Coloring the Coordinate Plane

Appropriate Level:  Geometry and Beyond

The Warm-up Question:  If every point of the plane is colored either red or blue, do there necessarily exist two points of the same color that are exactly 1 unit apart?

The Question:  If every point of the plane is colored either red, blue, or green, do there necessarily exist two points of the same color that are exactly 1 unit apart?

Source:  The main question is part (a) of problem A4 of the 1988 Putnam Exam

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About Aaron

I like good math problems.
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