MathDB

There are

n

clubs composed of

4

students out of all

9

students. For two arbitrary clubs, there are no more than

2

students who are a member of both clubs. Prove that

n\le 18

. Translator’s Note. We can prove

n\le 12

, and we can prove that the bound is tight.
(Credits to rkm0959 for translation and document)

Problem Statement