# ZZ Statue of Kitten - a somewhat new ZZ variant



## a small kitten (Dec 7, 2010)

I've been thinking about this lately because I wanted to find another way to exploit 2GLL. This variant is similar to Statue's CPLS but instead of solving an edge before permuting the corners, you solve a corner. 

This is Statue's CPLS thread: http://www.speedsolving.com/forum/showthread.php?24125-CPLS-and-2GLL-discussion&highlight=cpls

Here are my thoughts. Starting with the pros:

- Lessens the tedious recognition problem because solving one corner eliminates a corner you have to look at. With enough practice I think you even brute force recognize the corner cycle.
- Less algs. I believe it's something like 9. I guess that's good?

Cons:

- If you insert the corner too early, you can trap another f2l edge piece you need.
- Assuming that D is white....if you have one corner left and the white sticker is pointing up, it becomes a waste of moves and time to solve the corner by itself. 

Here are some thoughts about white corner sticker pointing up:

You can do normal CPLS if the corresponding edge piece is in

FR: CPLS right away
UB: RUR'+CPLS
UL: RU2R'+CPLS
UF: RU'R'+CPLS
UR: URU'R'+CPLS (or RU2R'U'RUR' and COLL+EPLL)

If the white corner sticker isn't pointing up, the corner is solvable in like 3-4 moves. Perhaps you can build a 1x1x3 strip and pair it with a single edge piece? 

Here are some questions I have about this variant. Hopefully someone with more knowledge can help.

1. How long/short/ugly are algs that solve the last edge piece while permuting the corners? 

2. For white sticker pointing up cases, what else can be done? I thought about orienting all the corners but there would be over 100 cases for that. Not good.

3. Turning a white sticker pointing up case into a regular CPLS case should reduce the number of CPLS cases. How many CPLS cases would be left?

4. What kind of time splits / movecount splits can you imagine?

I'm not crazy about this thing, but it is interesting to me. I just wanted to find the easiest way to a 2GLL finish because they are very fast for OH.


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## StachuK1992 (Dec 7, 2010)

Some quick thoughts and questions (to all)
-I'm trying to remember why I decided to do edge then CPLS rather than corner than CPLS back when I made the other thread.
-average movecount for set-up and CPLS-C (rather than CPLS-E)?
-some nice block-building methods to get the corner in while doing the 2x2x1?


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## BigSams (Dec 7, 2010)

No comment on method. LMFAO @ name of method.


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## Diniz (Dec 7, 2010)

I think would be only 6 algs for ZZ-SK ( 4 Js, 1 y and solved). Avg Move count is exactly 10.

Edit: 

RUL Optimal Algs:
Solved: R' U' R' U' R' U R U R (9)
Y: (U') R U R' L U' R U L' U' R' (10)
J right: R U2 L U2 R' U2 R U2 R' L' (10)
J back: (U2) R L U2 R' U2 R U2 L' U2 R' (10) 
J left: (U') R2 L U2 R' U' R U2 L' U R2 (10)
J front: R U L U2 R' U' R U2 L' U' R' (11)


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## Baian Liu (Dec 7, 2010)

Very interesting. But I would imagine that CPLS with a solved edge would be a lower move count. And solving the edge first would be easier than solving the corner first.


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## StachuK1992 (Dec 7, 2010)

While Baian is probably right above, the recognition for corner permutation would be MUCH nicer if the corner were in first rather than the edge.


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## Baian Liu (Dec 7, 2010)

I guess it'd be easier if you already knew CLL recognition. But for someone who is new to both, I think recognition would be about the same.


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## StachuK1992 (Dec 7, 2010)

How so?
I guess it's the same recognition concept as BRASS. Have you done anything with that?


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## Baian Liu (Dec 7, 2010)

CLL recognition is slightly faster, but I think CPLS recognition can match it if practiced well enough.
I have learned all the cases for BRASS step 1, but the recognition can be done during inspection so I haven't really tried to do it quickly.


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## Cyrus C. (Dec 7, 2010)

To solve the white on top problem, bring the cases up to 27 and allow the DFR corner to be misoriented.

EDIT: it could even be just 18 if you only set up with R U R', but knowing all 27 would be helpful.


