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.

...to the case of n-dimensional space colored with n colors?

Bractals has found a proof which works fine in three dimensions, but will it work in higher dimensions too?

Posted by JLo on 2006-08-28 16:42:45