Imagine that a painter went down to a mathematical plane and colored all of the points on that plane one of three colors.

Prove that there exist two points on this plane, exactly one meter apart, that have the same color.

(In reply to Could be right by Hank)

Your reasoning is flawed. Assume the center is Red. The circle can consist of all Green and Blue points.

Posted by Brian Smith on 2003-05-01 04:54:27