2005 AMC 8 第 16 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。
16.
一个五条腿的火星人有一抽屉袜子，每只袜子是红色、白色或蓝色，并且每种颜色至少有五只。火星人不看地一次取出一只袜子。为了保证有 只同色袜子，火星人必须从抽屉里取出多少只袜子？
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be socks of the same color?
答案：D
小提示：
最坏情况下，火星人先拿到每种颜色各 只
In the worst case, the Martian gets only socks of each color first.
大提示：
下一只袜子必然使某种颜色达到五只
The next sock must make five of some color.
解答：
火星人可能先取出每种颜色各 只袜子，而还没有 只同色。第 只袜子必然是某种颜色的第 只。
所以正确答案是 D。
Note that the Martian can pull out socks of each color without drawing of the same color. The th sock, however, must be the th sock of some color.
Thus, D is the correct answer.
其他年份的第 16 题
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