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About ternary families of an n-set

Source: Brazil Mathematical Olympiad 1995

March 17, 2006
ceiling functionfloor functioncombinatorics proposedcombinatorics

Problem Statement

XX has nn elements. FF is a family of subsets of XX each with three elements, such that any two of the subsets have at most one element in common. Show that there is a subset of XX with at least 2n\sqrt{2n} members which does not contain any members of FF.
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