# Turbo for centers on 4x4



## Sakarie (Sep 21, 2009)

I've just learned Turbo-corners for 3x3 with ULB as buffer. Now I want to modify it to work for 4x4 blindfolded. Right now I'm using r2, which I know pretty well, and it works, but are very slow, and a lot of moves, and therefore bigger chance of screwing up (I think).

For those of you (if anny) that doesn't know Turbo, it's a method where you setup two pieces to, in my case UFL and UBR, with any orientation. Then you make a three-cycle, permutating and orientating the three corners, with a simple commutator.

Does anyone use this? Is it possible? Is there a guide for this somewhere?


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## Stefan (Sep 21, 2009)

Centers, edges, or corners? I'm confused.


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## Sakarie (Sep 21, 2009)

What I HAVE learned and DO know, is commutators for three-cycle corners on a 3x3 (and off course also for bigger cubes, since corner's the same).

What I want to learn, is how to do commutators for centers on 4x4, and I would prefer if I could use the same technique, but change my algorithms/commutators a little, so that I cycle three centerpieces. My cycles (on 3x3) goes through ULB, UBR and UFL (and the other way around), so I wish I could find an easy guide (on 4x4) how to cycle any center piece from Ulb to Ubr/Bru/Rub to Ufl/Flu/Luf.


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## Stefan (Sep 21, 2009)

Sakarie said:


> cycle any center piece from Ulb to Ubr/Bru/Rub to Ufl/Flu/Luf.


Oh wow, that's an interesting approach, never seen this before. Would you do setup like for corners but using double layer turns, i.e., treat the 4x4x4 like a 2x2x2? A problem during setup would be that the two targets can be on the same 2x2x2 corner block, or on the UuLlBb block.


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## cmhardw (Sep 22, 2009)

Sakarie said:


> My cycles (on 3x3) goes through ULB, UBR and UFL (and the other way around), so I wish I could find an easy guide (on 4x4) how to cycle any center piece from Ulb to Ubr/Bru/Rub to Ufl/Flu/Luf.



There are only 9 algorithms for this if you must cycle in that direction. There are only 18 if you allow cycling in either direction. Really it's the same 9 as in the first group and their inverses. I can list them for you if you want. Also I think it is a very interesting idea.

Chris


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## Sakarie (Sep 22, 2009)

StefanPochmann said:


> Sakarie said:
> 
> 
> > cycle any center piece from Ulb to Ubr/Bru/Rub to Ufl/Flu/Luf.
> ...



All of these question am I also asking myself, since I haven't got any method yet.

I guess that as long as they're NOT on the same 2x2x2 corner block, and NOT on the UuLlBb block, it wouldn't be a problem (with the setupmoves). Infact, the setupmoves could (if you want) be much easier than on a 3x3, since if youre cycle ( on a 4x4) is Ulb->Ldb->Ubr you're required setup-move would be a simple L2, while on a 3x3 ULB->LDB->UBR would need two setupmoves D F, in order not to displace the buffer.

Also I'm not sure that setup would be too hard for Bul or Lbu, since both of them could be setup to a possible place using B' or u , resp. L' or u'.



cmhardw said:


> Sakarie said:
> 
> 
> > My cycles (on 3x3) goes through ULB, UBR and UFL (and the other way around), so I wish I could find an easy guide (on 4x4) how to cycle any center piece from Ulb to Ubr/Bru/Rub to Ufl/Flu/Luf.
> ...



I intend to use it both ways, giving 18 cycles. I know all of them on a 3x3, and the best for me personnaly, would be to just modify them a little, but keep the spine.

I will look at my algorithms, and see if I can get them too do as I wish, but if you would look at it too, it would be great! I guess you're using UBR as a buffer, while I use ULB (on a 3x3), but eventually converting the algorithms aftetrwards, won't be the hardest work.

You can see it a little like a childrens version of BH


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## cmhardw (Sep 23, 2009)

Spoiler



Ubl -> Ulf -> Urb : r' U' l' u2 l U l' u2 l r
Ubl -> Ulf -> Rbu : U' l' u' l U l' u l
Ubl -> Ulf -> Bur : l u2 l' U l U2 l' U'
Ubl -> Lfu -> Urb : r' u' r U r' u r U'
Ubl -> Lfu -> Rbu : f U2 f' u2 f U2 f' u2
Ubl -> Lfu -> Bur : L' u r' U2 r u' r' U2 r L
Ubl -> Ful -> Urb : b u b' U b u' b' U'
Ubl -> Ful -> Rbu : F r U r' u r U' r' u' F'
Ubl -> Ful -> Bur : u2 r' U2 r u2 r' U2 r

I'll let you figure out the inverses of each case for the other 9 cases. If you're not used to doing this, then click here.



