IMO 2015 Shortlist C2
Let V be a finite set of points in the plane. We say that V is balanced if for any two distinct points A,B P V, there ex...
Category: Combinatorics
Problem
Let V be a finite set of points in the plane. We say that V is balanced if for any two distinct points A,B P V, there exists a point C P V such that AC “ BC. We say that V is center-free if for any distinct points A,B,C P V, there does not exist a point P P V such that PA “ PB “ PC. (a) Show that for all n ě 3, there exists a balanced set consisting of n points. (b) For which n ě 3 does there exist a balanced, center-free set consisting of n points? (Netherlands)