My old school, Saint Ann’s, in Brooklyn Heights, has an ongoing problem of the week competition for its middle schoolers. The problems tend to be fun, and require a little more thinking (and explanation) than most standard math problems, and the teachers have fun brainstorming new ones.
This one is pretty cute, and I think you can solve it if you want to. On the front of asking good questions though, I think there are some pretty interesting followup questions you could ask about this problem. The main one is, what happens to the ball after it hits the right side of the table? It will keep bouncing around the table, but will it ever go into the corners? Will it ever hit its starting position again?
Following these questions up, you can start to vary the size of the table and the angle and placement from which you shoot the ball in the first place. I suspect there’s a whole theory of how the ball bounces around the table that is elegant and satisfying. You just have to follow the initial question with a few more of your own.
Anyone else have any thoughts on good questions to ask about the billiard ball bouncing problem in the link?