Question 105
There's a convex $3n$-polygon on the plane with a robot on each of its vertices. Each robot fires a laser beam toward another robot. On each of your move, you select a robot to rotate clockwise until its laser points at a new robot. Three robots $A, B$ and $C$ form a triangle, if $A$'s laser points at $B$, $B$'s laser points at $C$, and $C$'s laser points at $A$. Find the minimum number of moves that can guarantee $n$ triangles on the plane.