First of all the puzzle.

A barman's got 15 glasses which are initially somehow divided into several stacks. The barman repeats the following process a thousand times. He takes the top glass from each (nonempty) stack and forms a new stack with these glasses. Which set of stacks (in terms of their heights) will he come up with?

It's a nice one, give it some thought =)

Having toyed with this problem and its obvious generalizations for an arbitrary number of glasses I came up with the (totally intuitive) hypothesis that such a process and its long-term behavior might emerge in some more-or-less advanced field of research (algebra/geometry/mathematical physics). Can anybody comment?

**Update.** One can also notice that in this special case of 15 glasses both the problem's statement and the answer are pleasantly simple. I'd be very interested and even somewhat surprised to hear an accordingly simple proof.

The College Mathematics Journal. Among other things, it gives a detailed history of the problem and how it came by its name. – Barry Cipra May 15 '12 at 15:35