Problem

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

Tags: combinatorics proposed, combinatorics



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