Here are the algs from the BH method for the cases you need. I put it in spoilers so you can choose not to view it if you don't want to.

Chris


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## Sakarie (Sep 23, 2009)

cmhardw said:


> Here are the algs from the BH method for the cases you need. I put it in spoilers so you can choose not to view it if you don't want to.
> 
> Chris



That's great!

I have conversed the algorithms to work both ways, and I might as well post them here. I won't use all of yours, but the most of them. May I ask by what criteria you've picked this bunch of algorithms? Optimal all the time?



Spoiler



Ubl -> Urb -> Ulf: r’ l’ u2 l U’ l’ u2 l U r
Ubl -> Urb -> Ful : U b u b’ U’ b u’ b’
Ubl -> Urb -> Lfu : U r’ u’ r U’ r’ u r
Ubl -> Rbu -> Ulf : l’ u’ l U’ l’ u l U
Ubl -> Rbu -> Ful: F u r U r’ u’ r U’ r’ F’
Ubl -> Rbu -> Lfu : u2 f U2 f’ u2 f U2 f’
Ubl -> Bur -> Ulf: U l U2 l’ U’ l u2 l’
Ubl -> Bur -> Ful: R’ U2 r u2 r’ U2 r u2
Ubl -> Bur -> Lfu: L’ r’ U2 r u r’ U2 r u’ L

Ubl -> Ulf -> Urb : r' U' l' u2 l U l' u2 l r
Ubl -> Ulf -> Rbu : U' l' u' l U l' u l
Ubl -> Ulf -> Bur : l u2 l' U l U2 l' U'
Ubl -> Lfu -> Urb : r' u' r U r' u r U'
Ubl -> Lfu -> Rbu : f U2 f' u2 f U2 f' u2
Ubl -> Lfu -> Bur : L' u r' U2 r u' r' U2 r L
Ubl -> Ful -> Urb : b u b' U b u' b' U'
Ubl -> Ful -> Rbu : F r U r' u r U' r' u' F'
Ubl -> Ful -> Bur : u2 r' U2 r u2 r' U2 r


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## cmhardw (Sep 23, 2009)

Sakarie said:


> May I ask by what criteria you've picked this bunch of algorithms? Optimal all the time?



Yes, the criteria for BH is shortest number of moves. This does not necessarily mean that you always get a fast algorithm, so you might want to look at those 10 moves cases and see if your TuRBo alg from 3x3x3 corners might work?

I like the idea behind TuRBO and I think it can definitely be a fast method. Also I like how your adaptation of it is flexible enough to allow for easy setups. However, it's also small enough to not require a huge amount of learning, so you can use the entire method quickly.

Let us know how your progress is with this method! I for one am interested to hear!

Good luck!
Chris


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## Sakarie (Sep 24, 2009)

cmhardw said:


> Sakarie said:
> 
> 
> > May I ask by what criteria you've picked this bunch of algorithms? Optimal all the time?
> ...



I have looked at your algorithms, and mine, and have chosen mostly yours, but three+three of mine. It seems totally do-able!

The thing is that it's only 15 days left to World Championship, so I won't be able to learn this method good until then, and therefore, I will not study it very hard. 

BUT I will probably think of the setupmoves for a couple of days.

I'm glad you're interested too!

Ubl -> Urb -> Ulf: x l2 d2 l' U' l d2 l' U l' x'
Ubl -> Urb -> Ful : F r' F' l F r F l'
Ubl -> Urb -> Lfu : U r’ u’ r U’ r’ u r
Ubl -> Rbu -> Ulf : l’ u’ l U’ l’ u l U
Ubl -> Rbu -> Ful: l' Uu r Uu' l Uu r' Uu'
Ubl -> Rbu -> Lfu: u2 f U2 f’ u2 f U2 f’
Ubl -> Bur -> Ulf: U l U2 l’ U’ l u2 l’
Ubl -> Bur -> Ful: R’ U2 r u2 r’ U2 r u2
Ubl -> Bur -> Lfu: L’ r’ U2 r u r’ U2 r u’ L

Ubl -> Ulf -> Urb : x l U' l d2 l' U l d2 l2 x'
Ubl -> Ulf -> Rbu : U' l' u' l U l' u l
Ubl -> Ulf -> Bur : l u2 l' U l U2 l' U'
Ubl -> Lfu -> Urb : r' u' r U r' u r U'
Ubl -> Lfu -> Rbu : f U2 f' u2 f U2 f' u2
Ubl -> Lfu -> Bur : L' u r' U2 r u' r' U2 r L
Ubl -> Ful -> Urb : l F r' F' l' F r F
Ubl -> Ful -> Rbu : Uu r Uu' l' Uu r' Uu' l
Ubl -> Ful -> Bur : u2 r' U2 r u2 r' U2 r


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## cmhardw (Sep 24, 2009)

Sakarie said:


> Ubl -> Urb -> Ulf: x l2 d2 l' U' l d2 l' U l' x'
> Ubl -> Ulf -> Urb : x l U' l d2 l' U l d2 l2 x'



:fp

I can't believe I missed the obvious solution to these cases. Not only that, but I was using 10 movers to solve this.



