In a room of just 23 people, there's better-than-even odds two share a birthday
It sounds impossible: 23 people, out of 365 possible birthdays, yet the chance two of them share one already tips past 50%. The trick is that you're not checking one person against everyone else — you're checking every one of the 253 possible pairs in the room, and each pair only needs to coincide once. Roughly how many people would a room need before the odds of a shared birthday passed 99%?
Reveal the answer
Just 70 people pushes the odds above 99%. The problem was first rigorously analysed by mathematician Richard von Mises in 1939, and it remains one of probability theory's most reliable tools for showing how badly human intuition handles combinatorial growth.