Every point in 3D-space is colored either red, green or blue. Let R (resp. G and B) be the set of distances between red (resp. green and blue) points. Prove that at least one of R, G, or B, consists of all the non-negative real numbers.

(In reply to Solution (Some details required) by Bractals)

Nice one Bractals! There is however a minor gap in your proof, but I am sure you'll repair it easily:

How do you know that the set
sphere(N,b) ^ sphere(M,g) ^ sphere(L,r)
is not empty, in which case you would not arrive at a contradiction?

Posted by JLo on 2006-08-28 11:02:51