Exercise 529Combinatorics › Pigeonhole principleHigh schoolAdded 3 Nov 2026

More socks

#pigeonhole#socks#colors

Statement

A drawer has $10$ red, $10$ green, and $10$ blue socks. In darkness, how many socks must you draw to guarantee $3$ of the same color?

Hint

There are $3$ colors; to avoid $3$ of a color, at most $2$ of each.

Show solutionHide solution

Maximum without guarantee. $2$ per color: $6$ socks.

Guarantee. With $7$ socks, by pigeonhole some color has $\lceil 7/3\rceil=3$ .

Conclusion. $7$ socks.