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.

Because the painter has three colors, he would have to have two points next to eachother. Now, any way he would have painted it, the points would have been touching, because it probably would have been triangulated with a formation, if he did not place a color side by side. Because a triangle has 3 points, the first color would have had to touch another because its vertex would be one meter away from the other. If it was not made in triangles, than the painter would have intentionally tried to make colors match, unless he was retarded.

Posted by Chaz on 2003-05-02 13:19:00