Thursday, February 11, 2010

Not Exactly Rubiks Cube

Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black.  The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag.  A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube.  What is the probability that the outside of this cube is completely black?


  1. The probability that every type of cube is in the right place (0, 1, 2, & 3 black sides) is


    Then you must ensure that each cube is oriented correctly and each cube has 24 possible orientations. So the probability of that is


    Multiply the results of those together and you get the probability to be


  2. Woohoo, I got the same answer as Jay...

    (8!12!6!)/(27!) * (1/12)^12 * (1/8)^8 * (1/6)^6

    I'm just too slow with it.

  3. Did you think it was going to be so small when you started thinking about it?


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