Can you predict which pocket a snooker ball will fall into if it bounces at a 45 degree angle forever?

Question

A maths homework problem...

Imagine a snooker table marked out with squares... if the table is 4x5 and you roll a ball from the bottom left pocket at 45 degrees...if the ball keeps rolling, bouncing off the sides at 45 degree angles, can you predict which pocket it will fall into? We've worked out that it will take [(width + height) + 1] bounces to fall into ONE of the pockets, but we're trying to figure out if there's a formula to predict WHICH pocket the ball will fall into.

The formula needs to work for any size of snooker table. Assume the ball always starts from the bottom left pocket.

Any ideas?

Answer 1

No formula can predict that as with every table being a different size the calculated relief angles would bouce from different points along the rails, therfore making it impossible for any equations to accurately measure or predict which pocket the ball would fall.

But if you were only using one size table all of the time, then yes your simple calculated equation would work fine.

Answer 2

Diophatine equations.