# Permuting corners with last slot.



## Asheboy (Aug 25, 2009)

I had an idea which could be totally rubbish but I guess I'll find out.

I thought about permuting the corners with the last slot like winters variation (but instead of orientating the corners we permute them). If this was done with a method which left all of the LL edges orientated then you would be left with a 46 algorithm last layer? (6 OLLs * 7 Edge permutations) + (4 PLLs)

I'm not sure on how many algorithms would be needed for the last slot but I thought that it would be a low amount.


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## JLarsen (Aug 25, 2009)

Well normal CLL is somewhere around 40 cases, I think this would have a lot lot lot lot more algs. Like to put it into perspective, MGLS solves the last slot, and orients the corners of the last layer, and does this in two steps. Step 1 is inserting the edge and orienting ll edges (ELS), and then doing an alg to solve the case (CLS). Just for CLS there are 108 cases.


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## Asheboy (Aug 25, 2009)

But CLL orients and permute the LL corners. I'm just talking about permuting them so there would be much less algorithms.


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## StachuK1992 (Aug 25, 2009)

Asheboy said:


> But CLL orients and permute the LL corners. I'm just talking about permuting them so there would be much less algorithms.


that would be less algs, but algs for just orienting corners aren't pretty.


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## Asheboy (Aug 25, 2009)

Stachuk1992 said:


> Asheboy said:
> 
> 
> > But CLL orients and permute the LL corners. I'm just talking about permuting them so there would be much less algorithms.
> ...



Did you mean for permuting them? Recognition is hard at first but can be easy to get used to.

Does anyone know if I'm correct about the number of last layer algorithms?


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## LNZ (Aug 25, 2009)

There are commutator methods to permute corner pieces into the solved state. I use this one when solving the 3x3. It appears inthe 1981 book "Mastering Rubik's Cube" by Don Taylor.

Try this:

Put the corner cubie to be twirled clockwise into the solved state into the UFR corner. Do the alg R' D R F D F' . Then by rotating the top layer (but not the whole cube) so that the corner cubie that needs to go anti-clockwise into the UFR corner, do the alg F D' F' R' D' R and line up the top layer again.

This alg only changes the state of the two corner cubies and leaves everything else unchanged. And this alg is really good for solving a super cube or shepherds cube too.

The same book lists an alg for twirling two edge cubes into the solved state on the top layer by again using a commutator.


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## Asheboy (Aug 25, 2009)

I dont think its that much of a problem using the last slot. I think there are 12 algorithms needed which is not that much.

If you use Petrus or ZZ and leftthe FR slot till last there would only be 6 cases.


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## ardi4nto (Aug 25, 2009)

Similiar to this idea

I think we can modify EJF2L in CLS case. EJF2L CLS case only has 8x2 cases. Note that if you can do the mirror of algorithm, you just need 8 cases..

And if we also permute corners in the CLS case, I think we will get 2x8x7 cases, and removing symmetries, we get 2x8x7-4 cases or 108 cases, (note that 54 one to 54 other are mirrored)

108 cases isn't not that hard if compared to ZB


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## StachuK1992 (Aug 25, 2009)

that's not the point. The point is, what's after that permutation?
You're left with unoriented/permuted edges, and unoriented corners.
If you do this 1-step, it sucks, since there are already better methods for 1-stepping the LL.

If you do this 2-step, it still sucks, since if you did:

corners -> edges, the corner orientation algs suck, , and you have to learn ELL

edges -> corners, the algs suck even more, because you have to not mess up the edges, and you have to learn ELL

edge orientation + corner orientation -> edge permutation, the orientation algs suck, because corners again have to stay in place


However, if you used ZZ, part of MGLS, or Petrus, you're left with edges that are already oriented, in which case you'd end up with either:

1Look->corner orientation, edge permutation -> fail recog

2Look-> corner orientation+edge permutation; might as well just use WV, since corner permutation algs are nicer

2Look->edge permutation + corner orientation. Again, Corner algs suck


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## Asheboy (Aug 25, 2009)

Right then. Now I know this idea sucks. Thanks for your time 
I could just slot it and have 7 olls then 21 plls. Silly me eh?


