[seqfan] Re: How many configurations with n dots ?

[Felix Fröhlich]

I am not entirely sure I have understood the rules / physics of the game,
but by 'possible starting configurations', I assume you mean configurations
that are solvable under the given game physics, right? The physics appear
to be that a ball moves in vertical or horizontal direction until it hits
another ball, at which point it stops its movement. If that is true, then I
guess a configuration is solvable if there exists a graph with straight
edges on all balls starting positions and all the positions the balls move
to or something like that. That graph might also need to have some special
properties, like being a simple graph etc. Much of this are just guesses,
though, I would need to look at some things more closely.

Cheers,
Felix