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MathNet 2011 Question 73

Math Olympiad Vault · MathNet 2011

Question 73

The chromatic number of the (infinite) plane, denoted by $\chi$, is the smallest number of colors with which we can color the points on the plane in such a way that no two points of the same color are one unit apart.
Prove that $4 \leq \chi \leq 7$.