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Choosing a subset P of n+1 men [ILL 1971]

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January 1, 2011
inequalitiescombinatorics proposedcombinatorics

Problem Statement

A set MM is formed of (2nn)\binom{2n}{n} men, n=1,2,…n=1,2,\ldots. Prove that we can choose a subset PP of the set MM consisting of n+1n+1 men such that one of the following conditions is satisfied: (1)(1) every member of the set PP knows every other member of the set PP; (2)(2) no member of the set PP knows any other member of the set PP.
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