Problem: Marbles Game

[•Cosmin]

http://www.infoarena.ro/blog/cups-and-marbles

[•klamathix]

You mention you might end up putting a marble in the original bin, but it's not clear if you can wrap around the circle multiple times. In other words, is M <= N?

[•andreitheo87]

I tried looking for an invariant but then I noticed that from any position I can transition to a configuration where all the marbles are in the first bin (so I cannot easily eliminate any combination). If I could only find a way to go backwards from any position to the same "everything in one bin" configuration that would be great...

Mihai, I believe that having no limit on M makes the problem more interesting (and harder). Do you already have a solution for M <= N?

Later edit: for M <= N it is possible to create one big stack of marbles in one bin, distribute them and then take them one by one (from "right" to "left" modulo N) to form the second pattern.

[•klamathix]

@Andrei: Yes, that was the big picture I had in mind for M <= N. I don't have anything for M > N, at least for now.