配袜子 I

Matching Socks I

专题: Brainteaser / 脑筋急转弯
难度: L2
来源: QuantQuestion

题目详情

上班要迟到！抽屉里有 2 双黑袜、4 双蓝袜、5 双灰袜（只关心颜色）。你随机抓袜子。

问：至少需要抓多少只袜子，才能保证一定能得到一双同色袜子？

Your late for work! Your drawer has $2$ black socks, $4$ blue socks, and $5$ grey socks. If your grabbing socks at random, whats the minimum number of socks your need to grab to guarantee you get a pair of socks of the same color?

解析

最坏情况下，前 3 只袜子分别是三种不同颜色。

第 4 只袜子无论是什么颜色，都必然与前 3 只中的某一种颜色重复，从而形成同色一双。

因此至少需要 4 只。

Original Explanation

Consider the worst case scenario, the first $3$ socks your grab are each of different colors. Then the $4$ th sock you grab must match one of the previous socks. Hence by the Pigeon Hole Principle, you need to grab at least $4$ socks.