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points and segments

Source: Indonesia IMO 2007 TST, Stage 2, Test 2, Problem 4

November 15, 2009
combinatorics proposedcombinatorics

Problem Statement

Let X X be a set of k k vertexes on a plane such that no three of them are collinear. Let P P be the family of all (k2) {k \choose 2} segments that connect each pair of points. Determine τ(P) \tau(P).
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