# Interest in a BH method website?



## cmhardw (Mar 27, 2009)

Daniel and I have both been very busy lately, though most of the information for a BH (Beyer-Hardwick) blindfold method website is already created. Daniel has written most of the material already, and I will compile it into a site and fill in any remaining gaps to be filled.

Is there much interest for a single website with a description of the BH method? I believe most of the algs are able to be found already, but if there is interest in a site I will try to dedicate more time to actually trying to publish this. I know Daniel is busy, but if there is a lot of interest he might be able to help too.

Chris


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## Ellis (Mar 27, 2009)

I chose indifferent. I would definitely do a full read through of the method, I'm kind of stuck on the 4x4 bld, but it isn't something I'm dying for because I've already read the a lot of stuff on it. This is something I would have liked a while back, but it would still be kinda neat to have it all in one place.

Edit: I just want to be clear, this is personal interest. If the question had been rather "should this website be made", I would definitely say yes, I see no reason for it not to be.


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## Kian (Mar 27, 2009)

Chris, I think this is a fantastic idea. I'd love to see it and give it a try!


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## Mike Hughey (Mar 27, 2009)

I already have the algorithms stashed away on my computers, but of course you should put a website together if you get the chance! I'm sure it will catch on soon, so you might as well have a website ready for all the people who will start flocking to it as world records are set with it. 

I'm looking forward to starting to get serious about learning BH corners next week!


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## MatsBergsten (Mar 27, 2009)

Yes, I would be interested. There's always a chance to improve


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## dChan (Mar 27, 2009)

I am highly interested as, to be honest, I have no idea how the BH system works at all and since seeing your world record I have been very interested in at least gaining an understanding of it if not learning it.


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## Lucas Garron (Mar 27, 2009)

YES! Data-harvestin' time!
(We get $0.10 for each error found, right?)

Your main consideration for the site, I think, shouldn't be if someone wants it, but if someone will use it or if it inspires someone. Compare it to ZB - almost no one uses it, but it's often-discussed and has influenced other ideas. (And you end up with useful alg-subsets.)


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## Mike Hughey (Mar 27, 2009)

I know this wasn't really your point, Lucas, but I would like to point out that I don't think BH is anything like ZB. BH is MUCH less effort to learn than ZB (believe it or not, it's true!), and it has many applications to other events, such as fewest moves. I suspect there will be an explosion of use of BH after a while, as people learn better and better ways to teach it. I'm guessing that if you're really committed to it, you could learn all of BH for the 3x3x3 (probably not fluently and quickly, but enough to do a decent job with it) in a month or two.


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## Swordsman Kirby (Mar 27, 2009)

Zhuang Haiyan already uses it (with different starting pieces, though)


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## TheBB (Mar 27, 2009)

Personally, no. I don't need or want a site, just the algs.


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## Feanaro (Mar 27, 2009)

Yes! Do it! This is a great idea. This will help me blind big cubes better.


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## TheBB (Mar 27, 2009)

I don't think it will, unless I've completely misunderstood (in which case, please, go ahead and make the site).


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## deadalnix (Mar 27, 2009)

I was wrtting some stuff on your method. "Was" because a loose everything yesterday.

So I'm more than interested !


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## ManuK (Mar 27, 2009)

I'm interested.Hope you find time to put up the site soon.


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## SimonWestlund (Mar 27, 2009)

Definitely intrested!


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## rachmaninovian (Mar 28, 2009)

centres comms wld be fun...=P


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## Jacco (Mar 28, 2009)

I'm interested.


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## Neroflux (Mar 28, 2009)

didnt you already have a funny website with alot of algs?


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## JohnnyA (Mar 28, 2009)

Is there any documentation at all on this BH method? This is the first I hear of it and if it does have possibilities for FMC as said earlier, I would be very interested.


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## cmhardw (Mar 31, 2009)

Hi everyone,

I had no idea this many people were interested in a website about the method. Daniel is on vacation now, and is also busy with school so right now it's just me until he gets some free time.

The publication order, so far, will go like this:

1) BH corners (algs only)
2) BH edges (3x3) (algs only)
3) BH 3x3x3 method - explanation of how to apply the method in practice (definitely NOT just by memorizing all the algs, it's much easier than that)
4) BH x-centers? BH wings (4x4 and 5x5 edges)? Which would people prefer first?
5) The other one from group 4.
6) BH +centers for 5x5.
7) extension to n x n x n cubes.

I'll try to give updates on how far I am. So far I'm maybe 33% done with part 1 above of the site.

Chris

P.S. Lucas, Daniel and I have tried as hard as possible to avoid any typo errors, but I think there still might be some. I can't offer money for each error, but please post any errors you see if you find them *crosses fingers to hope we caught them all already* ;-)


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## deadalnix (Apr 1, 2009)

I'm most interested in :

1) Because of some non trivials cases.
3) Especialy dealing with parity and inactive pieces (well placed but wrongly oriented)
4) In my oppignon, BH is very powerful for big blind. The center safe resolution of corner is a great stuff to memorise them in last and solve them in first. 4x4x4 is the most important of big cubes (you should know how to blind 4x4x4 to succed with 5x5x5 and bigger ones).

Then come 1) and 6) to apply BH on 3x3x3 and 5x5x5.

7) Realy interest me. But I think it shouldn't be presented before more practical stuffs.

I don't understand the 5) point.


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## cmhardw (May 4, 2009)

Today we go LIVE!

Daniel and I are very excited to announce the first installment to our BH method website. This page is a small fraction of what we hope to be a very extensive resource to our blindfold solving method.

You will now have a list of one algorithm for all corner cases, as well as our naming scheme for all corner cases.

The edges page is soon to follow. After that we will include a page describing how to use the case names to construct the correct algorithm during a solve, so that you don't have to view this method as merely memorizing hundreds of algorithms (it is NOT that hard!).

Post comments and feedback here! We are very excited to have the first page up and running!

http://www.speedcubing.com/chris/bhcorners.html


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## byu (May 4, 2009)

Yes! Thank you!


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## Pedro (May 4, 2009)

Wow!

That's nice!

thanks a lot, Chris and Daniel


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## ShadenSmith (May 4, 2009)

Awesome guys, I can't wait for the rest of the site!


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## Mike Hughey (May 4, 2009)

I think it's useful to note at this point that, if it is really true that Haiyan Zhuang uses BH, it is now true that 3x3x3, 4x4x4, and 5x5x5 BLD world records are all currently held by people using the BH method!


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## a small kitten (May 4, 2009)

I'm pretty sure Haiyan uses BH. It's quite insane. lol


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## deadalnix (May 4, 2009)

You have explained somewhere in this forum Your différents notation (A9, toss up, drop and catch, etc . . .), but I can't find it.

Someone know where a can find it ?

EDIT: why have you choosen URB as a buffer ?


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## cmhardw (May 4, 2009)

deadalnix said:


> You have explained somewhere in this forum Your différents notation (A9, toss up, drop and catch, etc . . .), but I can't find it.
> 
> Someone know where a can find it ?
> 
> EDIT: why have you choosen URB as a buffer ?



This link is sort of pre-full BH, and the names have changed a little bit since then, but here is an explanation of some of the terms. Daniel and I had been communicating by this point on the algorithms for bigger cubes, but I don't think we had really started trying to move this over to 3x3x3 yet which is why we aren't using optimal commutators on the Per Specials. Also there is no mention of the columns cases or the cyclic shifts or orthogonals.

http://tinyurl.com/dm5frt

The reason we chose URB as a buffer is that Daniel uses URB and compiled all the 3x3x3 algs together into his .txt files. We also figured that UBL might be less common than URB. I'm not sure if this is true now that some people have mentioned they use UBL, but regardless we decided on URB and UR for corner and edge buffers for our algorithm lists.

If you need to reflect algorithms over the RL plane to the UBL buffer this might help:

http://tinyurl.com/cl3344

Chris


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## tim (May 4, 2009)

cmhardw said:


> We also figured that UBL might be less common than URB. I'm not sure if this is true now that some people have mentioned they use UBL, but regardless we decided on URB and UR for corner and edge buffers for our algorithm lists.



I think the complete opposite is true, since I don't know any method which uses URB as a buffer. And Classic Pochmann uses ULB as a buffer.

Anyway, mirroring the list shouldn't be a problem at all. If someone's interested, i could hack a small script to do the work.


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## deadalnix (May 4, 2009)

In fact, I use FRU as buffer. I wonder if it's a good choice or if I should switch for UBR (or UBL).

Symetries isn't a problem (for me as least). the questions wasn't related to the algs.

But I think UR isn't a good choice for edges. It lead to many S slice turn, with are not easy to do. Why not an M slice buffer ?


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## Pedro (May 4, 2009)

I use UBL and UF when I do freestyle

I don't use a buffer, though. I just move to a new unsolved piece when UBL/UF gets solved


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## tim (May 4, 2009)

I had some time and mirrored the corner algs (new buffer: UBL). I attached the list to my post.
And here's the ugly code which did the job.


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## Pedro (May 4, 2009)

thanks, Tim

can you make it a html page? (txt can look UGLY sometimes )


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## tim (May 4, 2009)

Nope, sorry. And there's no difference between a text file and a nicely formatted html page. You have to use CTRL+F anyway.


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## puzzlemaster (May 4, 2009)

i'd be interested in seeing how many cases there would be for solving a 3x3 blindfolded.


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## MistArts (May 4, 2009)

puzzlemaster said:


> i'd be interested in seeing how many cases there would be for solving a 3x3 blindfolded.



Maybe the same amount as the number of positions of a Rubik's Cube?


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## puzzlemaster (May 5, 2009)

MistArts said:


> puzzlemaster said:
> 
> 
> > i'd be interested in seeing how many cases there would be for solving a 3x3 blindfolded.
> ...



no for example on his site he has 300 something for the corners which should be the same as for a 3x3.. however for the edges naturally there will be a lot less... i am curious to see the full number for all of these algorithms... it's based off of commutators correct?


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## Pedro (May 5, 2009)

why less cases for edges?
corners have 24 stickers (8*3) and edges too (12*2)


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## Stefan (May 5, 2009)

puzzlemaster said:


> for the edges naturally there will be a lot less


Try again.

Alright, alright. More constructive...
Explain the 378 for corners.


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## puzzlemaster (May 5, 2009)

StefanPochmann said:


> puzzlemaster said:
> 
> 
> > for the edges naturally there will be a lot less
> ...



Wait, will there be the same amount of edge cases as all the edges can be solved using the same algorithms but on big cubes one would just turn the layer that it is in? Wouldn't the number of cases for the corners also remain the same as the number of stickers on a given corner doesn't change. The pieces will have the same number of cases. If this isn't the case, can someone please explain why not?


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## Stefan (May 5, 2009)

I repeat: Explain the 378 for corners. It's really easy. And then you'll have your answer and a better understanding.


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## blah (May 5, 2009)

tim said:


> I had some time and mirrored the corner algs (new buffer: UBL). I attached the list to my post.
> And here's the ugly code which did the job.





Pedro said:


> thanks, Tim
> 
> can you make it a html page? (txt can look UGLY sometimes )



C'mon I used _Notepad_ to mirror everything to my UFL buffer a looong time ago. I'm not saying Tim's work is useless; I'm just saying people should try putting in some effort to do their own work rather than making "kind requests" to others to do the work for them.


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## tim (May 5, 2009)

blah said:


> tim said:
> 
> 
> > I had some time and mirrored the corner algs (new buffer: UBL). I attached the list to my post.
> ...



Search & Replace? And how did you avoid cyclic replacement (R => L' => R)?


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## blah (May 5, 2009)

tim said:


> blah said:
> 
> 
> > tim said:
> ...



First replace with random stuff like XYZ. Couldn't have took me more than 10 minutes, really.


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## puzzlemaster (May 5, 2009)

StefanPochmann said:


> I repeat: Explain the 378 for corners. It's really easy. And then you'll have your answer and a better understanding.



Well the number of corners doesn't change and neither does the number of possible positions as all cubes have the same number of possibilities for corners.


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## deadalnix (May 5, 2009)

Try calculation now instead of useless considerations


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## puzzlemaster (May 5, 2009)

then i guess i can't explain it then.


