AMC 8 1986 Problem 21
AMC8 1986 年第 21 题
立体几何★★★☆☆
Suppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box?
假设八个标有字母的全等正方形之一与 T 形外框中的四个正方形合并。所得图形中有多少个可以折叠成一个无盖的正方体盒子？
- A.2
- B.3
- C.4
- D.5
- E.6
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Suppose the existing net is folded so that the square immediately to the right of is on the bottom. Then only the top and left sides of the folded cube would be missing. , and could be added as the left side of the cube, while , , and could be added as the right side of the cube. and could not be added, as at most three faces can share a vertex. Therefore, 6 of the lettered faces could be added to the existing net.
Fold the four squares into the four sides of a cube. Then, there are six edges "open" (for lack of better term). For each open edge, we can add a square/side, so the answer is .
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