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
Could be right by Hank)
Says who? Say the center point is red and that the circle is drawn in alternating bands of blue and green such that no blue point is exactly one meter from a green point (I don't know if this is possible, but that's not the point). The proof of this is going to be harder than the two-color variation.
re: Could be right
