Several boxes are arranged in a circle. Each box may be empty or may contain one or several chips. A move consists of taking all the chips from some box and distributing them one by one into subsequent boxes clockwise starting from the next box in the clockwise direction. Suppose that in each move one can take the chips from any box. Is it true that for every initial distribution of the chips you can get any possible distribution?
I think this question is about process in combinatorics, but I don’t know how to simplify it. Please leave any suggestions you have, it will be really helpful.