A painter went to a single mathematical plane, and colored every single point on that plane one of two colors.

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

Choose any equilateral triangle on the plane, with sides equal to one meter. As there are only 2 colors to go around, two of the vertices must lie on points of the same color and are one meter apart.

Posted by Charlie on 2003-04-27 04:08:59