Why 23 people are enough for a shared birthday: counting pairs, not people
30seconds
Put 23 people in a room and the chance that two share a birthday is already 51%. It feels far too low a number, because we picture one person matching our birthday. The real question is whether any two match, and that is about pairs. 23 people make 253 pairs, and every pair is another small chance.
Fill a year of 365 squares with random birthdays, slide the room size up and down, and watch the pink collisions appear. Then run 1,000 rooms to see the tally settle on the maths.
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