3 Red Socks and 3 Blue Socks: How Many Must You Take to Guarantee a Match?

This classic probability riddle asks how many socks you must take in the dark to guarantee a matching pair.

There are 3 red socks and 3 blue socks. If you pick one sock, you could get either color. If you pick a second sock, it could be the opposite color, leaving you with one red and one blue.

But the third sock must match one of the first two colors, because there are only two possible colors available.

Answer: 3 socks.

With three socks, a matching pair is guaranteed by the pigeonhole principle: putting three items into only two color categories means at least two must share the same color.

You might get a pair sooner, but three is the minimum number that guarantees it every time.

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