Exercise 892Combinatorics › Counting principlesL1Added 3 Nov 2026

Generalized pigeonhole

#pigeonhole#generalized#ceil

Statement

Show that among $100$ people, at least $\lceil100/12\rceil=9$ were born in the same month.

Hint

Generalized pigeonhole: with $n$ pigeons and $k$ holes, some hole has $\lceil n/k\rceil$ .

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Generalized. With $100$ pigeons and $12$ holes, at least $\lceil100/12\rceil=9$ pigeons share a hole.

Conclusion. At least $9$ people share a birth month.