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

Since it is not defined exactly how the sphere is painted, one can take any three equidistant points (e.g. three points of the sphere lying on any plane intercecting the center of the sphere where the three points form an equilateral triangle).  Paint these three points either black or white.

Posted by hoodat on 2007-02-13 12:15:41