# 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.

>

>