CONO-SUR 2006 Problem 6
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.
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Dataset text AI-MO AoPS. Quoted with source.
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