Andrei Dragus told me this cute puzzle a year or two ago.

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

M marbles are placed in N cups which 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).

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).

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

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

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