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24-element subset B containing neither of the sets A_1,...

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

July 19, 2009
algebrapolynomialcalculusderivativefloor functioncombinatorics unsolvedcombinatorics

Problem Statement

Each of the subsets A1 A_1, A2 A_2, …, \dots, An A_n of a 2009-element set X X contains at least 4 elements. The intersection of every two of these subsets contains at most 2 elements. Prove that in X X there is a 24-element subset B B containing neither of the sets A1 A_1, A2 A_2, …, \dots, An A_n.
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