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 re: Solution (Some details required)
They are points that exist in E^3 that our assumptions require, but our assumptions also show that they cannot have the colors red, green, or blue. Hence the contradiction.
Posted by Bractals
on 2006-08-27 20:13:52