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) by JLo)

The only way that 

  sphere(N,b) ^ sphere(M,g) ^ sphere(L,r)

would be empty is if b is greater than the
diameter of the space circle

  sphere(M,g) ^ sphere(L,r)

This would occur if

  b > 2h,
  g^2 = x^2 + h^2, and
  r^2 = (r-x)^2 + h^2

or

  b > g*sqrt(4 - [g/r]^2) > g

A contradiction since b <= g.

Posted by Bractals on 2006-08-28 16:17:34