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(2): Could be right by Ravi Raja)

Specifically, if the center is red, the circumference could be alternating 60 degree arcs of blue and green, with the counter-clockwise-most point included (a closed endpoint) and the clockwise-most point excluded (an open endpoint). None of the points on the circumference 1-meter apart would be the same color and the center is a different color altogether.

Posted by Charlie on 2003-05-01 05:24:13