Super robots and overpower laser beam
Source: Taiwan TST 2016 Round 3
April 23, 2016
combinatorics
Problem Statement
There's a convex -polygon on the plane with a robot on each of it's vertices. Each robot fires a laser beam toward another robot. On each of your move,you select a robot to rotate counter clockwise until it's laser point a new robot. Three robots , and form a triangle if 's laser points at , 's laser points at , and 's laser points at . Find the minimum number of moves that can guarantee triangles on the plane.