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.

I believe it is impossible to prove the existence in a plane. One would need three dimensions and a tetrahedron in order to prove it in 3 dimensions. But in the in the 2-D case, it is impossible...

Posted by DuCk on 2003-05-01 08:08:40