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## EricReese (Dec 7, 2010)

Definately looking forward to this. Phil I assume this is the project you spoke of?


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## Diniz (Dec 7, 2010)

Cyrus C. said:


> To solve the white on top problem, bring the cases up to 27 and allow the DFR corner to be misoriented.
> 
> EDIT: it could even be just 18 if you only set up with R U R', but knowing all 27 would be helpful.



And it will make the setup move count avg be sub3 (0+3+3+3+4/ 5 = 2.6). But will mess up recog again =/ (same difficulty as CPLS )

The avg move count for solve the corner is 4.8 with the bad up orientation and 3.9 without it.

And i think that are 18 =P


Edit: Iam dumb =/


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## Baian Liu (Dec 7, 2010)

Diniz said:


> And it will make the setup move count be always 3. But will mess up recog again =/
> 
> And i think that are 21 =P


 
Would a corner at UBR require 4?


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## Diniz (Dec 7, 2010)

Baian Liu said:


> Would a corner at UBR require 4?


 
Yes of course, im dumb =/


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## Cyrus C. (Dec 7, 2010)

Diniz said:


> And it will make the setup move count avg be sub3 (0+3+3+3+4/ 5 = 2.6). But will mess up recog again =/ (same difficulty as CPLS )
> 
> And i think that are 18 =P
> 
> ...


 
Mess up Recognition? How?


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## Baian Liu (Dec 7, 2010)

Cyrus C. said:


> Mess up Recognition? How?


 
You wouldn't be able to use regular CLL recognition if the corner at DRF is misoriented.


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## Diniz (Dec 7, 2010)

The avg move count of with the corner solved is probably 10 (RUL, so 1 move higher then CPLS), tomorrow i will finish this (2 am here =/)



The extended idea (just put the corner in place but not necessarily in correct orientation) has the same recognition, the same number of cases (of the respective subsets) and probably the same move count as CPLS.


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## a small kitten (Dec 7, 2010)

How does it have the same recognition? A corner is solved already.


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## Diniz (Dec 7, 2010)

a small kitten said:


> How does it have the same recognition? A corner is solved already.


 
The extended idea that Cyrus C. proposed i meant (just put the corner in place but not necessarily in correct orientation)


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## oll+phase+sync (Dec 7, 2010)

Only a question: Why place anything?

Is it possible (by means of recognition ) to just bring the cube into 2Gen state (is it 7 cases ?) - maybe doing some partila CO stuff by the way

And than happily solve 2-Gen


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## Diniz (Dec 7, 2010)

oll+phase+sync said:


> Only a question: Why place anything?
> 
> Is it possible (by means of recognition ) to just bring the cube into 2Gen state (is it 7 cases ?) - maybe doing some partila CO stuff by the way
> 
> And than happily solve 2-Gen


 
This would get rid of setups and would bring down the move count, but i dont see how recog would work... (and would still have to solve a F2L slot afterwards). 

And would be just 2 algs right? (Y and J)
J-> L' U R U' R' L (6)
Y-> R U2 L' U R' U' L (7)


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## StachuK1992 (Dec 7, 2010)

If you don't solve anything in the LS+LL area, then you would need to solve:
-EO, which is done in ZZ, so nothing to worry about here
-CP, which is only 6 cases or 5 algs.

To get to 2GLS+LL

However, I feel like just doing this is very little, and much more can be done in that step for the amount of recognition needed.


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## Matt S (Dec 7, 2010)

The biggest disadvantage I see with this variation is that you're less likely to get lucky with a pre-placed corner than a pre-placed edge, because any corner only has a 1/3 chance of being properly oriented. There's also the 1/3 chance that, if you wait for the last slot to place your corner, you'll have the ugly upside-down orientation.

But! There's few enough cases of CPLS-E and CPLS-C that you could reasonably learn both and get an extra chance to be lucky. Of course, you'd probably want to prioritize the systems for yourself so that you'd have an immediate plan if you came to the last slot without a lucky placement.


