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

(In reply to Underdefined solution by hoodat)

The assumption is that the sphere is already painted, by someone else, in some arbitrary manner, and the idea is to show that whatever that manner was, there must be three equidistant points of the same color.  You can't repaint it to make it that way.

Posted by Charlie on 2007-02-13 12:22:25