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Interview prep / Brainteaser/Logic

Socks needed to guarantee a same-colour pair

Question

A drawer contains plenty of socks in three different colours. Picking blind, how many socks must you take out to be certain of holding two of the same colour?

Short answer

Four. Three socks could all be different colours, but with four socks and only three colours the pigeonhole principle forces two to match.

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 2.6 The Pigeon Hole Principle, 'Matching socks', p.20; question and answer rewritten by SelfMadeQuant.com.

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