> Ubl -> Rbu -> Ful: l' Uu r Uu' l Uu r' Uu'
> Ubl -> Ful -> Rbu : Uu r Uu' l' Uu r' Uu' l



I never would have thought to do commutators like that! I'm not sure if Daniel has done ones this way either, I'll have to ask him. That's really great because it turns a number of the 10 move cases in to 8 movers in BTM (block turn metric)! I'm also curious how this block style turning can adapt to other cases, I'll have to look into this!

Wow thanks for the insight Sakarie! We should trade commutator cases more often ;-)

Chris


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## MatsBergsten (Sep 24, 2009)

Sakarie said:


> Ubl -> Ful -> Rbu : Uu r Uu' l' Uu r' Uu' l



Yes, I agree with Chris. This one is a marvel Arvid! 
It shouldn't work. You move all three pieces at the same time and then
get rid of the one normally blocking the others and therefore you don't
need any setup move. I thought I was doing the optimal way here.


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## cmhardw (Sep 24, 2009)

MatsBergsten said:


> Sakarie said:
> 
> 
> > Ubl -> Ful -> Rbu : Uu r Uu' l' Uu r' Uu' l
> ...



I'm happy to report that this style of alg is supercube safe! I checked this on a physical supercube 4x4x4, and supercube 5x5x5. This means you could apply this case safely even on the 6x6x6 or 7x7x7 as well! Very cool!

I see why it works too. You are moving the Rbu piece into the Ubl spot. Consider the Ubl as a small section of the inner l layer. To move it into that layer though you turn the large chunk the initial Uu turn, which moves a portion of the l layer to intersect the r layer. Now you do the r turn to place the piece into the section of l layer that has been moved over. The next Uu' moves restores that section of inner l layer back to its original position, with only the Ubl piece having been changed!

Beautiful!

Chris


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## masterofthebass (Sep 24, 2009)

if you didn't figure out how to use that commutator for + centers:

[m', 3U r 3U'] (on 5x5). It makes a lot of 10 movers, a quick 8 mover.


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## cmhardw (Sep 24, 2009)

masterofthebass said:


> if you didn't figure out how to use that commutator for + centers:
> 
> [m', 3U r 3U'] (on 5x5). It makes a lot of 10 movers, a quick 8 mover.



Dan, I do want to look at this for other cases and piece types too. That particular alg you wrote can be duplicated with: [u' R' u, m]

However, I think there might be other cases longer than 8 turns that can be reduced to 8 turns. Also I'll have to mess around with your triple layer U turn algs for that particular case, because it's quick to execute. Who knows, I might even change that case too if the new way is faster.

Very cool! This is exciting!

Chris


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## Mike Hughey (Sep 24, 2009)

masterofthebass said:


> if you didn't figure out how to use that commutator for + centers:
> 
> [m', 3U r 3U'] (on 5x5). It makes a lot of 10 movers, a quick 8 mover.



For that one, I always just used [u' R' u, m]. Still just 8 slice moves (I think being able to do this with + centers is one of the reasons I've always liked + centers better than X centers). But yours is nicer in that you have 4 block turns and 4 inner slice turns, whereas mine is 2 outer layer turns and 6 inner slice turns. So yours is probably better.

Sakarie, I agree with everyone else that these are really nice algorithms! I'm not sure if I'll ever migrate to BH for centers (for centers, I still do setup moves like Chris did before switching to BH), but if so, I'll definitely have to start doing these for these cases. And I agree with Chris that the idea of using TuRBo for 4x4x4 centers is a pretty cool idea - maybe it will get more people doing it!

Edit: I see Chris beat me to the alternate solution on that one. Sorry.


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## masterofthebass (Sep 24, 2009)

:fp ... i didn't even check to see. I think + centers would be tough. The similar case is Umb -> Fum -> Rus


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## trying-to-speedcube... (Sep 24, 2009)

Mike Hughey said:


> (I think being able to do this with + centers is one of the reasons I've always liked + centers better than X centers)


+ centers are stupid. X centers are cool.

That may be because I have done a whopping 3(!) attempts on a 5x5BLD, so I'm quite unexperienced with + centers... 

On topic: The idea is very cool, I'm looking forward to seeing how the setups turn out!


