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Suppose that each of the small squares of a 4-by-n chessboard is to be colored either green, red or yellow, and that the coloring

Suppose that each of the small squares of a 4-by-n chessboard is to be colored either green, red or yellow, and that the coloring is to be done in such a way that none of the rectangles consisting of 4 or more of the small squares has the same color in all of its 4 corners. What is the maximum possible value for n? Why?

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