The numbers game is a (one-player) game played on a finite graph with an initial assignment of numbers to its vertices, studied by Alon, Bj\"orner, Brenti, Donnelly, Eriksson, Krasikov, Mozes, Peres, Proctor, Wildberger, and probably others as well (see <http://arxiv.org/abs/math/0610702> for a detailed bibliography). It grew out of a problem that appeared in the 1986 International Mathematics Olympiad, in which the graph is the 5-cycle. But who came up with the problem, and why?


I am particularly intrigued by something Yuval Peres told me today, namely, that the original solution (unlike all the other solutions I'm familiar with) works only for the 5-cycle, and not for $n$-cycles in general.



Origin of the numbers game
The problem is due to [Elias Wegert](http://www.mathe.tu-freiberg.de/ana/mitarbeiter/elias-wegert), see [Relaxation procedures on graphs](http://www2.math.ou.edu/~jalbert/putnam/DAM6960.pdf).


[This blog post](http://mattbakerblog.wordpress.com/2014/02/25/the-pentagon-problem/) discusses the problem. 


