# I've found something with LL algs



## YouCubing (Nov 16, 2015)

This is hard to explain, so I'll show it instead of trying to talk about it.
Let's take a T-perm.
R U R' U' R' F R2 U' R' U' R U R' F'
Now let's separate all the Rs, Us and Fs from each other.
R R' R' R2 R' R R'
U U' U' U' U
F F'
Now, let's cancel these moves out. 2 Rs will cancel an R2, 2 R's also will cancel R2s, R2s will cancel each other, and Rs and R's will cancel each other. Same goes for F, U, B, L and D faces.
We're left with:
no Rs
U'
no Fs
All faces will cancel out, except for (sometimes) the U face. I've tried this with some other PLLs and OLLs, and it worked, so is this a general rule of LL algs, or are there some exceptions?
Here's one more example: a Ja-perm. 
L' U R' U2 L U' R U L' U R' U2 L U' R
Separate:
L' L L' L
U U2 U' U U U2 U'
R' R R' R
Cancel:
no Ls
U
no Rs


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## DTCuber (Nov 16, 2015)

YouCubing said:


> This is hard to explain, so I'll show it instead of trying to talk about it.
> Let's take a T-perm.
> R U R' U' R' F R2 U' R' U' R U R' F'
> Now let's separate all the Rs, Us and Fs from each other.
> ...



Interesting. I've never thought about that before, but it seems like there would be no exceptions. All LL algorithms should cancel out all moves besides U moves since you are only affecting the pieces in the U-layer.


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## shadowslice e (Nov 16, 2015)

Try creating an alg which preserves the F2L with differing numbers of R, F, L, B and D algs. My intuition tells me it's not possible due to the fact algs are made of commutators and conjugates which will cancel themselves out apart from the moves affecting the bit you want to effect. I refer you to the previous thread in this sub-forum.

EDIT: see above. He says the same thing as me.


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## Hssandwich (Nov 16, 2015)

R U R U R U' R' U' R' U2 R U R U R U' R' U' R'


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## Cale S (Nov 16, 2015)

R2 U2 R' U2 R2 U2 R2 U2 R' U2 R2


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## shadowslice e (Nov 16, 2015)

Hssandwich said:


> R U R U R U' R' U' R' U2 R U R U R U' R' U' R'



Hmmm... Interesting. Perhaps the rule should be even numbers of face turns? At least if we completely move all the pieces on a face.


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## YouCubing (Nov 16, 2015)

Hssandwich said:


> R U R U R U' R' U' R' U2 R U R U R U' R' U' R'



interesting, off by an R2 U2.
I also found this:
R2 U' B2 U B2 R D' R D R' U R U' R, It's a V-perm.
R2 R R R' R R
B2 B2
D' D
U' U U U'
Cancel:
R
no Bs, Ds, *or Us.*
weird.


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## shadowslice e (Nov 16, 2015)

Ok, going by this, it may be that the rule only works if you don't move all the pieces on one face as the reinsertion of all the pieces would cancel out when they were removed.

Try to find an alg which preserves centre orientation with mismatching numbers.


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## StachuK1992 (Nov 16, 2015)

R' L' F2 B2 L R D' R' L' B2 F2 L R 
Have fun explaining this LL alg.


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## DELToS (Nov 16, 2015)

StachuK1992 said:


> R' L' F2 B2 L R D' R' L' B2 F2 L R
> Have fun explaining this LL alg.



Let's see...
R', R, R', R
L', L, L', L
F2, F2
B2, B2
D'
=
No R
No L
No F
No B
D'

But anyway I find this concept he brought in EXTREMELY cool and interesting

Maybe this works on D too? Not sure.


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## StachuK1992 (Nov 16, 2015)

here, I made a thing to help you guys not have to do this stuff manually

https://dotnetfiddle.net/zt9mCj

Should be fairly self-explanatory


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## YouCubing (Nov 16, 2015)

StachuK1992 said:


> here, I made a thing to help you guys not have to do this stuff manually
> 
> https://dotnetfiddle.net/zt9mCj
> 
> Should be fairly self-explanatory



Thanks a lot!


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## DGCubes (Nov 16, 2015)

Very very cool. I feel like I've considered things like this before, but never really gave it a second thought. I wonder what the reasoning behind this is...

EDIT: JUST UNDERSTOOD SOMETHING! If it's off by like an R, that means the R center probably turned 90 degrees clockwise, yet the pieces were put around it correctly. Theoretically, it could be off by anything this way, right?


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## YouCubing (Nov 16, 2015)

DGCubes said:


> Very very cool. I feel like I've considered things like this before, but never really gave it a second thought. I wonder what the reasoning behind this is...
> 
> EDIT: JUST UNDERSTOOD SOMETHING! If it's off by like an R, that means the R center probably turned 90 degrees clockwise, yet the pieces were put around it correctly. Theoretically, it could be off by anything this way, right?



I guess it could. I just tried out the Vperm I showed earlier again, and it looks like the pieces are moved out and back in again on the red face. That would also explain the RU-gen Hperm (R2 U2 R U2 R2 U2 R2 U2 R U2 R2), because I can see it happening in there as well.


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## Ordway Persyn (Nov 16, 2015)

This is actually interesting
I made / discovered this alg: F R U' R' F' L' U L 
It has no F, R, U, or L moves...


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## StachuK1992 (Nov 16, 2015)

Protip: No one center can twist alone.


