Puzzles

The shared birthday bet

How many people do you need in a room before it's more likely than not that two of them share a birthday?

Reveal the answer

Just 23. With 23 people there are 253 possible pairs, and the odds of at least one match pass 50%. By 70 people it's 99.9%. Intuition fails because you instinctively compare everyone to yourself, not everyone to everyone.

Richard von Mises, Über Aufteilungs- und Besetzungswahrscheinlichkeiten (the classic 'birthday problem') — 1939

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