Question

将十二根长 $3$ 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 $3$ -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:

$24$ 英寸

$24$ in.

$12$ 英寸

$12$ in.

$30$ 英寸

$30$ in.

$18$ 英寸

$18$ in.

$36$ 英寸

$36$ in.

答案：A

知识点：正方体图论极端原理

难度评级：1300

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 $8\cdot3=24$ 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 $8\cdot3=24$ inches.

Therefore, the correct answer is A.

1957 AMC 12 第 17 题

答案：A

难度评级：1300

小提示：

大提示：

解答：

其他年份的第 17 题