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Find the maximal !

Source: Romania TST 2013 Day 3 Problem 3

January 21, 2015
combinatorics unsolvedcombinatorics

Problem Statement

Determine the largest natural number rr with the property that among any five subsets with 500500 elements of the set {1,2,,1000}\{1,2,\ldots,1000\} there exist two of them which share at least rr elements.