HMMT 2003 C9
- Combinatorics
At a certain college, there are 10 clubs and some number of students. For any two different students, there is some club such that exactly one of the two belongs to that club. For any three different students, there is some club such that either exactly one or all three belong to that club. What is the largest possible number of students?
Dataset text NuminaMath olympiads. Quoted with source.
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