MathDB
Super robots and overpower laser beam

Source: Taiwan TST 2016 Round 3

April 23, 2016
combinatorics

Problem Statement

There's a convex 3n3n-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 AA, BB and CC form a triangle if AA's laser points at BB, BB's laser points at CC, and CC's laser points at AA. Find the minimum number of moves that can guarantee nn triangles on the plane.