In the figure below, we see a checkered billiard table and part of the trajectory of a ball, which is hit from one corner of the table, such that every time the ball hits one of the edges of the table, it continues its movement forming angles of $45^{\circ}$ with the edge.

(a) In which of the four pockets will the ball fall?

(b) How many times will the ball hit the edges of the table before falling into the pocket?

(c) The ball will follow the diagonal of how many of these squares during its trajectory?

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-005.jpg?height=323&width=399&top_left_y=2380&top_left_x=1431)
The ball changes the direction of its trajectory each time it hits one of the table edges. Since the trajectory always makes an angle of $45^{\circ}$ with the edge, the trajectory of the ball, hit from a corner, will always follow the diagonals of the squares it crosses. By tracing this trajectory, we conclude that (b) the ball will hit the edges of the table five times before (a) falling into the upper left pocket.

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-040.jpg?height=380&width=479&top_left_y=1969&top_left_x=1371)

Counting the squares crossed, we see that (c) it will cross 23 squares diagonally.