Twenty-seven identical white cubes are assembled into a single cube, and the outside of that cube is painted black.
The cube is then disassembled and rebuilt randomly.
What is the probability that the outside of this cube is again completely black?
(In reply to re(2): solution
whoops. forgot about rotation. I agree completely with your solution then.
4 orienations out of 24 work for the face centers = 1/6
2 orientations out of 24 work for the face edges = 1/8
3 orientations out of 24 work for the corners = 1/8
orientation for the cube center doesn't matter.
Posted by matt
on 2007-04-05 14:33:47