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Paint it black (Posted on 2007-04-02) Difficulty: 3 of 5
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?

See The Solution Submitted by Federico Kereki    
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re: Too big numbers | Comment 4 of 9 |
(In reply to Too big numbers by Old Original Oskar!)

" There are 27! ways of placing the cubes in their places, times 24 ways of orientating them: T= 27! x 24."

That should be 23^27, as each cube is oriented independently. The same goes for the other parts of edges, vertices, faces, giving 12!*3^12, etc.

Your final number, 2/(27 x 25 x 23 x 19 x 17 x 13 x 13 x 11 x 7) = 3.06491500046902 * 10^-11, is very small, but the actual result should be closer to 5*10^-36, much smaller.

  Posted by Charlie on 2007-04-02 22:12:46

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