# How to learn BH efficiently



## blah (May 15, 2011)

Clicky. (Backup clicky hosted by James LaChance in case the first one doesn't work.)

*Update:* This zip file now contains all 378 corner cases and 440 edge cases.

I don't claim to be an authority of any sort on BH, but if you intend to learn BH seriously, this is definitely something you should take a look at. I promise it provides deeper insight. I will answer all questions in this thread, so don't hesitate to ask any (including ones about the naming ).

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This stuff has been sitting in my computer for over a year now. I'm never gonna get around to publishing it properly because I don't really have the time, so I'm leaving this out here for someone/anyone to make something useful out of it (video/website/tutorial/etc.)

Here's a quick summary:
Every BH edge case (440 of them) is one of 27 mutually non-isomorphic cases listed (and named) in the link. The ones with white backgrounds are rotation-isomorphisms, the ones with gray backgrounds are mirror-isomorphisms (listed directly below their mirror images). If a case is both a rotation-isomorphism and a mirror-isomorphism, then it's only listed as a rotation-isomorphism (for obvious reasons). And then there are inverses, but some inverses can be avoided because they also happen to be rotation-isomorphisms - these are not indicated anywhere, but are fairly obvious. Obviously, the buffer is UF.

*Update:* Corners are organized in pretty much the same way.

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I also have all the data for x-centers and t-centers, but I haven't started doing any coding work on them yet.


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## FatBoyXPC (May 15, 2011)

Did you do this because Mike contacted you about it? Gogogo w/the corners!


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## Mike Hughey (May 15, 2011)

Thanks for working on this, Chester. But I can't seem to get the document to download. The link above takes me to a page that says it has an all_edges.zip file for download, but the link there doesn't work.


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## rock1313 (May 15, 2011)

Mike Hughey said:


> Thanks for working on this, Chester. But I can't seem to get the document to download. The link above takes me to a page that says it has an all_edges.zip file for download, but the link there doesn't work.


 
Same here


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## FatBoyXPC (May 15, 2011)

For those of you who the google doc link won't work: Here you go


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## RyanReese09 (May 15, 2011)

Ah this looks amazing! I can't wait to see the final product .

PS-Chester you use wayyy too big of words .


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## EricReese (May 15, 2011)

Sweet. How long does it typically take to get comfortable with BH? Assuming you spend an hour or more each day working with it?


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## blah (May 15, 2011)

I don't know. I don't use BH. Never have.

As for the "final product" comment, I'm really sorry but there probably isn't going to be one in the near future. I'm giving you a tiny lump of coal I found after lots and lots and lots of digging in my own little coal mine. I can guarantee you that there's a diamond in there. But as of now, I'm not about to do the polishing. I've already found my own diamonds, but it takes too much work to polish it for everyone else to see. And I'm lazy. So I'm leaving it to someone else to do a proper tutorial, but I'm also willing to answer any one-answer-question you have, and hopefully someone can put everything together.

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Here's some (elaborate but not exhaustive) info about the naming/enumerating system:
The enumeration process for all 220 cases (excluding inverses) is pretty simple and systematic. I start by listing all 6 cases with *adjacent* edges (think UF-UR), then there are 2 cases with *opposite* edges (think UF-UB), then the final case with only *skew* edges (think UF-RB). These "cases" refer to the black cubes with blue cubies. I call these cases "*tri*s" (to be distinguished from the cases with the transparent cubes, which are simply called, annoyingly enough, "*cases*"). If you look at the filenames of the images, you'll see all 9 cases:

aao (U)
aaa (Donut)
aas (Snake)
ass (Scissors)
aos (Duck)
ase (Dog)
ooe (M)
oss (T)
sss (Tripod)

These are "a" for adjacent, "o" for opposite, "s" for skew, and "e" for end-to-end (think UF-DB), enumerated from U to E to D. *Good*, *Bad*, and *Weird* are used to indicate the number of interchangeable (in some cases, oriented) edge-pairs. *Duck* and *Dog* are good, *Goose* and *Cat* are bad. *Fat* and *Skinny* indicate the presence/absence of wide moves (due to slice setup moves). There's some other stuff I'm not mentioning that's kinda self-explanatory, I hope.


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## blah (May 18, 2011)

New clicky now has all 378 corner cases and 440 edge cases. I've updated the link in the first post too. Is anyone willing to download it and host it somewhere else as a backup (just in case Google Docs decides to be retarded again)?

