要 个。
所以正确答案是 B。
Every cube's single snap must be plugged into another cube's hole to be hidden. Two cubes can share only one face, so two cubes cannot hide both snaps. With three cubes, hiding all three snaps would require a three-cube loop in which every pair shares a face, but three unit cubes cannot be pairwise face-adjacent. Thus one, two, or three cubes cannot work.
Four cubes can be arranged in a square ring, each snap fitting into the neighbor's hole, so only receptacle holes show. The smallest number is
Thus, the correct answer is B .
其他年份的第 21 题
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