A sphere is painted black and white. Show that there are 3 equidistant points of the same color.

(In reply to Solution by Joel)

How about this painting of the icosahedron.

Let vertex A be white and each a1,a2,a3,a4,a5 be black.

Let the five unpainted vertices adjacent to these five black vertices be painted white and the last vertex be painted black.

Which three of these are painted the same color?

Posted by Bractals on 2007-02-14 13:16:25