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Find the greatest integer p

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August 29, 2010
functionalgebra unsolvedalgebra

Problem Statement

Given a positive integer nn, find the greatest integer pp with the property that for any function f:P(X)→Cf : \mathbb P(X) \to C, where XX and CC are sets of cardinality nn and pp, respectively, there exist two distinct sets A,B∈P(X)A,B \in \mathbb P(X) such that f(A)=f(B)=f(A∪B)f(A) = f(B) = f(A \cup B). (P(X)\mathbb P(X) is the family of all subsets of XX.)
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