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 re: Could be right by Brian Smith)

Infinite is all encompassing.
Assuming red is the center point.
Can you prove that red is not on the circle? Or the the circle is only made up of green and blue? Keep in mind that there are an infinite number of point on the circle. (seriously, I am curious if this can be proved)

Posted by Hank on 2003-05-01 05:29:46