Matching socks in the dark

Question

A drawer contains socks of just two colors: black and blue, mixed together, with plenty of each. The room is completely dark, so you cannot see the colors as you pull socks out. How many socks must you take out to be certain you have at least one matching pair? Follow-up: how many to be sure of a matching pair if there are three colors?

Accepted Answer

The answer is 3 socks. Worst-case reasoning. You want a guarantee, so imagine the unluckiest draw. With two colors, the most socks you can hold without a matching pair is 2, one black and one blue. The moment you draw a third sock, it must repeat one of those two colors (there are only two colors available), completing a pair. So 3 socks always guarantee a matching pair, and 2 do not (you might have one of each). The answer is \boxed{3}. This is the pigeonhole principle. The colors are "pigeonholes" (2 of them) and the socks are "pigeons." Once the number of pigeons exceeds the number of hole…

Matching socks in the dark

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