A sphere is painted black and white. Show that there are 3 equidistant points of the same color.
(In reply to re: Solution
Let the five unpainted vertices adjacent to the five black vertices that are painted white be called b1, b2, b3, b4, b5.
Then A and b1, b3 are all white. Same with A, b2, b4; or A, b3, b5.
Likewise with the last, black vertex and a1, a3, etc.
Posted by Charlie
on 2007-02-14 14:21:18