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## Ellis (May 5, 2009)

oh cmonnnn, it's so easy that even I could figure it out. Think about all the possible cycles with a fixed buffer.


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## Stefan (May 5, 2009)

puzzlemaster said:


> then i guess i can't explain it then.


Way to show your puzzlemaster skills. Spoiler:


Spoiler



378 = 21 * 18
I'm *not* going to explain any further.


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## cmhardw (May 5, 2009)

Update: Ok everyone, I have this Thursday off from work so I will be working on getting the 3x3 edges page up. Barring any weird unforseen circumstances the edges page will be up on the site by the end of the night Thursday (EST). After that I might take a couple days to put together the site explaining the 3x3x3 method. After that the bigger cubes pages will take longer. I had been working on the alg lists for the larger cubes, but the hard drive I was working on died. This means I have to make those pages and algs lists from scratch. Daniel might still have some of the files he started working on, so I'll get those from him first and try to post what I can as I can.

For the bigger cubes (wings and centers) do people want partial lists posted, which Daniel and I update a little bit from time to time? Or would you rather just have full pages posted when they're completed?

Chris


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## Lucas Garron (May 5, 2009)

I like applets. 

(Also, I recommend CSS)


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## cmhardw (May 5, 2009)

Lucas Garron said:


> I like applets.
> 
> (Also, I recommend CSS)



Wow! Lucas, if you can send me a copy of the HTML code that links to all those applets I'll make that the main page on my site (with due credit to you of course). Those applets are great! Let me know if you don't mind me doing this and I'll update the page to be your version, that looks great!

Chris

--edit--

If there a way to setup the applets so that they already have the inverse of the algorithm applied as the starting state? This way, upon completing the execution of the algorithm the cube will be solved. Even knowing the algorithms already, it takes a second of recognition to watch the alg being played and track what it's doing.


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## Mike Hughey (May 5, 2009)

Lucas Garron said:


> I like applets.
> 
> (Also, I recommend CSS)



I recently suggested to Chris that he have an option to choose a buffer sticker, and then reorient the algorithms based on the buffer sticker. And also it would be nice to have the ability to assign a label to each piece, so instead of seeing (URB UBL ULF), you could see (B A D) or whatever your lettering scheme is.

I was offering to try to do it someday, but Lucas, I bet you could throw that together in a matter of minutes. Might you be willing to do that for Chris? I know he'd appreciate it.


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## cmhardw (May 6, 2009)

cmhardw said:


> Lucas Garron said:
> 
> 
> > I like applets.
> ...



Oh the dangers of posting messages at work when I should be working.

[Paraphrase]
Hey Lucas, you know that HTML file you just posted online? Yeah, if you can get me a copy of that file, the one you already posted online, then I can update my page with it!
[/Paraphrase]

I'll update my site soon to show the links to the applets. Thanks again Lucas!

--edit--

@Mike and anyone interested
Anyone who knows how to do this, if you can provide the code I will certainly add it to my page. I think the ability to do this would be amazing for those trying to learn a personalized version of BH, rather than using the standard buffers we have chosen.


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## Lucas Garron (May 6, 2009)

cmhardw said:


> If there a way to setup the applets so that they already have the inverse of the algorithm applied as the starting state?


Oh yes, duh. Not sure why I didn't do that:
http://archive.garron.us/html/2009/bhlinked.html
(Feel free to use that HTML. Note that the link at the end needs to be fixed.)



Mike Hughey said:


> I was offering to try to do it someday, but Lucas, I bet you could throw that together in a matter of minutes.


Sorry, but I think I need to restrain myself before I completely rewrite Chris's page instead of doing my homework. 
(I would want to rewrite everything into something database/script-based. If you just want simple manipulation tools, ask Johannes for now.)


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## deadalnix (May 6, 2009)

Maybe the A9 cases should be splitted in sub cases (like A, Sarah, Czeslaw)

EDIT: Hey, you have updated the page to add applets ! Great ! Why have you changed solver mode to générator mode ? I find this less intuitive this way . . .

PS: Someone can explain me toss up ? I can't understand this (I'm not a native english speaker). I mean the meaning of the word, not the alg.


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## cmhardw (May 6, 2009)

@Lucas I updated the page with your new bhlinked.html, thanks again!

@deadalnix I hadn't thought to break the A9's into sub-cases, but I suppose you certainly could. Every A9 algorithm is a setup into an 8 move commutator. The only difference is that the setup move has a cancellation with the A part of the commutator at one of the points. Remember that we standardize to mean that the A part of the commutator is the placing algorithm (3 moves or more) and the B part of the commutator is the interchange move (1 turn only). This definition doesn't work as well with commutators like M U2 M' U2 but you get the idea.

For example, the first A9 on the list is: (URB UBL ULF) / L F' L B2 L' F L B2 L2 (9 HTM) / A9 

This algorithm is actually the algorithm: (URB DFL DLB) / L' F' L B2 L' F L B2 (8 HTM) / Direct Insert 

The only difference with the A9 is that it has a setup move. For the A9 version we are going to use the same commutator as the "Direct Insert" Algorithm, but use a setup turn of L2.

So you get:
(L2) (L' F' L) (B2) (L' F L) (B2) (L2)'

The setup move has a cancellation with the A part of the commutator giving:
L F' L B2 L' F L B2 L2

For edges you will also have lots of 9 move cases (STM) called "B9" because the cancellation of the setup is with the B part of the commutator.

As for breaking them into sub-cases they will break down into the same names as all the possible 8 move commutator cases. I don't think I will be putting the sub-cases just yet, as I am hard at work on formatting Daniel's edges .txt file to add case names and some alternate algorithms here and there too.

If enough people are interested in sub-case names for the A9's and B9's I can add them, otherwise I will just make a note that the sub-cases will be the same case names as the 8 move algs, and to try to discover on your own which sub-case your alg break down into. You do have to learn to visualize this to apply the algorithms for the A9's and B'9s so I guess it would be helpful to have sub-case names. What do people think?

Chris


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## dbeyer (May 6, 2009)

Its really a recognition of cases.
Just like OLL, or PLL, or F2L.

I'd say its like F2L, you recognize a case of the cycle, and how the pieces are around the cube relative to the others being cycled.

about 50% of them are actually optimally solved in 8 moves,
30% are like 9 moves, a commutator, with which the setup and the insertion (part A) have a cancelation. Sorta like in FMC.

The rest are really easy and they are longer to solve, they are even easier to recognize because there are so few of the rest of the cases.

I can show you how to recognize whether its an

8, 9, 10, 11, or 12 mover.

You can't just learn algs for the corner system, just like you shouldn't learn algs for F2L, it should be intuitive.

Later,
DB


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## dbeyer (May 6, 2009)

Ok
There are 5 types of cases, ranging from 8-12 moves.
Pure (8)
A9s (9)
Orthogonals (10)
Cyclic Shifts (10)
Columns (11)
Per Specials (12)

We called them this just for the sake of terminology, and having defined vocabulary.

As you can see, the Pures are 8 moves, using
dbeyer.110mb.com/BHcorners.txt as a reference
198 of the 378 cases are optimally 8 moves.

That means there is a 3 move part A, and then an interchanging. Then A'B'

ABA'B' or BAB'A' to solve the cube.

You've cubed enough that you should be able to see most of these pure cases.

----------
A9s
The concept of all of these cases there isn't an insertion that provides interchangeability. Yet the setup to give interchangeability actually leads to a cancelation with the insertion.

SABA'B'S'
The 1 turn setup and the insertion cancel a move creating a double turn for the first or last move.


URB -> DLB -> BRD
I see that L2 creates interchangeability with the DLB and URB. I also see that doing L' creates interchangeabilitity with the DLB and BRD.

So perhaps a setup of
L', then an insertion of L'U2L, and interchange with D2

S: L'
A: L'U2L
B: D2
SABA'B'S'
L2U2L D2 L'U2L D2 L


The A-perm is a commutator with a cancelation

S: R
A: R F2 R'
B: B'

R2 F2 R' B' R F2 R' B R'

Now the worst and smallest set of cases are the per specials. They are optimally 12 moves. The recognition thereof is Simple. The three stickers interchangeable by double turns with the buffer.

So the URBs 3 double turns are, U2 R2 and B2.

Giving you the ULF, DRF, and DLB The buffer permute to any combination of the other 3 pieces is a per special.

Orthogonals are a varitation of the per specials.
Same pieces, but different sticker permutations.

Buffer and two of the pieces, but all three stickers must be on orthogonal planes.

L/R are parallel,
U/D are parallel,
F/B are parallel,

So you need each sticker to be on a different set of planes.

One for the U/D (buffer)
One for the L/R, and one for the F/B.

The simple solution is do a quarter turn setup to create interchangeability then a commutator and unset. There are no cancelations.

Examples.

UBR -> LFU -> FDR
Do say F as the setup, or perhaps U'

Really there are only 54 cases over 9 moves.

Now the next concept are cyclic shifts.

You are actually getting a 10 mover that looks really wierd.

You're doing something along the lines of taking a 4 move insertion, and double turn interchange. Then you write the alg out but you start on 3 third move of the ABA'B' commutator and loop around to get a weird effect on the cube.

Heres the setup.
All three cubies are on 1 plane.
Say the R face.
That means there is a middle piece.
The target sticker of the middle piece isn't interchangeable with either of the other two target stickers on the other pieces.

But look.

URB -> DBR -> RUF

URB is the middle cubie. Its not interchangeable with anything but look ...
If you do,
F you see that URB and RUF are interchangeable by R2
if you do D' you see that URB and DBR are interchangeable by R2

Now

R2 is the interchanging
FD' R2 DF'D'F R2 F'D
or its inverse cycles the pieces.


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## dbeyer (May 6, 2009)

Columns are a personal preference.
The cases are a turn away from a cyclic shift. Or a turn away from an A9.

The move count is 11 moves.
So, if a cyclic shift is 10 moves, that means a move in the setup and the cyclic shift cancels.
An A9 is well 9 moves, meaning that it's a setup turn with no cancelations (besides the A9 itself).

2 pieces opposite and interchangeable.

Such as the BLU and say the FLD, and well the 3rd piece has to be the Buffer, URB.

Now the relationship between the first two pieces, and this 3rd piece.

The 3rd piece is adjacent to one of the others, but NON-interchangeable.

we call this "AnI". Adjacent, non-Interchangeable.
(Pronounced like the "anny" in 'Danny')

So this 3rd piece is on the parallel plane to the interchangability of the first two.

You could do something like
S: F2L'
A: L'F2L
B: B2

F2 L2F2L B2 L'F2L B2 L F2

Or why not.

S: D'
A: D'R
B: B2
C: RD'

Notice How A and C = eachother but the turns are switched.

SABA'CB'C'S'

D' D'R B2 R'DRD' B2 DR' D
= D2R B2 R'DRD' B2 DR' D

So a cyclic Shift is
ABA'CB'C' Do you see?
Its weird but
if A: RD' and C = D'R do you see the relationship between the two?


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## deadalnix (May 6, 2009)

Yes, I get how to do commutators (I use them for blind, but not in an « automatic » way, it's why I so interested by BH).

For me, the harder cases are All the A9. As you say, the 10+ algs are easy to get because they are 4 basic cases you can learn.

The 8 move algs are easy (at least for me) if you understand commutators.

The A9 case are not so difficult to solve, but I often du a set-up with o cancellation. I find the set-up with cancelation dificult to find. it's why i'm interested in sub cases.

Maybe just making the same cases as 8 moves cases could help, as chris suggest.

Dbeyer > Great post on commutators. I have not learned a lotn but understanding all these things by myself take me some (hard) time. So It will surely be realy helpful for others.


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## Mike Hughey (May 6, 2009)

For the A9 cases, if you just start to practice them, you'll soon get where you can see the cancellations without thinking. I thought the cancellations were hard to find at first, too, but once you've "pseudo-memorized" them, they become so very obvious. It's just a bit of practice (and really, not all that much practice - just a little bit). I'm very fluent with most of the A9's now.


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## deadalnix (May 6, 2009)

Ok, two more question :

1/ What toss up means ? I mean, i don't inderstand the meaning of the words.

2/ How do you handle inactives pieces (pieces which are in good position but misoriented) ?


