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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.

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  • $\begingroup$ I hear that Knuth studied it as well; can anyone provide a pointer to Knuth's article? $\endgroup$ Nov 14, 2014 at 2:23

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The problem is due to Elias Wegert, see Relaxation procedures on graphs .

This blog post discusses the problem.

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