Sorry I have never seen a pool table which doesn't have friction nor have I ever seen a point in space at which time reverses
I can however also produce the effect a number of other ways such as lift the end of the table, have a wind blowing and dozens of other cases. I only need a tiny amount of constant force going the opposite way to the ball movement to create the result. So Bill S needs to wave his fairy god wand and tell me no such forces exist in our thought experiment.
Given the magic wand has acted then I can sort of guess how a pool table without friction would work by extending the laws of physics. If I extend the physics of a point in space with time reversing, the entire universe collapses in on the point for exactly the logic you worked out with the blue spot. Bluntly there is no way to stop the collapse unless you create a time horizon (relative, absolute or event horizon) but the result of the ball then differs completely to what Bill S gives as the answer.
I can't construct the result within the thought experiment and the fairy god wand and so all I can do is say to Bill S that his answer is impossible, which you also worked out.
Now I have no intention of starting another stupid conversation with you, and so I will leave you and Bill S to sort out the physics of time reversing points in your own special physics. Engaging ignore factor warp 10.
