Interest in a BH method website?

[dbeyer]

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?

 

[deadalnix]

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.

 

[Mike Hughey]

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.

 

[deadalnix]

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) ?

 

[Mike Hughey]

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.

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.

 

[spdcbr]

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

 

[cmhardw]

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.

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

 

[dbeyer]

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

 

[deadalnix]

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.

 

[Mike Hughey]

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.

 

[byu]

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).

 

[dbeyer]

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.

 

[dbeyer]

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)

 

[byu]

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.

 

[dbeyer]

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.

 

[dbeyer]

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

 

[byu]

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.

 

[dbeyer]

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.

 

[byu]

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

 

[dbeyer]

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