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)

If for x=1, all the vertices are red, and for x=2 all the vertices are blue? There may well be other tetrahedra with other colors, as would be required if the conjecture is true, but two or more points of the same color on one tetrahedron doesn't prove what's sought here.

Posted by Charlie on 2006-08-25 15:58:03