Problem

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

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



Each of the subsets A1, A2, , An 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 A1, A2, , An.