1995 AMC 8 第 21 题
先试着解答 1995 AMC 8 第 21 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1995 AMC 8 解答，或核对答案。
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
小提示：
每个立方体都有一个凸扣，必须藏进另一个立方体的孔中
Each cube has one snap that must be hidden inside another cube’s hole
大提示：
试着把立方体排成一个小环，使每个凸扣都插入相邻立方体
Try arranging the cubes in a small ring so every snap plugs into a neighbor
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。两个立方体只能共用一个面，因此无法同时隐藏两个凸扣。若用三个立方体隐藏所有凸扣，就需要形成一个三立方体闭环，使每一对立方体都共用一个面；但三个单位立方体不可能两两以面相邻。因此，一个、两个或三个立方体都不行。
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
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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