A curious child looks across a crowded birthday party where people hold face-down cards.

Will any two share a birthday?

tap the face-down cards

Thirty people are at one party. A year has hundreds of possible birthdays. Would you expect any two people here to share one?

first, choose one person

One exact birthday is one question

The same child compares one coral birthday card with five face-down cards.

“Does anyone match this exact birthday?” compares every other card with one chosen date. That personal question is not the whole-room question.

follow one birthday

One new person adds one spoke

people in this small group12 people · 11 checks
2 people12 people

Each spoke asks: “Does this person match the chosen date?”

now ask the whole room

One new person adds many links

people in this small group12 people · 66 pairs
2 people12 people

Every unique link is another place a shared date could appear.

same party, different questions

Two empty meters wait

By 30 people, will neither chance, both chances, or only one reach halfway?

Both begin empty. The small-group links help you reason, but they did not calculate this new case.

The room will grow to 30 people.

By then, what has crossed 50%?