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## JLarsen (Aug 25, 2009)

That's what I do =P. Although for the last slot more than anything, I use "EJLS" as Garron called it, or "Erik Johnson Last Slot". All that this is is basically using ejf2l, but only on step 4b. As it was explained to me, there is a reason it's not called "MGF2L". I use EJF2L a small amount too though.


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## Asheboy (Aug 25, 2009)

If the corners were permuted like I said, you could then do 2gen OLL and have only one of the 4 edge perm PLLs which would also be 2gen. So that would be 11 cases plus the 6 to perm the corners at the last slot?

Yeah, you could just use winter variation but this is less algorithms and 2 gen. Then again, recognition is easier for WV.


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## Cride5 (Aug 26, 2009)

Sounds suspiciously like the ZZ-d 'missing link' 

Blah made a good effort to sort out the algs and recognition system. He used your same idea of only doing it at the last slot to reduce the number of cases and improve recognition. It turned out to be six *6 corner permutation cases* to do it during insertion (including the trivial case).

In terms of the LL alg stats I got:

*Total LL cases*:
Corner orientation: 3^3 = 9
Edge permutation: 4!/2 = 12
Total cases: 9 * 12 = *108*

*Total 'unique' cases*:
Unique cases with OLL skip = EPLL = 4
Unique cases with T OLL = 12
Unique cases with Headlights = 12
Unique cases with Bowtie = 12
Unique cases with Sune = 12
Unique cases with A-Sune = 12
Unique cases with Pi = 12
Unique cases with H = 6
So total = *82*

*Not including mirrors*:
Total = 35
(see the first 35 of Bernard Helmstetter's ZBLL algs)

It sounds really good in theory, because the LL can be completed with some really nice 2-gen algs, however the recognition for corner permutation is _terrible_, which is the main reason it's never really been taken seriously.

EDIT: Sorry I was assuming we were working form an edges pre-oriented scenario here - I must be going ZZ mad! 
Without edge pre-orientation, I think doing EO and corner permutation during last slot insertion (to set up for 2G 1LLL) would probably have some pretty nasty algs, along with equally terrible recognition  ... prob not worth it. Apologies if I misunderstood the original idea Asheboy


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## JustinJ (Aug 26, 2009)

Cride5 said:


> It sounds really good in theory, because the LL can be completed with some really nice 2-gen algs, however the recognition for corner permutation is _terrible_, which is the main reason it's never really been taken seriously.



The recognition's not _that_ bad. Assuming this is like WV (pair already made), you can look at the relationship between the two stickers that would be on the back if the UBR and UBL corners were twisted correctly, then the relationship between one of them and the sticker that would be on FUR.

It would be annoying to recognize at first, but as you did it a lot you'd be able the recognize the different corner twists.


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## Asheboy (Aug 27, 2009)

Yalow said:


> Cride5 said:
> 
> 
> > It sounds really good in theory, because the LL can be completed with some really nice 2-gen algs, however the recognition for corner permutation is _terrible_, which is the main reason it's never really been taken seriously.
> ...



Thats exactly what I'm working on atm.


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## TEGTaylor (Aug 27, 2009)

If I understand correctly there will be 4536 cases, I tried doing this and I had a few of the algs, thats what my signature means


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## qqwref (Aug 27, 2009)

This has been thought of before (I think by Tim Sun) and the only real problem is recognizing corner permutation while the last F2L pair is not placed. If you can do that, it's pretty nice - there are only 6 possibilities (+6 if you also want to learn what to do with a separated pair) and the last layer can then be done completely 2-gen and in one step. (This was called 2GLL and I remember there used to be algs online for it.)


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## Swordsman Kirby (Aug 27, 2009)

qqwref said:


> This has been thought of before (I think by Tim Sun)



How many years ago was this, three?


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