The Monochromatic Column problem

Let p1, p2,..., pn be a sequence of n pairwise coprime positive integers, and let P = p1p2...pn. Let 0, 1, ...,m − 1 be a sequence of m different colors. Let A be an n ×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. The solution for m = 3 colors is presented and proved.