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A set with 56 elements, and 15 subsets of his

Source: China NMO 2006, Problem 6

January 29, 2006
combinatorics unsolvedcombinatorics

Problem Statement

Suppose XX is a set with ∣X∣=56|X| = 56. Find the minimum value of nn, so that for any 15 subsets of XX, if the cardinality of the union of any 7 of them is greater or equal to nn, then there exists 3 of them whose intersection is nonempty.
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