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Spacy colors (Posted on 2006-08-25) Difficulty: 4 of 5
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.

See The Solution Submitted by JLo    
Rating: 4.0000 (2 votes)

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re(2): Solution (Some details required) | Comment 9 of 10 |
(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
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