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).
The problem was first proposed by John Myhill in 1957, and first solved by John McCarthy and Marvin Minsky in 1962.