Hans Zantema: The paint pot problem and common multiples in monoids

Event Details

On a finite sequence of paint pots the following steps are allowed:

* Swap two consecutive non-empty pots.

* If the two neighbours of a non-empty pot are empty, then divide the paint in the middle pot over the two neighbours, after which these neighbours will be non-empty and the middle one will be empty. Also the reverse allowed: if an empty pot has two neighbours of the same color, the paint of these neigbours may be put in the middle pot.

Is it possible to start by a sequence in which the first four pots contain paint in four different colors, and get the first pot empty?

We will solve this remarkably hard problem by a remarkably simple solution, and show its relation with monoid theory, and give generalizations of this problem, partly solving an open problem presented by Jan Willem Klop.