Xvii cono sur [argentina 2006] q6.
Source: Spanish Communities
May 11, 2006
analytic geometrycombinatorics proposedcombinatoricscono sur
Problem Statement
We divide the plane in squares shaped of side 1, tracing straight lines parallel bars to the coordinate axles. Each square is painted of black white or. To each as, we recolor all simultaneously squares, in accordance with the following rule: each square adopts the color that more appears in the
configuration of five squares indicated in the figure. The recoloration process is repeated indefinitely.
Determine if exists an initial coloration with black a finite amount of squares such that always has at least one black square, not mattering how many seconds if had passed since the beginning of the process.