1986 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.
在所示 T 形图中，分别把八个带字母的相同正方形中的一个与四个阴影正方形放在一起。所得图形中有多少个可以折成一个没有顶盖的立方体盒子？
Suppose one of the eight lettered identical squares is included with the four shaded squares in the T-shaped figure shown. How many of the resulting figures can be folded into a topless cubical box?
小提示：
无顶盒有 个面，所以四个阴影正方形加上一个新增正方形必须能折成缺少顶面的立方体
A topless box has faces, so the four shaded squares plus the one added square must fold into a cube missing its top
大提示：
逐个尝试带字母的正方形作为第五个面；若折叠后两个面重合，该位置失败
Try each lettered square as the fifth face; a placement fails when folding would force two faces into the same spot
解答：
四个阴影正方形折成开口盒子的四个面，新增正方形提供第五个面。想象折叠过程，正方形 、、、、 和 都能补成一个有效的无顶盒。
正方形 和 不行，因为折叠后会迫使四个面在同一个角相遇。因此有 个有效图形。
所以正确答案是 E。
The four shaded squares fold into four faces of an open box, and the added square supplies the fifth face. Picturing the folds, the squares and each complete a valid topless box.
The squares and do not work, because folding would force four faces to meet at a single corner. That leaves valid figures.
Thus, the correct answer is E .
其他年份的第 21 题
- 1985 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
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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