Problem

Source: Tuymaada 2009, Junior League, First Day, Problem 4

Tags: algebra, polynomial, calculus, derivative, floor function, combinatorics unsolved, combinatorics



Each of the subsets $ A_1$, $ A_2$, $ \dots,$ $ A_n$ of a 2009-element set $ X$ contains at least 4 elements. The intersection of every two of these subsets contains at most 2 elements. Prove that in $ X$ there is a 24-element subset $ B$ containing neither of the sets $ A_1$, $ A_2$, $ \dots,$ $ A_n$.