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Math Help - A rubik's cube wandering

  1. #1
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    A rubik's cube wandering

    If i could direct you ladies and gentlemen to here:

    Rubik's Cube -- from Wolfram MathWorld

    It states so far down the number of possible positions on the cube:

    8! 12! 3^8 2^12
    ------all over---------- =43 balzlillion and some more.
    2 x 3 x 2


    Anyway, does anyone know where that little sum has came from? I can't think of how to even approach it (whilst it is nagging me it may not be all that hard...)

    Thanks
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  2. #2
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    Quote Originally Posted by OnkelTom View Post
    If i could direct you ladies and gentlemen to here:

    Rubik's Cube -- from Wolfram MathWorld

    It states so far down the number of possible positions on the cube:

    8! 12! 3^8 2^12
    ------all over---------- =43 balzlillion and some more.
    2 x 3 x 2


    Anyway, does anyone know where that little sum has came from? I can't think of how to even approach it (whilst it is nagging me it may not be all that hard...)

    Thanks
    Notice you can simplify into 8! 12! 3^7 2^{10} (I wonder why they didn't do it).

    Quoting the wikipedia (I didn't check):

    The original (3󫢫) Rubik's Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving 3^7 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, since an odd permutation of the corners implies an odd permutation of the edges as well. Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 2^{11} (2,048) possibilities.[19] Finally, there are exactly
    permutations
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