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## Mike Hughey (May 6, 2009)

deadalnix said:


> Ok, two more question :
> 
> 1/ What toss up means ? I mean, i don't inderstand the meaning of the words.


I think it's just supposed to mean "as if you're throwing it up in the air". The idea is that you throw the piece up from the level of the interchangeable pieces to a place where it can be exchanged.



deadalnix said:


> 2/ How do you handle inactives pieces (pieces which are in good position but misoriented) ?


I can't wait to see Chris's response on this. I asked him in a PM and he neglected to answer (probably because of all the other questions in the same message ). I just do them independently with my old 3OP algorithms.

I'm also curious how exactly he handles parity.


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## spdcbr (May 6, 2009)

I've never heard of this method...I'm interested...


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## cmhardw (May 7, 2009)

Mike Hughey said:


> deadalnix said:
> 
> 
> > 2/ How do you handle inactives pieces (pieces which are in good position but misoriented) ?
> ...



This is only a short answer here, but Daniel and I will obviously handle this on the page that explains the 3x3x3 method. Short answer is that I orient correctly permuted but disoriented pieces with the buffer piece before I do any cycling. I use supercube safe algs for this on the bigger cubes, and fast algs for this on 3x3x3. If the buffer is solved completely at the scramble then I use a "pseudo-buffer" of URB for the entire solve (my usual buffer is UBL). I memorize these permuted but disoriented pieces in a purely visual fashion with no memory technique. This is one of the main reasons why I have not yet started to try multi-blind ; I have no system in place to memorize these pieces on more than one cube. I don't remember how Daniel handles them, we have tried a couple variations between the two of us (because of the bigger cubes), and this is the one I have settled on.

For parity I just setup the remaining pieces into a PLL using setup moves. Typically I setup the edge first using slice turns and conjugates, then I setup the corner using conjugates. Sometimes if I see something easy, like moving a corner and an edge together as a block into the U layer for an N or F perm then I just do that. I don't always setup to the U layer, I setup to whichever layer is easiest and lets me use fewer setup turns.

Again, much more detail to follow, but that is the short answer for how I personally handle those cases. I can't speak for Daniel on this, as I think he and I have been trying different approaches independently and I honestly can't say I remember the last approach he was using.

Chris


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## dbeyer (May 7, 2009)

Here is a really good method of approach. 
There are incorrect orientations for every piece. That means that there are two optimal commutator solutions, one for each orienation. I don't have the alg list. The concept is, base on the Corner orienation of said piece, you will target a certain sticker, on that piece, and cycle it to the buffer. You will then cycle, back solving the buffer and preserving the other two pieces orienation. 

Inherantly, solving the cube in cycles, you will be left with every other piece correctly permuted and oriented except for the buffer. (Yes I know that there can be a clockwise and counter-clockwise twist on two non-buffer pieces and the buffer will be solved)

In the event that only one corner is twisted, and the other 6 are solved, the buffer will be twisted the other way.

Anyway: The twisting action can be solved commutator-style
Cycle the misorient corner, the Buffer and its polar opposite (URB and DFL for example)
Picking the correct stickers on the twisted corner and the DFL (Assuming the URB is the buffer) you can do two 8 movers to preserve the permutation of the DFL, and to twist the buffer and the twisted corner.

Example:
L'U2L D' L'U2L D
F LB2L' F' LB2L'
will twist the corners.

Every piece is adjactent to either buffer or its polar opposite. And you, will pick the cycles that will not be AnI. Therefore you can get the 8 movers that will give you the correct cycles and desired effects.

Enjoy.

Later,
DB


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## deadalnix (May 7, 2009)

*Ok, here is my way to handle both parity and inactive edges :*

When you have a parity, you have one stcker remaining at the end of your solve. Orienting a piece can be done by addind two stickers of the pieces n the cycle.

For the explaination, I will consider you have A and B two stickers of the inactive piece. Solving A then B lead to a correction of the orientation of the piece.

I will call C the sticker remaining due to parity and D a sticker of you choice.

Then simply solve : (buffer)->C->A->B->D . You can do that in two algs with BH.

You can solve mor than one inactive piece this way like :
(buffer)->C->A->B->A2->B2->D

With A2 and B2 the two sticker to orient the second piece.

Finaly, the parity you'll get will be (buffer)<->D . So this trick can control the parity too.

*Solvind more than one inactive piece with no parity :*

We can't use the same tchnioque as before here, because You will have two sticker of the same piece to solve in one alg, something you cannot do.

So you will choose a « master » innactive piece. This piece have the stickers C and D, used to orient it.

Then, you will solve all the inactive pieces like this :
(buffer)->C->A->B->A2->B2->D

So in fact, you split the solve of the master inactive piece. A, B, A2, and B2 are sticker of two other inactive piece. Obviously, it wotk for any number of inactive piece execpt 1.

I have no « premade » method for more simple cases like only parity or only one inactve piece and I improvise for this.


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## Mike Hughey (May 7, 2009)

dbeyer said:


> Here is a really good method of approach.
> (good stuff about using commutators to solve inactive pieces)


Wow, Daniel, I can really see how this mostly works! But there are a lot of special cases to figure out. Like handling parity, handling a bunch of pieces not including the buffer, etc. I think I'm going to try to figure it all out, though, because if it works, it will remove a whole class of problems for me with memorizing multi, I think. And I can see where it should be just as efficient as Chris's approach.

By the way, using a similar approach to Chris, I memorize twisted corners for multi by using a separate location to memorize twisted pieces, and if they form clockwise-counterclockwise pairs, I use an image for each pair, with the counterclockwise letter first and the clockwise letter second. (And I turn the image upside-down just to double-remember that it's an orientation image.) I always use the U or D face for the letter, so I won't have to think about it. And if I have a group of 3 (or worse, 6) all clockwise or all counterclockwise, I memorize a person and an image, and then either they are pictured on the face of a clock (meaning they need to go clockwise), or they're sitting on a counter (meaning they need to go counterclockwise). It's ugly, but it allowed me to get 8/8 last night, so I can vouch that it works. 

But I still think I'd like to switch to Daniel's approach, if I can figure out all the details for it. Trying to figure them all out is making my brain hurt a little, though.


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## byu (May 7, 2009)

A few questions.

1) I don't understand how most of the algs work. I only understand Direct Insert and Drop and Catch. With A9, columns, etc. I'm totally lost. Can someone explain each one and how they work? Thanks.

2) How is parity set up? Just like 3OP?

3) Are there any people who actually memorize all 378 algorithms for corners? I think I might use the terms *intuitive BH* and *algorithm BH* to refer to the differences in methods (respectively to F2L, because of Mike's analogy).


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## dbeyer (May 7, 2009)

The algorithm I gave actually twisted the Polar Opposite (DFL) and the DRF. Oh well ... I didn't have a cube in front of me. 

By choosing the proper string of 
Buffer -> A1 -> B1 -> B2-> A2, you can actually find cancelations 
Letting A1 and A2 actually be stickers on the polar opposite of the buffer. 
You can cancelations chaining the 5-cycle that twists the corners.

Sune algorithms can orient corners and preserve permuation, and are center safe.

Such as
R'U'RU'R'U2R LUL'ULU2L'
There are other algorithms that can target the corners on a U/D column (Such as UFR and DRF, or perhaps ULF and DFL)

Here is a good point to make that by reducing the number of cases for permutaion by orienting corners first, you create a subset of 42 algorithms.
You limited yourself to the longer turn metric cases such as the 
six 12 move cases, and the columns cases.

You are increasing the move count by orienting to reduce the case count. Then you are increasing the average move count of each optimal solution. You are inherantly deciding to take steps to make other steps inadvertantly longer.


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## dbeyer (May 7, 2009)

Byu:

There are other links in the how-to section. On how to solve big cubes blindfolded with commutators. Mike, Chris, and I have all given comments and tutorials. I made a beginners method from a long time ago. Amazing I actually used that back then. 

I don't have anything memorized. The algorithms are now in muscle memory though. It's an awesome feeling. Its a method of concepts, just like F2L. There are optimal algorithms that can be used. Over time you use the optimal case, because well its just there. It's muscle memory you have concepts that you build upon and use. And you will see the relations and one day you will do 11-move case quickly without pause in recognition or in execution. There are some really fast cases and you are like really? Did I just do that?

Mind you I don't cube that much. It's a process of cubing experimentation that I have been working on for years. Amazingly enough 3 years later, all the world records are being held by the method that I developed, and had Chris help me with it. It took a long time. 

Cubing is now more so a hobby to pass the time and a quick trick rather than a competitive event for me (mind you I'm hurt now and can't do mixed martial arts, so I might cube it up again)


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## byu (May 7, 2009)

Can someone give me a clear explanation of each of the following cases?

A9
Columns
Per Special
Toss Up
Cyclic Shift
Orthogonals

Direct Insert and Drop and Catch I understand, I don't think there are any more.


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## dbeyer (May 7, 2009)

I don't have a compiled list of twist this corner clockwise by doing this algorithm. I never looked at the commutator cancelations in depth. I know its out there and you can use them, by preparing the algs ahead of time, using the proper concepts, you create your style and of course you will want to find out what works best, and understand why it all works. 

I will go into this with great detail later. Its a concept that I never compiled, but I know its out there. Sune algs are fast and 2-gen and very effective for orienting one corner at a time with the buffer.


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## dbeyer (May 8, 2009)

Look at the 6th and 7th page from me there are good posts there.
I explain everything
a toss up is an 8 move concept which is named based on the insertion technique. two pieces on a slice are interchangeable. The insertion is on a plane. 

Such at URB -> FLD -> RFD

L'U2L D' L'U2L D

Inserting the URB to the FLD by bringing the FLD do the ULF and doing U2 then returning the FLD to its original spot and interchanging.

You're tossing the FLD up to the U plane.

Everything else is described in great detail on pages 6 and 7 of this thread.
Enjoy Byu


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## byu (May 8, 2009)

Page 6 and 7? I'm on page 2.... but I'll look around anyway. Thanks for Toss Up, I understand it now. All I need now is A9, Columns, Cyclic Shift, and Orthogonals. I'll check further up on this page.


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## dbeyer (May 8, 2009)

Oh There are A9s and B9s
There are two parts to a commutator (generally speaking)
There are also setups and cancelations and other things once it gets more complex. The basic commutator is ABA'B'. The inverse is BAB'A'.
There can be setups that cancel with 
For the standard of our notation, we refer to the part A, as an insertion. We refer to the part B, as the interchanging.
An insertion is generally speaking 3-moves. The interchanging is only 1 move.
The setup moves can cancel. With corners, there are 9-move cases which the cancelation happens with the setup and the insertion.

An awesome case is URB -> DBR -> DLB 
is U [(UL2U') R2 (UL2U') R2] U'
(U2)L2U' R2 UL2U' R2 U'

An edge case is:
UR -> UL -> DF. 
The interchanging and the setups cancel. Its almost like a ferris wheel getting a complete 360 degree rotation of the interchanging. 
U [MD2M' U2 MD2M' U2) U' ->
U MD2M' U2 MD2M' U
Also here is a really awesome concept that we named.
This is center safe and has the same exact effect. Its called a slice-plane case. Where the same layer is used for interchanging and insertions. (So for example the U layer have two parts. The slice and the plane.
Since commutators go in ABA'B' form, we will refer to these as 'SP' algs.
For the example: UF -> UB -> DF.
M'U2M U2 M'U2M U2
--This is solvable by MD2M' U2 MD2M' U2 as well--

The insertion is on the U slice.
The interchanging is on the U plane you are not looking at the piece as a whole but whats happening and where the stickers are. 

The UF is on the U plane and the F slice.
The FU is on the F plane and the U slice

You are inserting the DF to the UF on the U slice. Then interchanging the UF and and UB locations by U2, on the U plane. Inverting the case. 

Its really an awesome concept, and why it works is crazy, because of the double turn action. Its a rather interesting conceptual application of an edges multiple facets.


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## byu (May 8, 2009)

Hm... I can't find your explanation of Orthogonals, Cyclic Shifts, or Per Specials.


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## dbeyer (May 8, 2009)

Byu:
Posts 59, 60, 61, 68, 72, 73, 75, 76, 78, (And now 80)
are by me
read them enjoy
Later,
DB


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## byu (May 8, 2009)

All right thanks. I think I'm going to compile all the posts together into one, single informative section about details for BH system.

