Exercise 531Combinatorics › Pigeonhole principleHigh schoolAdded 3 Nov 2026

Generalized pigeonhole with $100$ people

#generalized pigeonhole#ceil#months

Statement

Show that among $100$ people, at least $\lceil 100/12\rceil=9$ were born in the same month.

Hint

Generalized pigeonhole: some hole contains at least $\lceil n/k\rceil$ pigeons.

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Compute. $\lceil 100/12\rceil = \lceil 8.33\ldots\rceil = 9$ .

Conclusion. Some month contains at least $9$ birthdays.