Let ABC be an equilateral triangle. From the vertex A we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray reaches a side, it then bounces off following the law of reflection, that is, if it arrives with a directed angle α, it leaves with a directed angle 180∘−α. After n bounces, the ray returns to A without ever landing on any of the other two vertices. Find all possible values of n. geometrynumber theoryAPMOcombinatoricsHi