Discussion: This is an elegant solution to both parts using the pigeonhole principle. The student draws enough horizontal lines so that any vertical line intersect in one more point than colors and therefore two points have the same color. The number of possible patterns is finite, namely, N= n^{n+1}, since each point has n possibilities for its color. Then if one constructs N +1 vertical lines for two the pattern is the same and since two of the points of intersection of such vertical lines have the same color this yields a rectangle with its vertices all the same color.

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