1957 AMC 12 第 17 题
先试着解答 1957 AMC 12 第 17 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 1957 AMC 12 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。
17.
将十二根长 英寸的铁丝在各顶点正确焊接，制成一个立方体框架。一只苍蝇落在一个顶点上后沿棱行走，在不重复走过任何一段路的条件下，它第二次到达任一顶点之前最多能走多远？
A cube is made by soldering twelve -inch lengths of wire properly at the vertices of the cube. If a fly alights at one of the vertices and then walks along the edges, the greatest distance it could travel before coming to any vertex a second time, without retracing any distance, is:
英寸
in.
英寸
in.
英寸
in.
英寸
in.
英寸
in.
小提示：
一条尚未重复到达顶点的路径，至多能访问立方体的全部八个顶点
A path that never returns to a vertex can visit at most all eight cube vertices
大提示：
找出一条经过全部八个顶点的路径；它先走过七条棱，再沿下一条棱回到起点
Exhibit a path through all eight vertices, which uses seven edges before the next step returns to the starting vertex
解答：
立方体有八个顶点。一条路径可以依次访问全部八个顶点而不重复，共走过七条棱；随后从最后一个顶点沿一条棱回到起点，这次返回才是第一次重复到达顶点。因此，允许的最长路线共经过八条棱，长度为 英寸。
因此，正确答案是 A。
The cube has eight vertices. A path can visit all eight once, using seven edges, and then traverse the edge from its last vertex back to its starting vertex; the return is the first repeated vertex. Thus the greatest permitted walk uses eight edges. Its length is inches.
Therefore, the correct answer is A.
其他年份的第 17 题
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