Please let me know if you find any mistakes in there. Once again, if there's anything you don't understand, just ask - sadly, it's probably due more to my laziness/vagueness than to your incompetence :/


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## FatBoyXPC (May 18, 2011)

You're such a nice guy Chester 

Alternative New Cicky


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## RyanReese09 (May 19, 2011)

I'd add rotations before the algorithm. It confused me a lot when doing an alg backwards, and seeing UF wasn't even involved. I figured out eventually I had to undo a rotation...


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## blah (May 19, 2011)

I made it a point to present all the algs as <R,U,L> for corners, <R,U,M> for edges, and F for any non-canceling setup move. The effort to make everything as finger-friendly as possible should be evident.

I intentionally left out the rotations because they actually make it more confusing. Say I write an alg as x y Twizzle link y' x' in order for it to cycle from UF. Then whenever you get a rotation-isomorphism, you're gonna rotate it to the "standard" position, then do the x y, then the alg, then y' x', then undo the first rotation. That's retarded. It's much better to learn which pieces the alg affects in it's pure rotationless, finger-friendly form, then rotate the cube accordingly into that configuration.

In other words, why would I go out of my way to write a T-perm alg as U R U R' U' R' F R2 U' R' U' R U R' F' U' just to make the T "upright" (to look like a real T)? If I do that, then when I get a sideways T (the one we're all familiar with), I'm gonna have to do something stupid like y' U R U R' U' R' F R2 U' R' U' R U R' F' U' y. Is it starting to make sense now?


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## RyanReese09 (May 19, 2011)

Yeah, I just initially found it odd at the alg not affecting the proper pieces. It's not like anyone will be learning BH algorithmically. Either way, I can just find out what pieces the alg affects.


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## aronpm (May 19, 2011)

RyanReese09 said:


> Yeah, I just initially found it odd at the alg not affecting the proper pieces. It's not like anyone will be learning BH algorithmically. Either way, I can just find out what pieces the alg affects.


 I did.


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## RyanReese09 (May 19, 2011)

aronpm said:


> I did.


 
Well you're aronub .

Is your ULF fixed buffer? Aka, if I should have to break into a new cycle, and there are 3 corners left, should I learn to solve those remaining corners via rotation, comm, undo rotation? Seems like the smartest idea. I'd like your feedback on this . I just need to know if I need to know in depth what the alg does to the pieces, or if I can just learn what cases to apply it to, and learn that way.


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## Weston (May 19, 2011)

I'm special because he taught this to me months ago over facebook :3


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## RyanReese09 (May 19, 2011)

[01:58] <+aronpm> gimme alg and case
[01:59] <Piecez> (ULF LDF RBU)
[01:59] == keemy [[email protected]] has joined #rubik
[01:59] == mode/#rubik [+v keemy] by ChanServ
[01:59] <Piecez> U R2 U' L' U R2 U' L
[01:59] <Piecez> the alg obviously don't affect those 3 pieces
[01:59] <+aronpm> x does ULD FDL RBU
[01:59] <+keemy> aww
[01:59] <+aronpm> maybe typo
[01:59] <+keemy> no jey
[02:00] <Piecez> i found the x rotation
[02:00] <Piecez> but ended 3 twist
[02:00] <Piecez> perhaps chester f***ed up?
[02:00] <+aronpm> yes

Edit-Just saying I found a little mistake. I'd like to know the correct way to do this case though. I found a 10 mover. 

R [L' U' L, D2] R'

Edit-Aron told me 8 mover via IRC.


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## blah (May 19, 2011)

nope chester didn't f*** up

y x'


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## blah (May 19, 2011)

I colored all three stickers blue, black, and white for a reason. I generated all those images for a reason. I put them all next to each other for a reason. Watch how they behave.

Edit: osht I did f*** up the mirroring for corners. Edges are fine though. I'll fix it tomorrow I guess. For now, top-bottom white-gray pairs are still mirrors, there's nothing wrong with that, but they might be switched, as in the gray might have to be on top and the white might have to be on the bottom.


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## RyanReese09 (May 19, 2011)

Gracias. You can expect more idiotic remarks like that over the span of the next week .

Edit-Read your original post. I was just thinking you screwed up because neither me or aron found the rotation. I apologize for my nubness.

What did you mean you screwed up mirroring for corners? By mirroring, you mean doing the commutator as BAB'A'?

Edit-I'm tired, assumed you just edited your post, but instead you did two separate posts. Ugh I need sleep. Stupid 15 BLD solves today is making me idiotic. Thanks Mike....


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## blah (May 19, 2011)

No, that would be an inverse.

It's hard to explain what I messed up in text even though it's a really simple concept. I'll just fix it tomorrow and you'll have nothing to worry about.


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## tim (May 19, 2011)

I LOVE YOU, CHESTER! (YEP, MORE THAN KAI DOES!)


