2026-04-16

Problem — 2026-04-16

Easy

Easycombinatorics

A drawer contains 88 socks: 44 black and 44 white. You grab socks one at a time in the dark. What is the minimum number of socks you must grab to guarantee you have a matching pair?

Enter an integer

Show solution
There are 22 colors. By the pigeonhole principle, if you grab 33 socks, at least 3/2=2\lceil 3/2 \rceil = 2 must be the same color. The worst case with 22 socks is one black and one white, so 22 is not enough. Therefore 33 socks guarantee a matching pair.