Message #434

From: Jenelle Levenstein <jenelle.levenstein@gmail.com>
Subject: Re: [MC4D] Doing a class presentation on Rubik’s Cube and Group Theory… suggestions?
Date: Wed, 14 Nov 2007 10:17:58 -0600

If all you want to do is make a program solve a rublix cube you could
always solve it using the brute force method where you try all
possible combinations of moves until the you find the solution. This
works on the 2^3 and maybe on the 3^3 and only because the cube is
always within about 15 moves of being solved.

On 14 Nov 2007 10:27:02 +0000, David Vanderschel <DvdS@austin.rr.com> wrote:
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> On Tuesday, November 13, "iatkotep" <iatkotep@gmail.com> wrote:
> >I’ve never solved a rubik’s cube. the idea for my
> >presentation is to take the techniques that I’m
> >learning in my abstract algebra class, and use them
> >to derive a solution to the cube.
>
> Good luck! I would be surprised if you succeed in
> this venture; but it will be an impressive achievement
> if you do succeed.
>
> Yes, Rubik’s Cube is a good example of a non-trivial
> group.
>
> You might want to start with a simpler permutation
> puzzle - like the 2x2x2 analogue of Rubik’s Cube.
>
>
> >I want to extend that to also deriving a solution to
> >the 4D Magic Cube.
>
> If you do succeed for the 3D puzzle, then extending
> for the 4D puzzle should not be so hard. Aside from
> the fact that there are a lot more pieces to fool
> with, there is a sense in which manipulating the 4D
> puzzle is actually easier than the 3D puzzle.
>
>
> >I’m at the beginning now… I know what properties of
> >the cube make it a mathematical group, but that’s as
> >far as I’ve gotten. I have a strong feeling that
> >jumping from the cube as a group to a full blown
> >solution involves the study of subgroups, but I’m not
> >really sure where to start.
>
> There is plenty of information out there which
> addresses the puzzle from the Group Theory point of
> view. The source of this sort to which I have paid
> the most attention is W. D. Joyner’s Web page here:
> http://web.usna.navy.mil/~wdj/rubik_nts.htm
>
>
> >do we have any math people in there that could kind
> >of point me in the right direction?
>
> The truth of the matter is that every method I have
> ever seen for working Rubik’s Cube approaches it from
> a rather empirical point of view. There are some
> important facts about what you can and cannot achieve
> that are implied by the theory, but you don’t really
> need to know the theory to take advantage of the facts
> themselves. (Indeed, the facts can eventually become
> apparent even without having known about the theory
> which implies them.)
>
> I first laid my hands on a Rubik’s Cube in 1979. I
> was actually pretty well trained in Group Theory at
> the time, and I did realize that the puzzle could be
> regarded as a representation of a group. However, my
> knowledge of Group Theory played little role in my
> figuring out how to work the puzzle. I suppose it did
> lead me to try things like commutators and
> conjugation; but I probably would have done so even if
> I had not known what such operations were called in
> Group Theory.
>
> Regards,
> David V.
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