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problem 8 consider an infinite grid in the plane and...

Question: problem 8 consider an infinite grid in the plane and...

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Problem 8. Consider an infinite grid in the plane, and color every intersection with either red, green, or blue. Prove that for any possible choices of coloring, there always exists a rectangle in the plane such that al four of its vertices are the same color. Figure 3 depicts a piece of such a grid with a reetangle with red vertices. FIGURE 2. A piece of the grid colored with green, blue and red, and a yellow rectangle inside it with four red vertices

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