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I have the following problem: a light beam enters a mirror room with integer coordinates in the plane (consider it as a polygon). One of the walls of the room is removed and the light beam enters the room. The initial (not reflected) beam is defined by two points with integer coordinates. It enters the rooms, reflects a number of times and exits the room. The goal is to maximize the ratio $$\dfrac{\text {number of reflections}}{\text {number of sides of the room}}$$

All coordinates should be in the range $[0, 50]$.

Can you give me any hints or references to previous work on this problem. Thanks in advance!

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