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## Diniz (Dec 7, 2010)

Move counts:

CPLS+2GLL:
2.6 (Edge setup) + 9 (CPLS) + 14 (2GLL)= 25.6

Reduce to 2gen before last slot:
4.33 (Reduce to 2gen)+ 7.66 (RU-LS) + 14 (2GLL)= 26.00

Silly Way to go to 2GLL:
7.66 (RU-LS) + 6 (Reduce to 2gen) + 14 (2GLL) = 27.66

COLL+EPLL:
7.66 (RU-LS) + 9.78 (COLL)+ 10.75(2gen EPLL) = 28.19

ZZ SK (with the pointing up case):
4.8 (Corner setup) + 10 (CPLS variant) + 14 (2GLL)= 28.8


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## StachuK1992 (Dec 7, 2010)

Aha! I CPLS+2GLL is the lowest move-count; that makes me smile.
However, recognition for ZZ-SK would be nicer. (I'm pretty sure I've said "ZZ-SK" for some other method over a year ago, but I forget what it was for...)


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## Diniz (Dec 7, 2010)

The move count are mayble sightly off, 2GLL movecount based on your file is about 14.3 and the CPLS i think is lower then 9, so its still the better movecount.

If there was a way to recog reduce to 2gen before last slot would be the better, since is only 2 algs with 4.33 avg move count (0+6+7 /3) and then a 22 moves RU spam.


Edit:

RUL Optimal Algs for ZZ-SK:

Solved: R' U' R' U' R' U R U R (9)
Y: (U') R U R' L U' R U L' U' R' (10)
J right: R U2 L U2 R' U2 R U2 R' L' (10)
J back: (U2) R L U2 R' U2 R U2 L' U2 R' (10) 
J left: (U') R2 L U2 R' U' R U2 L' U R2 (10)
J front: R U L U2 R' U' R U2 L' U' R' (11)


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## oll+phase+sync (Dec 7, 2010)

Diniz said:


> Move counts:
> 
> Silly Way to go to 2GLL:
> 7.66 (RU-LS) + *4.66 *(Reduce to 2gen) + 14 (2GLL) = 26.32


 
I know this is the Silly Version but 4.66 is not possibe after the Slot is occupid I think 6,3 is correct (0+7+7+7+7+10/6)

To give Coll a better standing: Stachu compiled a list of "Last 5 edges" algorithmes as part of L2L4 methode but ther would be an option to:

[Corner last Slot (2gen) ] + COLL + L5E : ~3 + 9.78 (COLL)+ ~12 L5E = ~25 




@stachu I smile, too


EDIT: @diniz (0+6+7 /3) shouldn' it be (0+6+6+6+6+7 /6)


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## Diniz (Dec 8, 2010)

oll+phase+sync said:


> @diniz (0+6+7 /3) shouldn' it be (0+6+6+6+6+7 /6)



I dont think so, you can just do U, U' or U2 and do the same alg, so they are just 3 different cases (solved, adjacent swap, opposite swap). You are counting adjacent swap multiple times.

Example: Numbering from here: http://www.speedsolving.com/wiki/index.php/Special:AlgDB?mode=view&view=default&puzzle=3&group=COLL

#2 R' U' R U' L U' R' U L' U2' R 
#3 U' (R U' L' U R' U' L) 
#4 U (R U' L' U R' U' L )
#5 (R U' L' U R' U' L )
#6 U2 (R U' L' U R' U' L )


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## Baian Liu (Dec 8, 2010)

Diniz said:


> I dont think so, you can just do U, U' or U2 and do the same alg, so they are just 3 different cases (solved, adjacent swap, opposite swap). You are counting adjacent swap multiple times.


 
An adjacent swap would come up more often than the other two, so you can't weight them the same.


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## Diniz (Dec 8, 2010)

Baian Liu said:


> An adjacent swap would come up more often than the other two, so you can't weight them the same.


 
Thats right, but if we consider probabilities all move counts are wrong =/


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## oll+phase+sync (Dec 8, 2010)

Just for fun I calculated what the weighted movecount for RUL - placing the Last D-Corner in an empty Slot should be:
the .25/.75 comes from AUF

3.25 *4 + 3.75 *4 + 6.75 * 4 + 7 + 7 + 0 = 4.6

What this number doesn't tell is that it is maybe already just placed by some F2L magic.