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## masterofthebass (May 19, 2011)

SUCK SUCK SPIT SPIT!


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## StachuK1992 (May 19, 2011)

Awesome. Looking through this now


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## Escher (May 19, 2011)

Helping me boldly go where no man has gone before and know pretty much every single BLD method and have no idea how to memorise <3


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## tim (May 19, 2011)

Chester: You've obviously used PovRay to generate the images. Could you also put the source code into the ZIP file? I would like to rotate/mirror the images, because i use a different buffer.


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## blah (May 19, 2011)

Damn. My source files are all over the place. I generated the images like five months ago. I believe I used Python to generate the POV-Ray template, then Perl to generate the bash script that renders all the images  (This is what happens when you suck at coding and only know how to do things in the most inefficient way possible.) I'll start looking for them sometime later today...


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## tim (May 19, 2011)

Haha .
You don't need to put much effort in it just for me. I could also just use Conrad's Visual Cube. It should be possible to generate the same kind of images with it.


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## blah (May 19, 2011)

You're right. Ich liebe Kai mehr als Ich liebe dich.


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## RyanReese09 (May 19, 2011)

For F R' U2 R F' R' F U2 F' R , why did you choose that alg? How fast can you execute that? I have trouble sub2.5'ing that.

*Not to insinuate* it's a bad alg, just that I have slow TPS. I assume you know of other algs for that case, so I am just wondering. I'm just a nosey person.


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## Mike Hughey (May 19, 2011)

RyanReese09 said:


> For F R' U2 R F' R' F U2 F' R , why did you choose that alg? How fast can you execute that? I have trouble sub2.5'ing that.
> 
> *Not to insinuate* it's a bad alg, just that I have slow TPS. I assume you know of other algs for that case, so I am just wondering. I'm just a nosey person.



I've gotten where I don't think it's that bad (I did it sub-3.5 first try; if I can do that, surely you can sub-2.5!); I use the left ring finger from the bottom for the F and F'. I guess I've just done it so much that I've gotten used to it.

I remember Alex Yu asked me about this case and I showed my alg to him (which I executed particularly awkwardly back then - I'm better at it now), and he thought I was absolutely crazy for using this alg.


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## blah (May 19, 2011)

You're right. I don't use that alg. It just happens to be the optimal supercube-safe one.

There's a reason it's called That Sune. It's a COLL alg (one of the uglier Sunes). Just look it up the tons of algs that are already out there. Good luck.

I don't remember my alg lol.


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## tim (May 19, 2011)

RyanReese09 said:


> For F R' U2 R F' R' F U2 F' R , why did you choose that alg? How fast can you execute that? I have trouble sub2.5'ing that.


 
That algorithm is the only one which solves that case in 10 moves (according to Cube Explorer ). I've looked at some of the 11-movers and couldn't find anything nice. I haven't looked at the 12-move algorithms, though.


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## blah (May 19, 2011)

Holy crap I just tried Mike's execution. No regrip 

D R' F2 R D' R' D F2 D' R. The D turns are left pull, right pull, left pull, left push, in that order. Ring finger, of course.

@tim: I used to know a nice 11-mover that felt like a square-1 alg  I'mma have to find it again...


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## kinch2002 (May 19, 2011)

tim said:


> I would like to rotate/mirror the images, because i use a different buffer.


That would be awesome for lazy people like me who can't be bothered to figure out how to adapt it! I use UBL buffer btw


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## tim (May 19, 2011)

blah said:


> Holy crap I just tried Mike's execution
> @tim: I used to know a nice 11-mover that felt like a square-1 alg  I'mma have to find it again...


 
That one: R' D R2 D L2 D' R2 D L2 D2 R ? At least it has a lot of R2s and L2 in it 




kinch2002 said:


> I use UBL buffer btw


 
Yeah, me too


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## blah (May 19, 2011)

R' U2 R2 U' Rw2 D R2 D' Rw2 U' R

So fun to do  No regrip. Do the first three moves with "eclipsing". The rest shouldn't be too hard to figure out. First D left pull, second D can be left push or right index(!) pull


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## RyanReese09 (May 19, 2011)

I know an 11mover for that case. It's nice...but...

2.30 now. 2.28..2.05. I'll probably sub2 within a few more tries.

I execute more like..
From:
F R' U2 R F' R' F U2 F' R

To
F R' U2 R x U' R' U x' U2 F' R

Not a huge change.

Edit-2.00. 

Edit-1.84 and 1.83 consecutively. Lol. It's fun to perform.


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## cmhardw (May 19, 2011)

Wow, this file is awesome! Chester, do you mind if I link to this thread on the main BH site?


