Nº 061 · Numbers · 50 sec

How many people does it take to share a birthday?

Birthday cake with a chocolate 23 and lots of lit candles, two hands lighting the last ones
Photo: Francesca Cesa Bianchi, Milano · CC BY-SA 3.0 it · Original

Your guess

How many people make the chance of a shared birthday exceed 50 %?

It's about pairs, not about you

Intuition asks: does anyone share my birthday? For a 50 % chance of that, you really would need 253 other people. But the question is whether any pair matches. And 23 people already form 253 pairs – each one a separate chance of a match.

Where the paradox bites

The same math applies to digital checksums known as hashes. Finding any two texts with the same checksum is much easier than finding a second text that matches one given text. Attacks that exploit this are called birthday attacks.

Sources

Every statement in this discovery is backed by one of these sources and was checked before publication.

  1. Wikipedia: Birthday problem (accessed 2026-10-05)
  2. Wikipedia (German): Geburtstagsparadoxon (accessed 2026-10-05)
  3. Wikipedia: Stirling's approximation (accessed 2026-10-05)

Image credits

  • “Italy - birthday cake with candles 3.jpg”, Francesca Cesa Bianchi, Milano, CC BY-SA 3.0 it