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.

Bracket the statement into " colored (every single point on that plane){meaning the entire plane} (one of two colors)" Assume that (one of two colors) means one color from a possible selection of two, so the painter either painted the entire plane green, or the entire plane red (or whatever colors you want). Then the entire plane is the same color and any two points exactly one meter apart will be the same color.

Posted by jamie on 2003-08-30 02:52:30