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.

Similar to the solution from '2 colors':
select a point 'x' then draw a circle around it with a radius of 1 meter.
there are an infinite number of points on the circle. one must be the same color.
(or something like that)

Posted by Hank on 2003-05-01 04:16:30