Question 147
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 $\alpha$, it leaves with a directed angle $180^\circ - \alpha$. After $n$ bounces, the ray returns to $A$ without ever landing on any of the other vertices. Find all possible values of $n$.