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.

According to the grammar, the painter colored "all of the points" "one of three colors".... that seems like it would imply they are all the same color, and that he had three to choose from. If it had said "colored each of the points" it would mean how we've been discussing it. I am reminded of the same error in an old Eurythmics song "If I had a dollar bill for all the things I've done, there'd be a mountain of money piled up to my chin" (paraphrasing)

Let me know what everyone thinks. Also, there aren't enough puzzles being newly posted here.... I think I've solved most of these - is there some way to pick up the pace? I read that there are like 400 pending.

Later.

Posted by Ryan on 2003-05-07 18:38:50