A painter went to a single mathematical plane, and colored every single point on that plane one of two colors.
Prove that there exist two points on the plane that are exactly one meter apart and have the same color.
(In reply to
solution by Charlie)
When I first thought of a solution, I began with a point and the circle around it (of radius one meter) which must be of different color than the center. Then pick any two points on that circle exactly one meter apart (a one meter chord), and of course, they're the same color.
It boils down to your triangle. I like your triangle better. :-P
re: solution
