The Mazoyer Firing Squad
Page 65 of Feynman's Lectures on Computation introduces a problem of message passing. A 1D line of cells can only influence neighbors to each side. One cell is turned on, and all cells must reach an identical "firing" state. The nearest-neighbor character of this problem makes it soluble by means of cellular automata. This Demonstration uses a 7-color rule that would be about in base 10 (see the program for the exact value).[more]
The problem was first proposed by John Myhill in 1957, and first solved by John McCarthy and Marvin Minsky in 1962.[less]
 R. P. Feynman, Lectures on Computation, Boulder, CO: Westview Press, 1996.
 S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media, 2002 p. 1035.
 Wikipedia. "Firing Squad Synchronization Problem." (Nov 26, 2012) en.wikipedia.org/wiki/Firing_squad_synchronization _problem.