1986 AMC 8 第 18 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。
18.
一个矩形牧场要用一段 米石墙作为第四边，只在另外三边围栅栏。栅栏上每隔 米立一个柱子，包括栅栏与石墙相接处的两个柱子。围出一个 米乘 米的区域，最少需要多少根柱子？
A rectangular grazing area is to be fenced off on three sides using part of a meter rock wall as the fourth side. Fence posts are to be placed every meters along the fence, including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area m by m?
小提示：
要用最少柱子，让 米边靠墙，这样需要围的长度最短
To use the fewest posts, let the meter side lie along the wall, so the fenced length is as short as possible
大提示：
栅栏路径长 米；每隔 米放一根柱子，并计算两端
The fenced path is meters; place a post every meters, counting both ends
解答：
当石墙作为较长的 米边时，用的柱子最少；此时栅栏覆盖两条 米边和一条 米边，总路径长 米。
每隔 米放一根柱子并包括两端，共用 根柱子。
所以正确答案是 B。
The fewest posts are used when the wall serves as the longer meter side, so the fence covers two meter sides and one meter side, a path of meters.
Placing a post every meters, including both ends, uses posts.
Thus, the correct answer is B .
其他年份的第 18 题
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