Skip to content

Grabbing socks blindly until two match

Question

A drawer holds 22 black, 44 blue and 55 grey socks. You pull socks out without looking. What is the smallest number you must take to be sure of having two of the same colour?

Short answer

44. With three colours, three socks could all differ, but a fourth must repeat a colour by the pigeonhole principle.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution