MathDB

4

Part of 2009 Korea Junior Math Olympiad

Problems(1)

Students in Clubs

Source: Korean Junior MO 2009 P4

4/15/2016
There are nn clubs composed of 44 students out of all 99 students. For two arbitrary clubs, there are no more than 22 students who are a member of both clubs. Prove that n≤18n\le 18. Translator’s Note. We can prove n≤12n\le 12, and we can prove that the bound is tight.
(Credits to rkm0959 for translation and document)
combinatoricsKJMO