# Lets play Carrom!

**Geometry**Level 5

I have a 2D box in which I shoot a ball and it starts bouncing around the box infinitely. The starting shoot makes an angle \(A\) with the vertical:

Given that \[A=\arctan { (a+0.1b) } \]Where \(a\) and \(b\) are non-negative integers and \(a+0.1b\le 10\)

Find the maximum number of distinct points where the ball hits the box.

**Details and Assumptions**

The size of the ball is negligible

The collisions the ball makes with the box are elastic, that is, angle of incidence is equal to angle of reflection.

This case has \(4\) distinct points where the ball hits the box.