I really want to get fast at BH, my first corner attempt was 12 minutes DNF because I kept messing up the commutators.


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## Mike Hughey (May 8, 2009)

dbeyer said:


> The algorithms are now in muscle memory though. It's an awesome feeling. ... And you will see the relations and one day you will do 11-move case quickly without pause in recognition or in execution. There are some really fast cases and you are like really? Did I just do that?


A great description - that's exactly how I feel now at some point or another on almost every solve! I especially can't believe it sometimes when I sail through a columns case. They still mostly trip me up, but occasionally I'll just see it and do it, and that's just amazing.


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## byu (May 8, 2009)

For some reason I just can't see commutators blindfolded. If you set up an 8 or 9 move commutator, I can look at it, and almost instantly see what moves need to be made. But if all I know is URB->FLU->DFR, I have a really hard time doing it? Any suggestions?


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## Mike Hughey (May 8, 2009)

byu said:


> For some reason I just can't see commutators blindfolded. If you set up an 8 or 9 move commutator, I can look at it, and almost instantly see what moves need to be made. But if all I know is URB->FLU->DFR, I have a really hard time doing it? Any suggestions?



See it in your head. It should be just like you're looking at the cube, but you don't actually have your eyes open. I find it's much easier to do a commutator blindfolded than it is with eyes open, because in my head, I only see the 3 pieces being cycled - I'm not distracted by all the other pieces.


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## byu (May 8, 2009)

Can you please try to explain exactly what is happening in your head? It just doesn't work for me. Give me an example commutator, and tell me what you think. I used Ryan Heise's tutorial for finding a commutator, so I look at what color the stickers are...


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## dbeyer (May 8, 2009)

Psst: Lucas helped a lot with the corner commutators. He created a program to load into CubeExplorer to generate the final file, because there were some errors (did each case by hand ... ugh ... 378 corner cases)


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## dbeyer (May 8, 2009)

URB->FUL->DRF <-- Corrected for the proper notation of the pieces

URB and DRF are interchangeable by R2
FUL is the piece being inserted.

The Insertion: D'LD
Interchange: R2

so ABA'B'
D'LD R2 D'L'D R2
done


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## dbeyer (May 8, 2009)

The concept of a commutator is it is an experiment. With a high level of control. 

As a little kid you would find a vhs tape on the floor. You don't want to watch that movie, and for some odd reason you actually go to put it back in the box. You open the case and find that another video is in the box. You take it out Putting the correct vhs in the box. Then you take that movie and put it in its correct box, which of course has another wrong video inside. You take that swap the two and decide if this is the one you want to watch or not. You go from there.

Eventually you will sort out all the videos into the correct cases. Your problem is solved. Likewise with a cube, you take the lone piece, put it where it belongs, then now you have that cubie in its place. You then put that cubie where it belongs. Then take care of a few cubies at a time.

Likewise, you don't move or touch that movie until you find the right movie box. You rearrange the movies so they are in the correct boxes. Then you of course make sure to put them in order on the shelf like they should be.

Its random and silly. but it makes sense, I hope...


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## byu (May 8, 2009)

dbeyer said:


> The concept of a commutator is it is an experiment. With a high level of control.
> 
> As a little kid you would find a vhs tape on the floor. You don't want to watch that movie, and for some odd reason you actually go to put it back in the box. You open the case and find that another video is in the box. You take it out Putting the correct vhs in the box. Then you take that movie and put it in its correct box, which of course has another wrong video inside. You take that swap the two and decide if this is the one you want to watch or not. You go from there.
> 
> ...



An excellent analogy. I laughed at the part where you said "for some odd reason you actually go to put it back in the box".


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## cmhardw (May 9, 2009)

As of May 8th 93/440 or about 21% of the edges cases are finished. Daniel has already written the algs, and I have already formatted them into the table. Right now I am going through adding case names and in some cases additional and alternate algorithms for 3x3x3.

Also, and I think this might disappoint people a bit but it's so important I have put it at the top of the page.

This is quoting from the page:



> It is very important to note that Daniel and I have taken special care to optimize the supercube safe edge algorithms for use of BH on any odd sized cube. In doing so we occasionally use another metric called WTM or Wide Turn Metric. This includes turning double layers on 3x3x3 and multiple adjacent layers in the larger cubes. Lower case letters are used in this page for double layer turns. For example the turn *r* is done as *R M'* simultaneously.
> 
> For those learning this method it is important to know that no special care has been taken to optimize these algorithms for use on the 3x3x3. This may mean that the given algorithm(s) is/are not optimal in STM for 3x3x3 edges; this is a possible improvement to the BH method that we will explore at a later date. Anyone interested in optimizing the 3x3x3 cases is certainly welcome to do so, and please contact us if you would like us to update this page with your results (with due credit given).




I am trying my best to also include optimal or at least near optimal STM algs for the most obvious 3x3x3 cases as I work on the list. Note that these additional algs are not supercube safe and will not be useful on larger cubes blindfolded. I will not do this for the entire list right now.

Sorry for not posting the list sooner, but yesterday I actually ended up buying a used computer to replace my broken one. This means that I can spend more time and get the algs done hopefully quite soon. I am doing about 50-100 algs a day right now, but I hope to finish sooner.

Chris


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## Mike Hughey (May 9, 2009)

cmhardw said:


> It is very important to note that Daniel and I have taken special care to optimize the supercube safe edge algorithms for use of BH on any odd sized cube. In doing so we occasionally use another metric called WTM or Wide Turn Metric. This includes turning double layers on 3x3x3 and multiple adjacent layers in the larger cubes. Lower case letters are used in this page for double layer turns. For example the turn *r* is done as *R M'* simultaneously.


I'd like to point out that this hurts absolutely no one, since you should ideally either be:
a. for cases where you have no idea how to do it yet (mostly for the first cases you learn), studying the algorithm carefully to truly understand how it works, in which case you'll be playing with it enough to see any other useful way to look at it, or
b. for most cases, trying to figure out the algorithm yourself, and then comparing against Chris's list to see if you "got it right". It's much better to learn them by trying to figure them out yourself, once you have done others of the same type. It helps you see them during a solve if you learn to look for them yourself. So if you figure it out yourself, you'll already see any better ways of doing it by virtue of that.



cmhardw said:


> For those learning this method it is important to know that no special care has been taken to optimize these algorithms for use on the 3x3x3. This may mean that the given algorithm(s) is/are not optimal in STM for 3x3x3 edges; this is a possible improvement to the BH method that we will explore at a later date. Anyone interested in optimizing the 3x3x3 cases is certainly welcome to do so, and please contact us if you would like us to update this page with your results (with due credit given).


I figure this will be the difference someday between the WR holders and the more ordinary, mostly sub-1 people. The barely sub-1 people will probably just use pure BH, and the WR holders will have a bunch of super-optimized algorithms chosen for finger speed, etc. But I suspect even the WR holders will mostly understand the pure BH algorithms, but will have chosen to use other algorithms after learning them, because they know they can do them faster. So getting WR speed means a somewhat more "freestyle" method.


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## dbeyer (May 9, 2009)

The great thing about understanding BH is that you can understand the concepts to create optimal algorithms. Then you can also create algs on the fly. That are actually sub-optimal HTM, and you've created an optimal execution. The great thing about this method, is its a bunch of techniques that can be applied to correctly solve any cycle.


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## byu (May 9, 2009)

I think I _kind of_ understand BH now, I can do ALMOST all the commutators if I'm looking at them, and I think I can do Pure commutators (8-moves) blindfolded, but I'm not sure. Can someone test me (for example, list three cycles that can be done in 8 moves and see if I can do them, like just saying UBR UFR LUF)

Another question: Is there a specific order for the last two letters of a corner piece? Like, what is the rule for determining whether to write LUF or LFU, since they are the same sticker/piece.


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## cmhardw (May 10, 2009)

byu said:


> Can someone test me (for example, list three cycles that can be done in 8 moves and see if I can do them, like just saying UBR UFR LUF)



(URB BRD LBD)
(URB LBD RFD)
(URB FRU LFU)

If you can do those blindfolded, you have the 8 movers down.



> Another question: Is there a specific order for the last two letters of a corner piece? Like, what is the rule for determining whether to write LUF or LFU, since they are the same sticker/piece.



I go counterclockwise around the corner. Daniel said that he goes counterclockwise around the corner, and to be honest before he and I started talking to standardize BH I had never thought about it (I considered the letters to be interchangeable with no effect). I think most people go clockwise around the corner, or don't have a system for it.

Chris


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## deadalnix (May 10, 2009)

Any information for name convention for 8 move algs ?

It's not a problem for me to figure out what to do when it's a 8 moves case, but I realy don't know if it's a direct insert or a drop and catch or whatever.

PS: some algs are using [AB2A',C2] structure, which can always be done like [ABA',C2] or [AB2A',C]

For exemple :
(URB UFR DLB) D F2 D' B2 D F2 D' B2 (8 HTM)

Can be done :
B2R'F'RB2R'FR which is more optimal (if more optimal make sens).


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## byu (May 10, 2009)

cmhardw said:


> byu said:
> 
> 
> > Can someone test me (for example, list three cycles that can be done in 8 moves and see if I can do them, like just saying UBR UFR LUF)
> ...



First one - Success
Second one - Failure
Third one - Success

First and third one took about 1-2 minutes to figure out, so I'm really SLOW. Second, one, I'm stuck on it blindfolded, I could figure out that LBD and RFD are interchangeable by D2, but I couldn't figure out anything else. Am I doing bad? I've only been trying this for 3 days... well actually more like 2 1/2.



cmhardw said:


> > Another question: Is there a specific order for the last two letters of a corner piece? Like, what is the rule for determining whether to write LUF or LFU, since they are the same sticker/piece.
> 
> 
> 
> ...



OK, I'll try to conventionally go counter-clockwise from now on.


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## deadalnix (May 10, 2009)

byu said:


> Second, one, I'm stuck on it blindfolded, I could figure out that LBD and RFD are interchangeable by D2, but I couldn't figure out anything else. Am I doing bad?



You have seen something important. So you know now your interchange move : D2. You have to think about your inserting move.

Your insertion move will be something like AA' Because of 2 as insertion move.

You have 4 possibilities :
1/ R, but R move URB corner too, it's not the good one.
2/ L, but the sticker of the corner don't go on U face, si it's not good.
3/ F', it looks good.
4/ B', as R, it move URB corner too.

So you have tour second move : F'UF .


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## cmhardw (May 10, 2009)

byu said:


> cmhardw said:
> 
> 
> > byu said:
> ...



Actually, you're doing pretty well. I intentionally gave you some of the more difficult 8 movers to see. If it helps, and I posted it in the BH resource center just now, I consider "viewpoint shifting" an absolute staple in my solving. I use it at least once every solve or every other solve.

http://tinyurl.com/ozg5p8

Hope this helps,
Chris


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## byu (May 10, 2009)

cmhardw said:


> byu said:
> 
> 
> > cmhardw said:
> ...



I'm doing good? I never thought of it like that. All I know is that it takes me 1-3 minutes to see an 8-mover, and I can't even see all of them. My goal is to be able to see 8-movers in 30 seconds or less, and A9s in 1-3 minutes, like my 8-movers are now.


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## cmhardw (May 10, 2009)

byu said:


> I'm doing good? I never thought of it like that. All I know is that it takes me 1-3 minutes to see an 8-mover, and I can't even see all of them. My goal is to be able to see 8-movers in 30 seconds or less, and A9s in 1-3 minutes, like my 8-movers are now.



You will get used to the patterns. Again, imagine that you are learning F2L all over again. At first it seems like you can't spot how to pair a corner and an edge, and over time it becomes second nature.

Trust me, check out viewpoint shifting in my post above. I guarantee that it will take 30 seconds to a minute off your hardest cases in no time. Over time it makes spotting even the most difficult to see cases effortless.

Chris


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## Mike Hughey (May 10, 2009)

deadalnix said:


> Any information for name convention for 8 move algs ?


I honestly don't see any reason why you need a naming convention for them. I honestly didn't bother to learn the names. I know the general shapes and what they look like, and can move them around on the cube. Since I can see them really quickly, I don't see any need for actual names for them. I think the names are mainly good for explaining them to people who can't see them.

