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 Two Or Three ? by Ravi Raja)

A plane is a two-dimensional space. A three-dimensional equivalent is called a hyperplane. I think we can safely assume that the problem refers to a two-dimensional plane.

Posted by friedlinguini on 2003-05-01 06:02:43