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 treja vu - solution by Leming)

> Rinse and repeat for all real values of x.

How can you be sure that the colour which occurs twice in the tetrahedron will be the same each time?

Posted by vswitchs on 2006-08-25 15:50:15