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 Spacy colors (Posted on 2006-08-25)
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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 treja vu - solution | Comment 1 of 10

Choose a real number x.

Take any point in space and find three additional points that are each distance x away from the original point and distance x away from each other.  This should take the shape of a tetrahedron.

Two of these points will be of the same color.

Rinse and repeat for all real values of x.

Reminds me of a previous 2D problem

 Posted by Leming on 2006-08-25 14:54:16

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