Exercise 260Combinatorics › Pigeonhole principleHigh schoolAdded 3 Nov 2026

Socks in the dark

#pigeonhole#socks#drawers

Statement

A drawer contains black socks and white socks. In total darkness, how many socks must you pick to be sure of getting a matching pair?

Hint

There are $2$ colors ("holes"). How many socks guarantee $2$ of the same color?

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Pigeonhole. $2$ colors, so picking $3$ socks forces two of the same color.

Conclusion. $3$ socks are enough to guarantee a matching pair (in the worst case).