Pigeonhole principle
Counting and combinatorics (advanced) · Mathematics
Study notes
Q: In a class of 30 students, prove two share a birth month. 12 months (boxes), 30 students (items). ⌈30/12⌉ = ⌈2.5⌉ = 3. Some month has at least 3 birthdays - even stronger than 2! (Pigeonhole guarantees it without checking anyone!)