Problem: Marble Game

Cosmin Negruseri
31 ianuarie 2016

Andrei Dragus told me this problem on a road trip a year or two ago.

M marbles are placed in N cups. The N cups are arranged in a circle. One move consists in choosing a cup, taking all the marbles within that cup and placing them one by one in the following cups in clockwise order (since the cups are in a circle you might end up putting marbles in the original cup as well).

How can we tell given two placements A and B of marbles in cups, if we can reach B starting from A.