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Group theory and Rubik's cube

  1. Jul 19, 2005 #1
    I've always been fascinated by Rubik's cube. I have developed solutions for it and
    all the related cubes 2x2, 3x3, 4x4, 5x5. For me the cube it is to group theory
    (of a partcular type of group) what a slide rule is to real arithmetic. Even "laboratory"
    might not be too stong a label for it.

    For example it's immediately obvious how [tex] xy \neq yx [/tex]. If you turn the front of the cube
    and then the right you get a very different set of faces than the right followed by front.
    Also, you can discover marvelous "operators" (my terminology) by doing some random
    series of twists (abc) followed by a particular twist (Z) then undoing the first
    twists (via cba), that is: abcZcba where the letters stand for some particular oriented
    twist. What happens is that most of the cube is unperturbed except for some
    marvelous little permutation like a twisted corner in place or three swapped edges.

    My solutions then consist of applying these "operators" in sequence by inspection
    to see which one is "needed" next.

    Alas however, I am not formally trained in group theory and I would like
    to know: How would one go about using GT to develop a more effective
    or efficient solution to something like Rubik's cube? I know it has been
    done, but my question is very specifically: Can anyone explain to the group theory novice
    (but Rubik's cube expert) how one would actually go about using GT to
    devise (more) efficient solutions to such a puzzle?
  2. jcsd
  3. Jul 19, 2005 #2

    matt grime

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    find the book by dik winter.
  4. Jul 19, 2005 #3
  5. Jul 19, 2005 #4
    Hello Antiphoton,

    you could contact Chris Hardwick, he is a speedcuber and interested in math too. Go to
    www.speedcubing.com > Chris Hardwick's Corner > at the bottom is his e-mail.

    Also try the Yahoo Speedcubing group. I'm sure there are also some math interested people there:
    (You have to sign up and join the group).

    P.S. By the way, what's your 3x3 average time?
    Last edited: Jul 19, 2005
  6. Jul 19, 2005 #5
    Never really measured it, but I think maybe 1+ minutes. I'm more interested
    in optimality (number of turns) and coming up with novel
    operators (i.e. combinations of turns which do something interesting.)
  7. Jul 19, 2005 #6
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