If you can already seen them, I figure you've already grown past the need to be able to name them. Again, unless you're teaching them to others, in which case the naming could be useful.

I remember I found those names somewhat helpful back when I was learning center commutators. (Chris has been using most of those names for years.) The names helped me see what was going on, so I could understand the algorithms. Then I promptly forgot the names, once I could just see the algorithms.


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## deadalnix (May 10, 2009)

Yes, but as you explain, it's easier to explain with names. And I don't understand the name (even if it's not a problem to find the good alg).


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## deadalnix (May 11, 2009)

Hi chris, here ar some improvements for BH corners page :

L2 D R2 D' L2 D R2 D' : B'RBL2B'R'BL2
U2 F' D2 F U2 F' D2 F : RDR'U2RD'R'U2
U2 L D2 L' U2 L D2 L' : B'D'BU2B'DBU2
D F2 D' B2 D F2 D' B2 : B2R'F'RB2R'FR
L' F2 L B2 L' F2 L B2 : B2UFU'B2UF'U'
U2 R D2 R' U2 R D2 R' : F'D'FU2F'DFU2
D2 L' U2 L D2 L' U2 L : D2BUB'D2BU'B'
U2 B' D2 B U2 B' D2 B : LDL'U2LD'L'U2
F U2 F' D2 F U2 F' D2 : D2R'U'RD2R'UR
F' R2 F L2 F' R2 F L2 : L2URU'L2UR'U'
R2 B L2 B' R2 B L2 B' : D'L'DR2D'LDR2
D R2 D' L2 D R2 D' L2 : L2B'R'BL2BRB'
R2 U' L2 U R2 U' L2 U : FLF'R2FL'F'R2
R2 D' L2 D R2 D'L2 D : BLB'R2B'L'BR2
U' L2 U R2 U' L2 U R2 : FLF'R2FL'F'R2
R' F2 R B2 R' F2 R B2 : B2DFD'B2DF'D'
U F2 U' B2 U F2 U' B2 : B2L'F'LB2L'FL

I hope you'll use them (And i hope I have made no mistake)


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## Mike Hughey (May 11, 2009)

deadalnix said:


> Hi chris, here ar some improvements for BH corners page :



I agree with these. In fact, these are the ones I learned. (At least, the first few are - I'm too lazy to check them all.) I guess that shows everyone I wasn't completely honest. If I was really sure that the moves were optimal, I didn't bother checking your list sometimes to see if I was right. Apparently I didn't do that for any of these either. 

Chris, I think it's worth it to go for QTM optimal (as second priority, after HTM optimal). If you're going for optimal anyway, you might as well go all the way. And these are certainly every bit as easy to see as the ones you have, once you get used to them.


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## MatsBergsten (May 11, 2009)

I must say I have no time for learning BH-corners now (mainly because I am rebuilding
part of our house and have no spare time at all). 

But I cannot resist, I have to check whenever I have a scramble and need to use one 
of my worse algs. And more often than not it is an alg I immediately want to learn. 
Commutators are so nice 

Maybe I end up with only commutators and then become center invariant too so I can 
solve the corners first on 4bld & 5bld 

Thanks for your effort, B & H!


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## dbeyer (May 11, 2009)

I am now working on the Wings portion of BH. I am actually listing the most effective QTM solutions.

R'F2R b' R'F2R b 
vs
b U'FU b' U'F'U

Both are quite fast, as you can use a quick cube rotation and a Wide-Turn to make the solution into a U/R layers alg (that is to include U, u, d, L, l, r, R)

(3L')U2R d' R'U2R d x'
vs
y r U'LU r' U'L'(3D)

This is just a simple 8 move example. I will give none (or at least very very few) solutions on wings that involve cube rotations.

Later,
DB


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## flee135 (May 11, 2009)

I have a few things I need to get straight about corner commutators. If anything I state is wrong, please correct me or add on to what I say if I miss something. These all deal with recognition. I need more information about this because I am still a little shaky on recognizing which cases are which. I am only truly comfortable with executing pure commutators at the moment, so maybe when I learn some more later, it will come to me.

1) For pure commutators, you will see two interchangeable pieces, with a third piece on a different plane that can be swapped with one of the other pieces.
2) I have trouble recognizing A9 commutators. How do you know what your set-up move is and how do you know it will cancel with another move prior to execution?
3) Orthogonal commutators involve cycling three stickers on three different planes, none of which are parallel, such U, F, and R. 
4) Cyclic shifts have three pieces on the same plane, but the piece in the middle is not interchangeable with either of the other two pieces. So how about these other two pieces? If they are interchangeable, then does that always make the middle piece interchangeable with something?
5) Columns are when there are two pieces interchangeable, but the third piece cannot be swapped with any of the two.
6) Per specials are when all the pieces can be interchanged with double turns. Or something to that effect. I notice that there are two stickers on the same side, and the other one is opposite and diagonal.

Please correct any of these if they are wrong, or help me out with any questions. Thanks for any help provided!


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## cmhardw (May 11, 2009)

Daniel and I are doing something quite different for edges than for corners, and I will probably end up doing the same for corners eventually. For edges we are posting multiple algs for many cases, sometimes as many as 3 different algs for a case.

I won't overwrite algs with more QTM optimal ones, but rather include both so that people can choose. I don't always use the most QTM optimal alg in every situation, because I do to some extent prefer to use the easier to execute alg. I would gladly use an alg with an interchanging M2 rather than an alg with all quarter turns. I have learned from the speed of M2 that interchange moves by double slice turns tend to be faster in some cases.

Any algs that people post as alternatives I will include on the site as alternatives, rather than replacing.

I am still working on the edges, formatting about 50 algs per day. It is turning out to be much more work than I expected. I am hoping to finish within the next few days. Meanwhile Daniel is typing up the algs for bigger cubes, and when he is done with the first set I will format and post while he types up the following set, etc.

Stay tuned for more updates! To be honest I want to get the edge algs posted first, then I will go through and add any suggested alternatives that people provide. Remember that the goal of BH is to construct the correct algorithm for a given case from the case name. If the correct alg for you is different than the alg we list, then use your alg. Not everyone solves F2L the same way, so I see no reason at all that people should use the BH method the same way. To be perfectly honest there are a handful of corner cases where I use a B9 alg rather than the optimal 8 move alg because the B9 is much faster. Eventually we may add these alternatives on the site, but for now my priority is getting the edge algs posted.

Thanks all for the comments, any suggested algs will be added to the site after the edges are posted, so keep them coming!

Chris


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## Mike Hughey (May 11, 2009)

cmhardw said:


> To be perfectly honest there are a handful of corner cases where I use a B9 alg rather than the optimal 8 move alg because the B9 is much faster.



I'm really tempted for the case (URB ULF DBR) to use the algorithm I've used for years for 3OP (I learned from Macky's site): (R2 D R2 D' R2 U2) * 2. Since I hate columns anyway, and it's only one move more (but admittedly lots of QTM), and I've had so much practice with the longer one, I figure I may never get faster with the columns algorithm, no matter how much I practice it.

I think offering alternatives makes a lot of sense. But I still think it would be nice if the primary algorithms listed were maximally efficient. But don't get me wrong - I think your priorities are well-placed. I would just like to see this happen when you run out of other good things to do.


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## cmhardw (May 11, 2009)

Mike Hughey said:


> I'm really tempted for the case (URB ULF DBR) to use the algorithm I've used for years for 3OP (I learned from Macky's site): (R2 D R2 D' R2 U2) * 2. Since I hate columns anyway, and it's only one move more (but admittedly lots of QTM), and I've had so much practice with the longer one, I figure I may never get faster with the columns algorithm, no matter how much I practice it.



Mike, I used to feel the same way. Try to stick with it though, with the columns algs. I personally prefer the setup into the A9 case (URB ULF DBR) I would do as L U R2 U L' U' R2 U L U2 L'. I admit that it took me a long time to get used to the columns algs, but just try that alg as an alg that you were trying to learn to finger trick. I can guarantee you that if you stick with it you will fall in love with the columns algs. They are difficult to see at first, I agree 100%, but they are so much faster than any other alternative once you are used to them.

If it helps, I used to use Columns algs when I could see them easily, then use my old algorithms during competitions or solves where I felt I was going really fast and might get a good time. Now I use columns algs exclusively only because I stuck with it and am so used to them. I can't think of any columns case that I would do with my alg algorithms, but then again I've been practicing them for a long time. Try to transition yourself into the columns algs slowly, but I do recommend to use your old algs when you see those cases much easier. Just try to slowly wean yourself onto the columns algs. They are so super nice.



> I think offering alternatives makes a lot of sense. But I still think it would be nice if the primary algorithms listed were maximally efficient. But don't get me wrong - I think your priorities are well-placed. I would just like to see this happen when you run out of other good things to do.



I agree with that actually. I will probably mark the pages to show that the optimal QTM alg is Optimal with an asterisk or something, but provide other alternative algs with the same HTM. I do agree that would be a good idea.

Chris


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## rahulkadukar (May 11, 2009)

Please put the Edges up fast so that I can give up TuRBO


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## Mike Hughey (May 11, 2009)

cmhardw said:


> Mike, I used to feel the same way. Try to stick with it though, with the columns algs. I personally prefer the setup into the A9 case (URB ULF DBR) I would do as L U R2 U L' U' R2 U L U2 L'. I admit that it took me a long time to get used to the columns algs, but just try that alg as an alg that you were trying to learn to finger trick. I can guarantee you that if you stick with it you will fall in love with the columns algs. They are difficult to see at first, I agree 100%, but they are so much faster than any other alternative once you are used to them.
> 
> If it helps, I used to use Columns algs when I could see them easily, then use my old algorithms during competitions or solves where I felt I was going really fast and might get a good time. Now I use columns algs exclusively only because I stuck with it and am so used to them. I can't think of any columns case that I would do with my alg algorithms, but then again I've been practicing them for a long time. Try to transition yourself into the columns algs slowly, but I do recommend to use your old algs when you see those cases much easier. Just try to slowly wean yourself onto the columns algs. They are so super nice.



I have already been following your advice. I've stuck with the columns algorithms for a while, and I admit I'm starting to see them. It still typically takes me 10-15 seconds to do one, but I'm doing it. It's cost me some really fast times on a couple of solves, I think. But I can see where it could be fast. I'll hang in there with it for a while longer.


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## dbeyer (May 12, 2009)

The great thing about the High-move count algs is that there are only so many of them. 
8 turns: 198 cases
9 turns: 126 cases
10 turns: 30 cases
11 turns: 18 cases
12 turns: 6 cases

54 cases use 10+ moves. 
12 Orthogonals
18 Cyclic Shifts
18 Columns
6 Per Specials

The system is really awesome. The similarities in patterns are so simple. All the cyclic shifts are quite nice. I like them. The key is recognizing the patterns quickly, execution will come with time.

I'm getting back into it myself actually. Everybody enjoy.
Later,
DB


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## cmhardw (May 12, 2009)

Update: As of 10:51pm EST I have formatted 220 of the edges algs, so I'm exactly half way through. I'm going to try to keep working tonight to do as many more as I can. Still looking at 2-3 days from now I'm thinking to finish all of them.

--edit--
Going to bed. 160 cases left to go. Might take 2 more days and the page will be done.

Chris


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## deadalnix (May 12, 2009)

Chris, you are my heroes


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## cmhardw (May 12, 2009)

OK everyone, Enjoy! :-D

BH Edges

--edit--
I'm leaving the case counts off the page temporarily as I am trying to verify and double check my numbers. I'll add them back once I'm done.

Chris


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## Mike Hughey (May 12, 2009)

Wow, Chris - looks like you've been working hard! Thanks for this!

I'm sure I won't get to learning edges anytime real soon, but I must admit I'm becoming a believer. Today I got 4 successful 3x3x3 BLD solves under 1:50, and I had a very close DNF (I forgot to flip 2 edges) that was 1:27. If those two edges hadn't been flipped in the original scramble, I could have had my first sub-1:30 solve. Clearly I'm capable of much faster solves with BH corners than I was able to do with 3OP. And I suspect that as bad as I am at M2, and as slow as I am in general, learning optimal edges will probably help me greatly on edges, too.