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## CubeWizard23 (Nov 16, 2015)

StachuK1992 said:


> Protip: No one center can twist alone.


do a t perm with a dry erase marker on all the centers.


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## Cale S (Nov 16, 2015)

StachuK1992 said:


> Protip: No one center can twist alone.



Unless you have parity (odd alg length in QTM)


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## MoyuFTW (Nov 16, 2015)

StachuK1992 said:


> Protip: No one center can twist alone.



Definitely not right. How do you solve parity on a crazy fisher cube then? 

So what's the conclusion about this? What happens when you get one of the leftover moves? Does it twist a center?


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## StachuK1992 (Nov 16, 2015)

Neat.


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## vcuber13 (Nov 16, 2015)

CubeWizard23 said:


> do a t perm with a dry erase marker on all the centers.



I may be wrong, but I'm fairly confident a T-perm does more than rotating one centre.

Also, I'm sure he meant to say by 90 degrees.


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## JustinTimeCuber (Nov 16, 2015)

This is cool, but...
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L' (z2)
Good luck.


Spoiler: breakdown



R2 B2 U2 *F2* U' R2 D' L2 U B2 D L D R' U' *F* D R2 *F'* U *F* R *F2* L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' *F* D *F'* D' *F'* D' *F* D' L D L'
F2 F F' F F2 F F' F' F = *F*
*R2* B2 U2 F2 U' *R2* D' L2 U B2 D L D *R'* U' F D *R2* F' U F *R* F2 L' B' U2 D' L' D2 L D2 B D' B' *R'* D *R* D' *R* D *R'* D2 L D L' F D F' D' F' D' F D' L D L'
R2 R2 R' R2 R R' R R R' = *R2*
R2 B2 *U2* F2 *U'* R2 D' L2 *U* B2 D L D R' *U'* F D R2 F' U F R F2 L' B' *U2* D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
U2 U' U U' U2 = *U'*
R2 *B2* U2 F2 U' R2 D' L2 U *B2* D L D R' U' F D R2 F' U F R F2 L' *B*' U2 D' L' D2 L D2 *B* D' *B*' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
B2 B2 B B B = *B'*
R2 B2 U2 F2 U' R2 D' *L2* U B2 D *L* D R' U' F D R2 F' U F R F2 *L'* B' U2 D' *L'* D2 *L* D2 B D' B' R' D R D' R D R' D2 *L* D *L'* F D F' D' F' D' F D' *L* D *L'*
L2 L L' L' L L L' L L' = *L2*
R2 B2 U2 F2 U' R2 *D'* L2 U B2 *D* L *D* R' U' F *D* R2 F' U F R F2 L' B' U2 *D'* L' *D2* L *D2* B *D'* B' R' *D* R *D'* R *D* R' *D2* L *D* L' F *D* F' *D'* F' *D'* F *D'* L *D* L'
D' D D D D' D2 D2 D' D D' D D2 D D D' D' D' D = *D'*


wut


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## guysensei1 (Nov 16, 2015)

MoyuFTW said:


> Definitely not right. How do you solve parity on a crazy fisher cube then?
> 
> So what's the conclusion about this? What happens when you get one of the leftover moves? Does it twist a center?



It's true, no center can twist 90 degrees by itself. The fisher cube can show this because it has a center with no orientation too, so you can twist that one, and one other with orientation, and it looks like you've twisted only 1 center 90 degrees.


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## MoyuFTW (Nov 16, 2015)

guysensei1 said:


> It's true, no center can twist 90 degrees by itself. The fisher cube can show this because it has a center with no orientation too, so you can twist that one, and one other with orientation, and it looks like you've twisted only 1 center 90 degrees.



Yeah. I knew that  Kind of. I know you can't twist one 90 but 180. Or you could just do the cyoubx thing and cheat.


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## Lucas Garron (Nov 17, 2015)

Rule of thumb: Do any cross pieces become detached from their side colors during the alg before coming back home?

If not, then the moves on the sides *have* to cancel out: the center stayed attached to the cross edge, and the journey of cross edge canceled out.
Since many LL algs work by manipulating a few F2L pairs in clever ways, the moves will cancel for many of those.

(Technically, the aren't guaranteet won't cancel out, but the center on each site will come back. It's possible for the cross edge to travel around by a full revolution like R4, but this won't be the case for more efficient algs; they'll simply cancel out.)

U-perm is a well-known counter example. It's not supercube-safe.


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## qqwref (Nov 17, 2015)

Yeah, all you really did was discover that a lot of LL algs don't orient any centers (except maybe U). There are good reasons for this. Lucas correctly points out that if the cross edges remain attached to their respective centers then the centers can't end up misoriented (except possibly the D center). It's also true that a lot of nice LL algs are made of only commutators and setup moves, and the structure of those types of algs means that.

This is not a rule, though, as there is no guarantee that a LL alg will leave the center orientations alone. Cube Explorer will happily generate LL algs that orient the centers in any possible way.

For instance, Ben found this T perm that rotates every center:
D' F2 L2 D F2 U2 F2 R2 D F2 D L2 U' F2 U2 B2 L2


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## guysensei1 (Nov 17, 2015)

qqwref said:


> This is not a rule, though, as there is no guarantee that a LL alg will leave the center orientations alone. Cube Explorer will happily generate LL algs that orient the centers in any possible way.


Unless you activate the center orientations


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