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## Mike Hughey (Sep 24, 2009)

trying-to-speedcube... said:


> + centers are stupid. X centers are cool.



X centers are stupid. + centers are cool. Obliques are the coolest! 

But really, the reason I think so is because obliques seem to have the most options for solving any given 3-cycle. + centers have less options than the obliques, but still more than the X centers. That may not actually be true, but in terms of the options I can easily "see" while solving, it is true, which is why I like obliques most and X centers the least of the center pieces. The X centers get in the way of each other more than the + centers do, and the + centers still get in the way sometimes where the obliques don't.

But this new set of commutators seems to open up the possibility that they don't really get in the way of each other, as long as you can see how they don't. It suggests that they're really all the same, as long as you can see them.


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## trying-to-speedcube... (Sep 24, 2009)

Mike Hughey said:


> trying-to-speedcube... said:
> 
> 
> > + centers are stupid. X centers are cool.
> ...


But everybody knows that wings pwn them all  (Wing edges, not chicken wings... Well, chicken wings pwn as well, but that's irrelevant)


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## cmhardw (Sep 24, 2009)

trying-to-speedcube... said:


> Mike Hughey said:
> 
> 
> > trying-to-speedcube... said:
> ...



Corners are by far my favorite 

;-)

Chris


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## trying-to-speedcube... (Sep 24, 2009)

cmhardw said:


> trying-to-speedcube... said:
> 
> 
> > Mike Hughey said:
> ...


Well, in the end it's the fixed centers on odd cubes that I love most. They're the least in each other's way, and with a certain orientation, you can solve them all without turning!


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## cmhardw (Sep 24, 2009)

trying-to-speedcube... said:


> cmhardw said:
> 
> 
> > trying-to-speedcube... said:
> ...



While I have to agree with you on that one, I think that if I were to truly search deep for my absolute favorite cube part - it would have to be the logo sticker. I mean come on, it's the only one that's different out of the whole bunch.

That takes guts. Mad props to the logo sticker for that one.

;-)

Chris

[/ridiculous thread hijack]


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## Stefan (Sep 24, 2009)

Sakarie said:


> Ubl -> Ful -> Rbu : *Uu r Uu' l' Uu r' Uu' l*


Reminds me of M2 for 3x3x3 and Lucas (?) replacing my *l U' R' U M2 U' R U l'* with *u R u' M2 u R' u'*. Not trying to take away from Sakarie's discovery, but I guess we should always try tricks found for one puzzle/method for others as well.


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## Sakarie (Sep 24, 2009)

cmhardw said:


> Sakarie said:
> 
> 
> > Ubl -> Urb -> Ulf: x l2 d2 l' U' l d2 l' U l' x'
> ...



I think the only thing that is needed sometimes is the amateurs (in this company!) point of view. It's only to use the most of the algorithms you've got!

You can of course do algorithms like r 3u l' 3u' r' 3u l 3u'



StefanPochmann said:


> Sakarie said:
> 
> 
> > Ubl -> Ful -> Rbu : *Uu r Uu' l' Uu r' Uu' l*
> ...



I would never made it up if no one made U R U' L' U R' U' L up from the start. You could almost never take full credit!

I've thought about the setupmoves, and I do not think they are much of a problem, since most of the pieces can go to so many places, with one move!

If any one else care, I write up all the possible setupmoves, separated with a ; semi-colon. I will only write the easiest solutions, but everyone can go in a lot of ways, but with more moves. I will write with slicemoves, but sometimes it can work with double-layer moves. " - " means that no setupmove is required.

Ufl: -
Urf: r; f’
Ubr: -
Flu: - ; u2
Fur: F’; r
Frd: F2; r2
Fdl: F’
Rfu: R; f’; u
Rdf: R2; f2
Rbd: R’; 
Rub: - ; u2
Bru: - ; u2
Bdr: B
Bfd: B2
Buf: B’; u; u’
Lbu: L; u’; u
Ldb: L2
Lfd: L’
Luf: - ; u
Dlf: f
Dbl: D f; D2 f2; D’ r’; D2 r2 
Drb: r’
Dfr: r2; f2 

It's only Dbl that always requires two setupmoves, but hopefully, you may combine that with the other setupmove, for the first piece.


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## Sakarie (Oct 12, 2009)

So, World cup is over, and 4x4 blindfolded went as good as it possibly could. 

But now it's time to learn thos algorithms, since I no longer have a reason not to do it. Since I know some of them, and thery're all very logical, it will probably take just a couple of days to learn them, some days to know which algorithms is which, and maybe I could do some solve sighted within a week or two.

I do learn some other things parallell, so I can't lay all my time on it thou.


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