With BH corners, if there are no twisted-in-place corners and there is no parity, it feels almost like cheating. I must have done the corners on that 1:27 solve in under 20 seconds, memorization + execution. It's just ridiculous. But unfortunately, it can still be pretty bad for me if I have both twisted corners and parity. It didn't seem like the disparity was as bad between good and bad solves with 3OP.


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## Pedro (May 12, 2009)

no 2-gen algs for the U perms?  I can do them much faster than the STM optimal...

anyway, great work, Chris 

I'm not sure yet if I'll ever try this...maybe when (if) I finish my letter-pairs list


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## cmhardw (May 12, 2009)

Pedro said:


> no 2-gen algs for the U perms?  I can do them much faster than the STM optimal...
> 
> anyway, great work, Chris
> 
> I'm not sure yet if I'll ever try this...maybe when (if) I finish my letter-pairs list



Hey Pedro, Mike, glad you like the site. Daniel really did all the work to write down the algs. All I did was to format them into a webpage and occasionally add my preferred alg to a case as well as Daniel's when we use different ones.

Keep in mind that learning the edges is just like corners. Treat it like learning to recognize F2L cases, and you see a lot of the same kinds of things for edges that you see for corners. Only some of the cases (ex. being the B9's and the Slice-Planes) are completely different.

Some of the A9's break down into different subcases than what you see for corners, but otherwise it's all the same idea.

Now Daniel and I are working on a page explaining the BH method, and how to recognize the patterns. Think of the pages with the algs simply as a lookup reference if you want to check the alg you are using for a particular case.

You can't write a math book without a forward on set theory, and similarly we can't post the method without a reference of the algs for all cases. Those sites are only the reference sites though, the method pages are soon to come.

Chris


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## Rubixcubematt (May 13, 2009)

yay, well done chris! I liked your explanation on 4x4 edges in your 4x4 BLD tutorial, which is very helpful explanation on BH corners. awesome job on posting it up!


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## deadalnix (May 13, 2009)

Pedro said:


> no 2-gen algs for the U perms?  I can do them much faster than the STM optimal...



Not sure, the MU gen is really fast. And fit better with « BH mind ».


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## cmhardw (May 13, 2009)

deadalnix said:


> Pedro said:
> 
> 
> > no 2-gen algs for the U perms?  I can do them much faster than the STM optimal...
> ...



I'm thinking that eventually, after the 3x3 version of the method has been speed optimized that there will be two version of the method, one for 3x3 and one for all other sized cubes.

I personally don't use U perms much on 3x3 because you can't use them on 5x5 for edges. Sometimes on 3x3 I will use a 3x3 optimal alg, but at this point I'm so used to thinking of the optimal commutator that those algs come to mind first if I have a U perm say on the R face.

Obviously you can use the 2 gen U perms and other 3x3 optimized algs for 3x3, that was part of my note that we haven't really done any work at all to optimize for 3x3. What it is optimized for is 5x5, 7x7, etc.

Chris


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## byu (May 14, 2009)

I finally returned from my trip, and earlier than I expected. The first thing I looked at was this thread, and I am really grateful that the edges are finally up. However, I although I am tempted to look at the page I have told myself I WILL NOT learn BH edges until I have at least become decent with BH corners. 

(My definition of "decent" for BH corners:

1) All commutators can be planned out sub-30
2) Can solve 2x2 BLD (or 3x3 Corners BLD) sub-3.
3) I feel like I really understand all the commutators

)

Anyway, thanks Chris. Can you quiz me on three more 8-move commutators?


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## cmhardw (May 14, 2009)

byu said:


> However, I although I am tempted to look at the page I have told myself I WILL NOT learn BH edges until I have at least become decent with BH corners.



I see no reason why you can't learn both. In fact most of the case types are the same, and maybe seeing an A9 on edges will make some of the corner A9's make more sense. There are lots of correlations between piece types.

The only completely new case types for edges are B9's and Slice-Planes. Either I or Daniel can explain these in more depth soon on the website, but other than those cases most cases are similar to corner cases.

--EDIT--
Also there are the Wide turn setup cases which are seen in edges but not in corners. Daniel explained those in the BH Resource Center thread if you want to read more about them.



> Anyway, thanks Chris. Can you quiz me on three more 8-move commutators?



Sure.

(URB LFU RFD)
(URB RDB RFD)
(URB BDL FDR)

Chris


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## byu (May 14, 2009)

Chris's Pure Commutator quiz

1) 10.9
2) 14.0
3) 10.7

I got them all sub-15! The second one I kind of messed up, so I re tried, so I guess you can call that a DNF. Time to work on A9s


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## cmhardw (May 14, 2009)

byu said:


> Chris's Pure Commutator quiz
> 
> 1) 10.9
> 2) 14.0
> ...



Great job! I was trying to again give you more difficult cases!

Ok A9's. I'll start easy and they'll get more and more challenging.

(URB FRU DRF)
(URB RFD BLU)
(URB RUF BDL)

Chris


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## byu (May 15, 2009)

Complete FAIL at all of these, Chris. I can't seem to figure out A9s, I can't see any cancellations even if I'm looking? Can you give me a "walkthrough" of these commutators and explain how you find the cancellation? Thanks.


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## Pedro (May 15, 2009)

(URB FRU DRF)
can be done as an A perm on the right layer


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## cmhardw (May 15, 2009)

byu said:


> Complete FAIL at all of these, Chris. I can't seem to figure out A9s, I can't see any cancellations even if I'm looking? Can you give me a "walkthrough" of these commutators and explain how you find the cancellation? Thanks.



They key to doing the A9's is to find the setup move into an 8 move commutator. Don't care at all about finding the setup move or one of the setup moves that cause a cancellation. Just, can you find any setup move at all that creates an 8 move commutator?

Once you get used to doing that, consider the options of all setup moves you have to create an 8 move commutator. At that point you'll start to see which one creates a cancellation. Daniel and I were talking about how to explain seeing the A9's and he came up with a really eloquent way to see them. I'll let him post it when he has the time.

But for now, as a warmup, can you find any 10 move algorithm at all that solves each of those three cases? Give me a 10 move alg for each one, and I'll show you how to find the setup that causes the cancellation.

Chris


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## byu (May 15, 2009)

Chris- for the first nine move case:

D' R' U L' U' R U L U' D

There's my ten mover. I'm tired now, I'll see if I have energy for 2 and 3

EDIT: Second one in 10 move form done.

L2 F' U F D F' U' F D' L2

EDIT 2: Third one In ten

B' L2 F' L F L2 F' L' F B


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## Rubixcubematt (May 15, 2009)

i think i know the second and third one!


Spoiler



L2 D' L' U2 L D L' U2 L'

F' U2 F' D F U2 F' D' F2


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## cmhardw (May 16, 2009)

byu said:


> Chris- for the first nine move case:
> 
> D' R' U L' U' R U L U' D
> 
> ...



Brian only the second algorithm works for me. The 1st and third don't seem to solve the cycles.

Try the first and the third one again. Now for the second one, come up with a *different* 10 move algorithm that solves the same cycle. Meaning I want you to solve it again, but use a different setup turn than the one you used.

What I am asking you to do is to learn to see *all* possible setups into an 8 move commutator. Then you will choose the one that gives the canellation.

Chris


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## dbeyer (May 16, 2009)

A commutator that uses 9 moves is rather interesting. You find cancellations with the setups and the insertion or the interchanging. 

You want your setup move to be a quarter turn that creates interchangeability with one other piece. You will notice, that another quarter turn in the same direction will make that cubie interchangeable with the third cubie.

You are looking for two consecutive quarter turns of a face that make one piece interchangeable with the other two.

URB -> DFL -> FDR.

You will notice that 
L, and L2 created interchangeability between the DFL and the FDR, then the DFL and the URB.

L [D2, LU2L'] 
S [A, B]

L D2 LU2L' D2 LU2L2

Another good example is a quarter turn setup move that preserves existing interchangeability between two pieces. Then the double turn allows for the insertion of the lone cubie.

Such as URB -> RDB -> DLB
URB and RDB are interchangeable on the B slice.
DLB and RDB are interchangeable on the B slice as well.

URB and and DLB are interchangeable opposites: this is a good thing. It shows you part of the commutator.

Possibilities for the setups are 
D or R'.

D [L', DR2D'] => D L' DR2D' L DR2D2
R' [R'D2R, U] => R2D2R U R'D2R U' R

D and R' both move the RDB. 
D moves DLB along with the RDB, preserving interchangeability.
R' moves the URB along with the RDB, preserving interchangeability.

Either D2 or R2 preserver interchangeability of the DLB and URB, while moving the RDB with one of the other corners respectively.


Later,
DB


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## trying-to-speedcube... (May 16, 2009)

dbeyer said:


> A commutator that uses 9 moves is rather interesting. You find cancellations with the setups and the insertion or the interchanging.



Huh?

The cancellation is always in the insertion, not in the interchanging move... Right?

P.S. my 8-movers are pretty good, most of them are sub-10 now  My A9s need some more work to do. What Brian's doing is very smart, just asking other people to test him 

Test me too !


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## cmhardw (May 16, 2009)

trying-to-speedcube... said:


> The cancellation is always in the insertion, not in the interchanging move... Right?



For corners only that is correct. All cases that are 9 moves long are A9's, meaning the cancellation is between the setup turn and the A (insertion) part of the commutator. This is not always the case for edges, where you do get cancellations with the interchanging part of the commutator, the B part. We call these, for consistency, B9's. Colloquially we call B9's "Ferris Wheel" cases, because the interchanging side does a full 360 degree turn if you choose your turn direction to match the interchanging and setup move direction.



> Test me too !



(URB FUL BLD)
(URB DFL FDR)
(URB BRD BDL)

That is a mix of A9's and 8 movers, but I won't say which are which.

Chris


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## trying-to-speedcube... (May 17, 2009)

26.74: I was trying to shoot to BLD, instead of FUL...
DNF: really couldn't find a cancelling setup, so gave up.
6.74: really easy 

1: F R' F' L2 F R F' L2
2: L2 U' L' D2 L U L' D2 L' (found it now)
3: R D L D' R' D L' D'


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## byu (May 17, 2009)

I can execute A9s pretty quickly now, as well as orthogonals. My only problem is I can only find cancellations a little over half the time. So, I know how to execute A9s, but they are not all optimal. I hope to improve this soon.

Questions:

1. Chris- can you explain Per Specials to me again? The previous explanation didn't make mud sense. Thanks.

2. Of the 30 ten-movers, how many are orthogonals and how many are cyclic shifts?


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## tim (May 17, 2009)

byu said:


> 2. Of the 30 ten-movers, how many are orthogonals and how many are cyclic shifts?



Daniel answered that in your own thread:



dbeyer said:


> Look check this out:
> There are 30 cases that are 10 moves.
> There are two case types:
> 18 cyclic shifts
> 12 orthogonals.


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## byu (May 17, 2009)

I think I fully understand A9s and how to find cancellations (thanks to an extensive AIM chat with Daniel). Can someone quiz me on three commutators that are either pure or A9s, but don't tell me which?


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## AvGalen (May 18, 2009)

I am interested in BH for FMC. I really suck at corner insertions and knowing/studying this would greatly improve that.

I am pretty good at edge-insertions, but last week I found a very weird start in about 10 minutes. I needed almost the entire rest of the hour to find good edge-insertions. I couldn't find short ones at all, 9 moves was the shortest I could find. In the end I ended up creating 3 * 10 move insertions that cancelled really nicely, but I am wondering if there were easier/shorter insertions that I missed. This is what I am talking about: 
*Scramble: *L2 D2 F2 U B2 D' F2 D' R2 U' L2 R2 U2 R' B L F' R D' U
Explanation:
Corners first: D2 B2 R D' B' U * B' D2 R B R2
Insert 3 edges at *: R L' D' F2 ** D R' L B' D2 B
Insert 3 edges at **: F' B R U' R' *** F B' D R D'
Insert 3 edges at ***: R' L U' B' U R L' B' D B

It took me about 30 minutes to test all 3 cycles at all the 12 original positions (start and after each of the corners first moves)
Then it took me about 15 minutes to test the other 2 cycles at the newly created positions (about 20 test) and finally a couple of minutes for the remaining cycle at the latest newly created positions (about 10 tests)

Don't get me wrong, I am really pleased with getting a 29 move solution that has 3 10 move insertions, but I am wondering:
1) If I missed short cycles
2) What the distribution for edge-cycles is (a * 6 moves, b * 7 moves, c * 8 moves, etc) where a+b+c+.. seems to be 440
3) A big difference between the corners and edge cycles is the amount of different ways to do the same optimal cycle. Some 8 move corner-cycles can only be done in 1 way, others can be done in 2 ways, but none can be done in 3 ways. For edges it seems that there are often many ways to do an 8 move edge-cycle. Is anything known about this?

