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 friedlinguini)
Fried, I think Hank is correct since he is considering Infinite number of points lying on the circumference of the circle. Even if it consisted of alternating bands of blue and green then there must be at least one such pair of same colors which are unit distance apart and if in case the red color is there on the circumference, then the centre being red, there remains nothing to prove. I do not know if this reasoning of mine is correct.
re(2): Could be right