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## blah (May 19, 2011)

I'mma have to charge you some kind of fee. What sounds reasonable?


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## cmhardw (May 19, 2011)

My undying gratitude?  I could also buy you a cookie at our next competition (if I remember correctly, there was a bet going around the blindfolded forums recently involving the loser giving the winner a cookie, and the parties involved actually paid up at their next competition!)

I would, of course, give credit where credit is due in the link description!


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## Mike Hughey (May 20, 2011)

blah said:


> D R' F2 R D' R' D F2 D' R. The D turns are left pull, right pull, left pull, left push, in that order. Ring finger, of course.


 
Yeah, that's how I do it, except that, for me, the right pull is sort of both right pull and left push at the same time. After a few more practice tries, I was able to do a sub-3 average 10/12 of it, so I'm satisfied I don't need better. I would imagine a decent speedsolver could very easily sub-2 it.

Chester, you should hold out for one cookie per file!


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## FatBoyXPC (May 20, 2011)

Mike Hughey said:


> Chester, you should hold out for one cookie per file!


 
I sure hope you're counting each image as a file


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## riffz (May 20, 2011)

RyanReese09 said:


> F R' U2 R F' R' F U2 F' R



x L2 U L2 U R' U' L2 U R U2 L2 x'


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## RyanReese09 (May 20, 2011)

riffz said:


> x L2 U L2 U R' U' L2 U R U2 L2 x'


 
x' U2 R2 D RU2R' D' RU2R


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## tim (May 20, 2011)

I've just parsed Chester's page and extracted the corner cases into a single YAML file. It's pretty easy to change the buffer now, but generating the sticker definitions for Conrad's Visual Cube will probably be a pain...

And thanks Chester for that algorithm - it's pretty nice .


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## riffz (May 20, 2011)

RyanReese09 said:


> x' U2 R2 D RU2R' D' RU2R *U2*


 
Oh, that's nice.


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## RyanReese09 (May 21, 2011)

Sorry.

[00:45] <Piecez> (ULF DRF BDL)
[00:45] <Piecez> U R' U' L2 U R U' L2 is supposed to be able to solve that.
[00:45] <Piecez> can you find the rotation? i can't :/
[00:47] <+aronpm> Piecez: maybe also an error?
[00:47] <+aronpm> idk
[00:47] <Piecez> :/
[00:47] <Piecez> ok ill post
[00:48] <Piecez> i'll try another alg
[00:48] <+aronpm> wait
[00:48] <+aronpm> y'?
[00:48] <+aronpm> do y then alg
[00:49] <+aronpm> nope


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## blah (May 23, 2011)

Sorry. Just saw this.

y x2

Edit: Oops, U R U' L2 U R' U' L2.


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## RyanReese09 (May 25, 2011)

You have more wrong with your site, I lost the little notepad I had going, but I just noticed right now that your ULF DRF LUB (That cycle) is listed as A9 on your site. However, after 15 minutes of very annoying searching, mirrors, inverses, etc, I was unable to find the rotation. I go to Chris's site and he lists (UBR buffer) this alg. Column. Not A9. This is 11 moves.
U B U2 B D' B' U2 B D B2 U'

I wish I didn't lose the notepad.

On that note,if you setup the alg Chris uses, and do y' to make it ULB buffer, anyone have a fast execution for that cycle? . ~42% done my project...


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## riffz (May 25, 2011)

RyanReese09 said:


> On that note,if you setup the alg Chris uses, and do y' to make it ULB buffer, anyone have a fast execution for that cycle? . ~42% done my project...


 
Not optimal, but z [R U R2 U' R', F2] z'

EDIT: Or optimal: x' L2 U' L2 U' R2 U L2 U' R2 U2 L2 x


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## RyanReese09 (May 25, 2011)

riffz said:


> Not optimal, but z [R U R2 U' R', F2] z'
> 
> EDIT: Or optimal: x' L2 U' L2 U' R2 U L2 U' R2 U2 L2 x


 
Funny because after I went to bed I got up, and tried that insertion, literally that same alg, but I ended up with a twist. I musth ave some something wrong, held wrong or something.

I feel dumb. I like the alg though so thanks Riffz.


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## blah (May 26, 2011)

Wait, what? Ctrl-F ULF DRF LUB takes me to Eleven, which is aptly named. None of my algs are named A9 

And here's a good 12-mover for Eleven: [Rw U L2 U' Rw', U2].


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## RyanReese09 (May 27, 2011)

blah said:


> None of my algs are named A9


 
Listed as A9, as in, an A9 alg.


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## blah (May 27, 2011)

But it's not. It's listed under Eleven. I honestly have no idea what you're talking about.


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