I guess I just want to know if I am right in assuming that 
a) short corner-cycles are more common than short edge-cycles and 
b) Edge-cycles have a better probability for cancellations because there are more to choose from


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## dbeyer (May 18, 2009)

Arnaud: For Edges, we use 3 move insertions and setup moves. We find cancellations if there are any. 

You are looking at 8-10 moves to purely cycle 3 cubies with commutators.
All of the commutators cycling 3 edges use slice moves in the insertion or interchanging.

So ... using an actual commutator for cycling 3 edges is a bad idea, since slice turns count as two moves, etc etc.


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## cmhardw (May 18, 2009)

Today's Quiz:

I won't restrict anything here. Any commutator is fair game now.

(URB DBR RFD)
(URB FLD DRF)
(URB DBR FUL)

First can you solve each case BLD at all? Second, can you solve them optimally? Use the algs page to lookup each case to find the optimal length after you've tried it.

Chris


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## byu (May 18, 2009)

First competitor!

1. Solved - Optimal - 16 seconds
2. Solved - Non optimal - 20 seconds
3. Solved - Optimal - 18 seconds

I like these quizzes. Chris, can I post the quizzes with 10 cases each? 3 just isn't enough.


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## cmhardw (May 18, 2009)

byu said:


> First competitor!
> 
> 1. Solved - Optimal - 16 seconds
> 2. Solved - Non optimal - 20 seconds
> ...



Nice! Try to learn the cases like the second one. Those are some of my favorites actually. You can viewpoint shift if it helps, but I've learned to see them with the stickers exactly as they are in the cycle.

And yeah, Brian feel free to post the quizzes. I might occasionally pipe in with some of my favorite cases, but feel free to take over at this point.

Chris


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## AvGalen (May 18, 2009)

dbeyer said:


> Arnaud: For Edges, we use 3 move insertions and setup moves. We find cancellations if there are any.
> 
> You are looking at 8-10 moves to purely cycle 3 cubies with commutators.
> All of the commutators cycling 3 edges use slice moves in the insertion or interchanging.
> ...


Oh, so you would only use commutator cycles and not use edge-3-cycles like (U2 B2 D2) R' (B2 U2 F2) L'? Cycles like this can be shifted to (B2 D2) R' (B2 U2 F2) L' (U2) and to (D2) R' (B2 U2 F2) L' (U2 B2) giving lots of chances for cancellations

For the 3 insertions I did use slice based commutators, but because of the way I wrote it down (FMC-style) you might not have noticed.
Insert 3 edges at *: (*R L'*) D' F2 ** D (*R' L*) B' D2 B
Insert 3 edges at **: (*F' B*) R U' R' *** (*F B'*) D R D'
Insert 3 edges at ***: (*R' L*) U' B' U (*R L'*) B' D B
The A and A' parts are slice moves and the B and B' parts (slightly hidden in this notation style) are then obvious


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## cmhardw (May 18, 2009)

AvGalen said:


> Oh, so you would only use commutator cycles and not use edge-3-cycles like (U2 B2 D2) R' (B2 U2 F2) L'? Cycles like this can be shifted to (B2 D2) R' (B2 U2 F2) L' (U2) and to (D2) R' (B2 U2 F2) L' (U2 B2) giving lots of chances for cancellations



Hi Arnaud,

That's correct that we would not use those types of cycles for edges. The reason is that we can't use such a cycle on 5x5x5 blindfold, which our method is optimized for, and thus also optimized for 7x7x7, 9x9x9, etc..

Personally, learning how to see those types of 3x3x3 cycles is at the top of my to do list, since they appear to be very powerful for fewest moves. I have to be honest that I don't yet understand how they work, but learning to see them is something I have on my to-do list, probably after we finish the BH method website, or hopefully sooner.

Since we can't use that cycle on a big cube and only affect the central most edges, then we wouldn't use that alg for BH. Let me comment again that no effort has been put into optimizing BH for 3x3x3, only for 5x5x5 ;-)

Chris


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## byu (May 18, 2009)

*BH QUIZ: May 18, 2009*

OK, so I'm going to post 10 cycles of corners, and the goal is to do the following things.

1. Perform them
2. Perform them optimally
3. Perform them in a minimum amount of time

If you can only do 8-movers, highlight below.
2, 4, 7

Here are the 10

1. (URB FRU DBR)
2. (URB RDB FLD)
3. (URB BDL DBR)
4. (URB FUL BDL)
5. (URB FUL LBD)
6. (URB DBR DLB)
7. (URB DRF LFU)
8. (URB BLU FUL)
9. (URB FUL RUF)
10. (URB UBL UFR)

*HINTS*
Highlight below to see.


1. What move makes UBR and DBR interchangeable?
2. Which two pieces are interchangeable? This case is pure.
3. None of the pieces are interchangeable, they are all on the same face, what case does this have to be?
4. Which pieces are interchangeable? This case is pure.
5. All of the pieces are opposites, none are interchangeable, and they are all twisted differently. This must be a _______.
6. The setup move should not disturb the interchangeable pieces.
7. In three moves, how can you get LFU to URB without disturbing the rest of the R-Slice? This case is pure.
8. Since these are all on the same face, and nothing is interchangeable, what case is this?
9. What move will make URB and FUL interchangeable?
10. What commonly used PLL is this?


*SOLUTIONS*
NOTE: For some cases, there will be more than one optimal solution (for example, case number 5). The solutions shown below are simply the ones that are on the BH website.

Highlight below to see.


1. U R2 U L U' R2 U L' U2 (A9)
2. R' F2 R B R' F2 R B' (Pure)
3. L U' B2 U L' U' L B2 L' U (Cyclic Shift)
4. F R' F' L2 F R F' L2 (Pure)
5. U L' B R2 B' L B R2 B' U' (Orthogonal)
6. U2 L2 U' R2 U L2 U' R2 U' (A9)
7. B L' B' R2 B L B' R2 (Pure)
8. R' F U2 F' R F R' U2 R F' (Cyclic Shift)
9. F2 D' F U2 F' D F U2 F (A9)
10. R2 B2 R F R' B2 R F' R (A9)


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## Mike Hughey (May 19, 2009)

It's hard for me, because I use UBL as my buffer, and I'm totally not used to this kind of notation. So what I did was, I would set the cube at a 90 degree angle, start the timer, put my fingers on the three stickers, and then rotate the cube back to my normal orientation and see what the case was. Then execute. I think the whole translation bit was the majority of my time, in most cases.

12.28, 11.58, 19.88, 13.83, 15.17, 17.08, 15.58, 24.41, 13.19, 11.73

I need to work more on the cyclic shifts; I get confused which way to cycle the pieces and it slows me down.


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## byu (May 19, 2009)

Here I go with the cycles for today:

My procedure went like this:
1. Look at the number
2. Start timer
3. Place fingers on stickers
4. Determine cycle
5. Execute cycle

N refers to Non-Optimal

15.21, 6.31, DNF, 8.00, 13.27, 24.15, 6.43, 38.94, 16.26 (N), 5.78 = 17.32

The average is an 8/10.

Oh, and Mike, tomorrow I'll post the same cycles with both UBR and UBL buffers.


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## cmhardw (May 19, 2009)

byu said:


> 1. Perform them
> 2. Perform them optimally
> 3. Perform them in a minimum amount of time
> 
> ...



I figured I should probably give this a try to see how it goes. Here were my times. All cycles were performed in the optimal number of moves.

1) 11.78
2) 7.75
3) 3.31
4) 3.08
5) 6.50
6) 3.81
7) 9.22
8) 5.33
9) 6.09
10) 2.64

--edit--
Averaging all times comes out to: 5.95 seconds


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## dbeyer (May 19, 2009)

(3.08), 4.11, (10.14), 3.08, 3.20, 4.18, 3.82, 6.78, 5.42, 3.42 => 04.72
I found myself looking at the number, and I guess determining the cycle then letting go of the timer.

I think a more practical application:
Take an average of 12, using random cube scrambles, and completely solve the cube with BH methods.


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## dbeyer (May 19, 2009)

1. R2 U2 D F2 B2 D B' R2 B D B L2 B F' U F' R L U F' L' F2 D U2 R' 
2. B2 D2 L' B' L' R2 B2 D2 F B U D2 B2 U R2 F R F D' U R B U2 B' F' 
3. B2 L' D2 R' L' U' B2 F R' B2 R' L' D' B' R2 B D2 B2 R2 U2 B' F D2 U2 B
4. U D2 R2 U F L2 R' F R2 F2 U' F' R2 B2 L D R2 D2 R F L' R2 B' U2 F 
5. R2 D2 F2 D' R D2 B D2 R2 L' D' B2 R D' L F2 R' L' D' R2 L2 B2 R B2 R2 

(108.21), 77.24, 106.22, 95.01, (56.11) => 88.56 average complete solves
I treated it like a speedsolve, commutators only, but I maybe took a glance before making making any turns.


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## byu (May 19, 2009)

*BH QUIZ - May 19, 2009*

*Part 1*
In Part 1, you will be given 10 cycles (with a choice of URB or UBL for buffer) and you are to attempt the following three things.

1. Perform them
2. Perform them optimally
3. Perform them in a minimum amount of time

If you can only do 8-movers, highlight below.
3, 4, 9

Here are the 10. Note that I provide two cycles for each one, if you use URB buffer, use the FIRST cycle, if you use UBL buffer, use the SECOND cycle. They are the same thing, just the UBL one is rotated 90 degrees counterclockwise.

1. (URB FRU DBR) (UBL RBU DLB)
2. (URB FDR LBD) (UBL RDB FDL)
3. (URB FDR FLD) (UBL RDB RFD)
4. (URB FUL LUB) (UBL RUF FUL)
5. (URB FUL LBD) (URB RUF FLD)
6. (URB RUF BLU) (UBL BUR LFU)
7. (URB FDR LFU) (UBL RDB FRU)
8. (URB ULF DRF) (UBL UFR DBR)
9. (URB FUL FLD) (UBL RFU RDF)
10. (URB UBL DLB) (UBL ULF DFL)

*SOLUTIONS*
NOTE: For some cases, there will be more than one optimal solution (for example, case number 2). The solutions shown below are simply the ones that are on the BH website. They are the cycle solutions from the URB buffer.

Highlight below to see.


1. U R2 U L U' R2 U L' U2 (A9)
2. U F' L2 F R F' L2 F R' U' (Orthogonal)
3. F L B2 L' F' L B2 L' (Pure)
4. L F L' B L F' L' B (Pure)
5. U L' B R2 B' L B R2 B' U' (Orthogonal)
6. L F' U2 F L' F' L U2 L' F (Cyclic Shift)
7. U R' F L2 F' R F L2 F' U' (Orthogonal)
8. U F2 U' F2 U' R2 U F2 U F2 U' R2 (Per Special)
9. F' L B2 L' F L B2 L' (Pure)
10. D L2 D R2 D' L2 D R2 D2 (A9)


*Part 2*
For those of you who also know 3x3 edges BLD, I will give three scrambles, and you will time yourself on solving it with only BH commutators, but sighted (15 second inspection allowed, all other speedcubing rules apply)

1. L2 D U L D' U2 F L2 B' F' L B2 F' L2 B2 F' L2 U2 B2 U'
2. F R' B2 U2 L2 B F U L R' U R' U R2 U' B' D2 F U2 F
3. L' U L D' L' U L2 U' B2 F U' L R F U F R U' B' D'


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## blah (May 20, 2009)

And so people can't have other buffers huh?


