Twentyseven 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
solution by Charlie)
The 12 edge pieces must be oriented to the edge with the painted
pair of faces is along the edge of the big cube, with probability, for
all 12:
(1/12)^12
Why is it 1/12?  I think that there are only 6 ways to orient a cube. All pieces are interchangeable with their same type  edges can be used in any edge spot, middles in any middle
For the faces:
(1/6)^6
and for the vertices:
(1/8)^8
Why is it 1/8  I think that there are only 6 ways to orient a cube.
All pieces are interchangeable with their same type  edges can be used
in any edge spot, middles in any middle, with only 1 orientation of the 6 working to complete the pattern.
Except the chewy center, which has no orientation preference and only one way to choose....
In all the probability is
12! * 6! * 8! / (27! * 12^12 * 6^6 * 8^8)
I get 12!*8!*6!*1/( 27! * 6^26)
can someone else settle this?
Cheers.

Posted by matt
on 20070404 14:09:17 