# Solving Twisty Puzzles with Commutators



## Vincents (Oct 25, 2011)

Last Thursday, Nan Ma gave a short lecture on Solving Twisty Puzzles with Commutators during the Rubik's Cube DeCal at UC Berkeley. Here's the video; it's highly informative. Thanks again to Nan.





(Ignore my announcements at the beginning; they're not relevant.)


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## Ranzha (Oct 26, 2011)

Finding that 3-cycle comm for FTO was a pain >_>
If only I had this video as an aid! xD
Great vid, Vincent. Very informative! =O


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## Stefan (Oct 27, 2011)

Very nice lecture. The introduction with all those puzzles reminded me what lazy noob I am, and the main part explained commutators well. I especially liked the visualizations of the supports. Only complaint I have is that his key theorem is wrong - if the support overlap is one piece, the commutator is *not* always a 3-cycle:
[R' E' R2 E2 R', U']
I also like orienting this way better than using two 3-cycles, feels more direct/pure/natural. Wish he had at least shown that possibility quickly. On the other hand, his way might be easier with really complex puzzles where I can't just intuitively make up something like R' E' R2 E2 R'.


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## Vincents (Oct 27, 2011)

Yeah, I know there was a lot Nan wanted to talk about, but we were limited to approximately 40 minutes, with an audience that had just learned to solve the cube. Some other things that were left out include exactly what you mentioned, Stefan; as well as example solves of different cubes. I'll pass along your suggestions, though!


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## Stefan (Oct 27, 2011)

So make a second lecture . I'd also like to watch him talk about the "remotely connected pieces" and "hidden orientation" he mentioned in the end. I think I roughly know what he means, but I'm not sure and there's probably a lot I could still learn.

Btw, the inventors in the audience, do they live there or did they come from farther away for the lecture? Quite neat that they were there.


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## schuma (Oct 28, 2011)

Stefan said:


> Only complaint I have is that his key theorem is wrong - if the support overlap is one piece, the commutator is *not* always a 3-cycle:
> [R' E' R2 E2 R', U']
> I also like orienting this way better than using two 3-cycles, feels more direct/pure/natural.


 
Hi I'm Nan Ma. Nice catch! Actually I would say the theorem is not wrong but I phrase the definition of "support set" wrong. I should say supp(X) is the set of pieces MOVED by X not CHANGED by X. Flipping a piece in place is "changing" but not "moving". I found it the day after the lecture but it was too late. I should've clarified it in the lecture. My only hope is that, in my first example of supp(U), I made it clear that it didn't include the center. Because the center is not super stickered, the rotation is not notable. So people may interpret my words in different ways. And I can only hope people would understand it the way I intended.

I know your way of changing orientations and I use that technique. I avoided it simply because I want to minimize the details to the audience. I believe for a beginner who just learned how to solve the Rubik's cube, this is already overloaded. This is just a style of teaching.


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## schuma (Oct 28, 2011)

Stefan said:


> So make a second lecture . I'd also like to watch him talk about the "remotely connected pieces" and "hidden orientation" he mentioned in the end. I think I roughly know what he means, but I'm not sure and there's probably a lot I could still learn.
> 
> Btw, the inventors in the audience, do they live there or did they come from farther away for the lecture? Quite neat that they were there.


 
By "remotely connected pieces" I mean something like the small circle edge pieces in Circle 4x4x4 type-II, some one calls them "virtual pieces" but I don't think that term is explanatory. By hidden orientation I mean the puzzles that can only be solved under certain assumptions of the global orientation. The void cube is one example, half of the orientations are allowed. But for some edge turning dodecahedra puzzles only one orientation is correct and you have to deduce it from a lot of other pieces in the beginning. If you don't find it in the beginning and start solving you are going into a dead end. I know my description here is not so clear. Let me know if I need to expand on it.

All my guests are living in the san francisco bay area. I know them from the forum of twistypuzzles.com, and the MC4D Yahoo group.


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