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## cmhardw (May 20, 2009)

byu said:


> *BH QUIZ - May 19, 2009*



First ten average: 4.26
6.97, 4.22, 2.47, 2.31, 2.66, 6.75, 6.91, 3.88, 2.72, 3.70

Full solves average (sighted): 1:01.83
1:23.02
49.36
53.11

I spent inspection looking for permuted but disoriented pieces. I orient them first, before cycling. Then I cycle until parity. Lastly I set up parity pieces into a PLL.

Chris


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## byu (May 21, 2009)

*BH Quiz - May 20, 2009*

Trying out a new format. Ten cycles, highlight next to it to see solution.

For only pure commutators test, use the following cases (highlight below to see)
2, 3

Today's Specialty (Most Commonly Occurring Commutator Type): Cyclic Shift

1. (URB FUL LBD)	U L' B R2 B' L B R2 B' U' (Orthogonal)
2. (URB FRU UBL) R' F' L F R F' L' F (Pure)
3. (URB FRU LFU)	R' F' L' F R F' L F (Pure)
4. (URB RUF LFU)	B L' U2 L B' L' B U2 B' L (Cyclic Shift)
5. (URB RUF FLD)	B2 L B R2 B' L' B R2 B (A9)
6. (URB BLU FUL)	R' F U2 F' R F R' U2 R F' (Cyclic Shift)
7. (URB BLU DBR) D L' B2 L D' L' D B2 D' L (Cyclic Shift)
8. (URB LUB ULF)	F' L2 F' R2 F L2 F' R2 F2 (A9)
9. (URB LBD FDR) U R F' L2 F R' F' L2 F U' (Orthogonal)
10. (URB DLB ULF) U B2 U' B2 U' L2 U B2 U B2 U' L2 (Per Special)


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## dbeyer (May 21, 2009)

Blah: There are 24 buffers you can choose from. The reason that we are listing the URB and UBL as the buffers is because this is an advanced method. Since it's advanced, that means that other experience must have been gained to be able to approach this method. As such, they have created old habits that die hard. A sticker on the U layer is chosen as the buffer for numerous reasons. Orient First Users, well they Orient to the U layer, and why would you change your buffer now? Other methods, such as Pochmann's 2-cycle method use U layer buffers. You are able to see the U layer very easily.

With this method, the buffer is relatively objective, but up until this point you were bound to a standardization of methodology, because of the narrow mindedness of a few algorithms with many setups. 

Parity Fixes are best don't with PLLs which again are done on the U layer.

Changing your buffer now, when all these reasons had limited you to a few choices in the past, would be foolish. There is no greater buffer relative to the solving methods. Parity fixes, perhaps are different and better with U layer PLLs, but that's neither here nor there.

The move count and case count is still the same. For all my good algorithms, we found that Chris would have a bad algorithm.
For all my bad algorithms, we found that Chris would have a good algorithm.

We found that a case for me that is good as an AB pure commutator (that is Insert, Interchange, Insert', Interchange': ABA'B'). It could be bad for him.
However, he would have an opportunity for a good BA pure commutator.

Orthogonal Cases and Columns have a lot of freedom to optimize the setups to give you that personal favorite. If you pick a bad setup move that gives you a bad commutator that's your fault.

Since all 24 buffers are arbitrarily equal, it would seem foolish to change your muscle memory, and would hinder your learning process, because the application to blindfolded cubing would be awkward, as you would want to sometimes memorize from your old buffer.
Later,
DB


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## byu (May 21, 2009)

*BH Quiz - May 20, 2009*

Ten cycles, highlight next to it to see solution.

For only pure commutators test, use the following cases (highlight below to see)
4, 5, 7

Today's Specialty (Most Commonly Occurring Commutator Type): A9

1. (URB UBL RUF) B U2 B D B' U2 B D' B2 (A9)
2. (URB FUL UFR)	R U2 R D R' U2 R D' R2 (A9)
3. (URB FUL LBD)	U L' B R2 B' L B R2 B' U' (Orthogonal)
4. (URB FDR RDB) R F R' B' R F' R' B (Pure)
5. (URB RFD LUB) L F2 L' B L F2 L' B' (Pure)
6. (URB RFD RUF) F2 L F' R2 F L' F' R2 F' (A9)
7. (URB FRU DLB) L' F2 L B2 L' F2 L B2 (Pure)
8. (URB RUF LFU)	B L' U2 L B' L' B U2 B' L (Cyclic Shift)
9. (URB BLU FRU) L' B2 L' F2 L B2 L' F2 L2 (A9)
10. (URB FLD BLU) U B2 D' B' U2 B D B' U2 B' U' (Column)

---------------

Chris, I'm having some difficulties with Per Specials? Can you try to explain them a little simpler to me? I've got all other corner cases but these.


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## deadalnix (May 21, 2009)

Yeah, I found this quizz pretty cool ! I feeling more confidet into BH for corners.


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## byu (May 21, 2009)

You should post your results, deadalnix!

My results:
16.35, 16.29, 21.35, (6.35), 7.25, 20.35, 15.26, 8.35, 20.68, (29.12) = 15.73

I'm getting better!


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## dbeyer (May 22, 2009)

2.90, 2.92, 3.09, (2.09), 4.31, (8.05), 2.96, 6.36, 3.31, 3.54 => 03.95

Quite Fun ... Just lubed the cube and reassembled!


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## dbeyer (May 22, 2009)

1. (URB UBL RDB)
2. (URB FRU BDL)
3. (URB RFD FUL)
4. (URB UBL LBD)
5. (URB FDR BLU)
6. (URB FLD UFR)
7. (URB FUL LBD)
8. (URB LDF UBL)
9. (URB RFD ULF)
10. (URB ULF DLB)


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## dbeyer (May 22, 2009)

3.53, 2.45, 3.67, (1.93), 3.04, 2.01, (10.80), 5.63, 2.17, 3.60 => 03.88

Kind of unfair because I created the list and I knew what the 10th one was ... still pretty fast.


Quiz #10.
2.96, 2.95, 2.84, 3.79, 4.20, 2.57, 3.17, 3.21, 2.92, 3.12, 2.65, 2.87, 3.09, (4.42), 2.95, 2.90, 3.29, 2.70, 4.06, 3.76, 2.73, 3.21, 3.45, (2.68) => 3.21

Quiz #10 again.
2.84, (2.37), 2.37, 2.76, 2.64, 2.90, 2.70, 3.28, (5.10), 3.78, 3.53, 2.81 => 2.96 haha sub-3

Point and case. If a 12 move case can be done sub 3. That is a decent speed of 4 turns/sec.
The average move count for a BH corner case is 8.7 moves.
Hence, an average of 26 moves at 4tps. Could you solve corners in less than 7 seconds?

Oh, here is an optimized algorithm for this 12 move case.
The (URB DRF DLB) set.
U R2 D' R2 U' R2 U R2 D R2 U' R2 -> (U l2 U' l2 U') R2 (U l2 U l2 U') R2


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## byu (May 23, 2009)

*BH Quiz - May 22, 2009*

Ten cycles, highlight next to it to see solution. Note that some cases, such as case 8, have more than one possible optimal solution.

For only pure commutators test, use the following cases (highlight below to see)
3, 4, 5, 7

Today's Specialty (Most Commonly Occurring Commutator Type): Pure

1. (URB FUL BLU)	F R' U2 R F' R' F U2 F' R (Cyclic Shift)
2. (URB ULF DFL)	R U2 R' U' L2 U R U' L2 U' R' (Columns)
3. (URB FLD FDR)	F' D B' D' F D B D' (Pure)
4. (URB FDR LDF)	D' F U2 F' D F U2 F' (Pure)
5. (URB UBL FUL)L F R' F' L' F R F' (Pure)
6. (URB UFR DBR) D2 F2 D' B2 D F2 D' B2 D' (A9)
7. (URB FDR RDB) R F R' B' R F' R' B (Pure)
8. (URB UFR DBR) D2 F2 D' B2 D F2 D' B2 D' (Orthogonal)
9. (URB LFU RUF)	L' B U2 B' L B L' U2 L B' (Cyclic Shift)
10. (URB DLB LDF) U B2 U' B' D2 B U B' D2 B' U' (Columns)


---------------

Chris, I'm having some difficulties with Per Specials? Can you try to explain them a little simpler to me? I've got all other corner cases but these.


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## dbeyer (May 25, 2009)

2.76, 2.97, (1.59), 1.76, 1.87, 2.88, 1.91, 2.62, 2.79, (3.60) => 0.00
This is with actually practicing these cases like PLLs


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## Lucas Garron (May 25, 2009)

Shoulda done this a while ago.
Anyone know a good way to regex things like this robustly.


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## cmhardw (May 27, 2009)

Lucas Garron said:


> Shoulda done this a while ago.



Thanks Lucas, I updated the main page on speedcubing.com to show your applet links, with due credit of course 

Chris


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## Lucas Garron (May 27, 2009)

cmhardw said:


> Lucas Garron said:
> 
> 
> > Shoulda done this a while ago.
> ...


You're welcome. 

Small issue: A few cases had 4 algs each (missing stars on the third), and I didn't catch the fourth. If you want them fixed, just get the updated HTML from the same link.


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## dbeyer (May 29, 2009)

Oh, very nice and quite interesting.
URB -> UBL -> xyz
This 18 case BH time attack in as fast as 58.73 => 3.26s/case
6 cases are 9 moves, 12 cases are 8 moves.
Mind you I was quite happy with my 72s time attack (4s/case)
And happy with my 66s time attack (3.66s/case)

This is just a small subset of BH with a low move count.
I am recalling letter pairs, imagine moving at this speed, simulating fluid recall and execution!

Later,
DB


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## blah (Jun 18, 2009)

Is the centers page coming out anytime soon? Or have I missed something?


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## cmhardw (Jun 19, 2009)

Next is the overview of the 3x3x3 method page, but I think Daniel and I have both been very busy lately. We're working on it, albeit slowly right now.

Chris


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## riffz (Jun 25, 2009)

I would love to see it.


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## trying-to-speedcube... (Jun 25, 2009)

Then look at it. It's online for a few months already :/

http://www.speedcubing.com/chris/bhcorners.html and
http://www.speedcubing.com/chris/bhedges.html.


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## blah (Jun 25, 2009)

trying-to-speedcube... said:


> Then look at it. It's online for a few months already :/
> 
> http://www.speedcubing.com/chris/bhcorners.html and
> http://www.speedcubing.com/chris/bhedges.html.



Read further up. Hint: My post.


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## MatsBergsten (Jul 12, 2009)

*Commutator ??*

One of the hardest corner 3-cycles for me is the one for UBR - BLU - RUF or the other way around. (And UBR BUL LDB and UBR RUF FDR). 
The BH-arsenal for those are commutators like: *F'LU2L'F LF'U2FL'.* (10)

But, is this really a commutator or just an alg that happens to fit in??
However I try to pair letters together in (in groups) I cannot find an A and B
to make ABA'B'. Please group it to me


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## blah (Jul 12, 2009)

MatsBergsten said:


> One of the hardest corner 3-cycles for me is the one for UBR - BLU - RUF or the other way around. (And UBR BUL LDB and UBR RUF FDR).
> The BH-arsenal for those are commutators like: *F'LU2L'F LF'U2FL'.* (10)
> 
> But, is this really a commutator or just an alg that happens to fit in??
> ...



[ (L F') : (F , L) , U2 ] or [ (F' L) : U2 , (L' , F) ]. Of course, I may very well be wrong 

Edit: Explanation of conjugate/commutator notation can be found in the wiki.


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## trying-to-speedcube... (Jul 12, 2009)

It can be seen as a 10-move commutator with 2 setup moves and 4 moves cancelling.

F' L
(U2, L' F L F')
L' F


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## MatsBergsten (Jul 12, 2009)

trying-to-speedcube... said:


> It can be seen as a 10-move commutator with 2 setup moves and 4 moves cancelling.
> 
> F' L
> (U2, L' F L F')
> L' F



Thanks Marten! Now I get it . I did not understand Blah's notation. (I know DB has used 
it before but I just tried to scan all posts in this thread by him but found no explanation of it)

Edit: And now, thanks Blah for the wiki-link .


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## stric (Jan 23, 2017)

Hi- new here. looking for the overview of the method page, did that ever get posted?

I found the corners and edges page only.

Thanks!!


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