2010 AMC 10B 第 3 题

Question

一个抽屉里有红、绿、蓝、白四种颜色的袜子，每种颜色至少

2

只。至少要从抽屉里取出多少只袜子，才能保证有一双同色袜子？

A drawer contains red, green, blue, and white socks with at least

2

of each color. What is the minimum number of socks that must be pulled from the drawer to guarantee a matching pair?

3

4

5

8

9

考虑出现一双袜子之前的最坏情况。

Use the worst case before a pair appears

你可能先各取出四种颜色的一只袜子。

You can draw one sock of each of the four colors first

为了尽量延迟出现同色一双，最多可以先取出每种颜色各一只袜子。

一共有

4

种颜色，因此取出四只时仍可能没有同色一双。

再取一只就必然与其中一种颜色配成一双，所以需要

4 + 1 = 5

只。

所以正确答案是 C。

To maximize the number of socks, we want to grab as many single socks as possible before getting a pair.

There are

4

colors, which means that we can draw one sock of each color before drawing a pair.

This means that it takes at least

4 + 1 = 5

socks to be drawn before a pair is guaranteed.

Thus, C is the correct answer.

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