2003 AMC 12A 第 13 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。
13.
图中实线围成的多边形由 个全等正方形边对边连接而成。再把一个全等正方形接到图中标出的九个位置之一的某条边上。九种所得多边形中，有多少种可以折成一个缺少一个面的立方体？
The polygon enclosed by the solid lines in the figure consists of congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?
答案：E
解答：
缺少一个面的立方体有 个面，所以第五个正方形必须折到四正方形拼块尚未占据的面上。追踪每个连接位置折到的面可知，位置 和 会折到已占据的面并与之重叠。位置 和 都会折到未占据的面。因此九个位置中有 个可行。
所以正确答案是 E。
A cube missing one face has faces, so the fifth square must fold onto a face not already occupied by the four-square piece. Tracing the face reached by each attachment, positions and fold onto a face already occupied and overlap it. Each of positions and folds onto an unoccupied face. Therefore of the nine positions work.
Thus, the correct answer is E.
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