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## Robert-Y (Nov 3, 2013)

I just had a thought about this. What if you do this instead:

(Assume EO and F2L-1 is complete, and that the last pair isn't 3-4 moves)

1. Separate the pair: Place the corner in the correct slot, and leave its corresponding edge on top
2. Solve the last pair and permute corners on top. There will be many new corner permutation cases to "learn" however there will still be only a few algs. If the FR slot is the last slot, then you will only have to learn 18 algorithms. (6 CPLLs * 3 orientations of the last F2L corner).
3. 2GLL to finish the solve.

If you're ambitious enough, you could learn the second step for each possible last slot, which totals to 72 algorithms.


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## elrog (Nov 3, 2013)

I think this would work well if you also included the cases with the edge placed in the slot just in case you end up with the edge and corner in the slot already. This would up the algorithm count by 8 (9 minus the solved case) and it would slightly reduce the average move count for setting the pair up.


I think it would also be useful if you made the algorithms end with the pair left in thetop layer so that you can intuitively phase before doing 2GLL.


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## Robert-Y (Nov 3, 2013)

There's a reason why I deliberately mentioned that you separate them. I've looked at http://cube.garron.us/MGLS/I.htm before and the algs seem kinda long. So I figured that perhaps CPLL+twisted corner may not be a good idea. Let me just generate some algs first...


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## Robert-Y (Nov 3, 2013)

FRD twisted clockwise:

No swap:
R U R' U' R U2 R' U' R U R'
R U' R' U' R U R' U' R U2 R'
R U' R' U' R U R' U2 R U' R'
Backswap:
L R U' R' U L' R U' R' U' R U R'
Diagonal swap:
R U' R' U R L U' R' U R L' U' R'

FRD twisted anticlockwise:

No swap:
R U R' U2 R U' R' U R U R'
R U' R' U R U2 R' U R U' R'
R U2 R' U R U' R' U R U R'
Back swap:
R U' R' U R U R' L U' R U R' L'
Diagonal swap:
R U R' L U' R U R' L' U' R U R'

Here are some algs. I think I'll take back what I said, these algs seem ok and not very long IMO. So I guess it's worth learning algs for these cases.


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## elrog (Dec 9, 2013)

Robert-Y said:


> I just had a thought about this. What if you do this instead:
> 
> (Assume EO and F2L-1 is complete, and that the last pair isn't 3-4 moves)
> 
> ...



I have came up with algorithms for this (by hand, so they're not all optimal), but I also included cases where the edge was in the slot. There are 26 algorithms total with an average move count of 11-12. I would make pictures using VisualCube, but I don't know how to use the arrows to show corner permutation.



Spoiler: Algorithms






Spoiler: Edge in slot cases






Spoiler: Corner in slot oriented correctly



Right swap:
L' U R U' L U R' // 7
L U' R' U L' U' R' // 7

Diagonal swap:
L' U2 R U' R U2 L U R U2 R' // 11





Spoiler: Corner needs to be twisted clockwise



No swap:
(R U' R' U) (R U2 R') L' (U' R U R') // 13
(R U2 R') U (R U' R' U) (R U R') // 11

Right swap:
(U') (R U' R' U) (R U R') L (U' R U R') L' // 13

Diagonal swap:
(R U R') L U' (R U R') L' (U' R U R') // 13
L' U R2 U' L (U' R2)3 // 11





Spoiler: Corner needs to be twisted counter-clockwise



No swap:
(R U R' U') (R U2 R') (U' R U R') // 11
(R U' R') U' (R U R' U') (R U2 R') // 11

Right swap:
U' L (R U' R' U) L' (R U' R') (U' R U R') // 13

Diagonal swap:
(R U' R' U) R L (U' R' U R) L' U' R' // 13








Spoiler: Edge in the UR position






Spoiler: Corner in slot oriented correctly



No swap:
(U2) (R' U')2 (R U)2 R // 9

Right swap:
(U') R2 U R U' R2 D R' U' R D' // 10

Back swap:
(U') F' (R U R' U') R' F R // 8

Left swap:
(U2) R2 U' L U2 R' U R U2 L' R2 // 10

Front swap:
R' F' R (U R U' R') F // 8
U L R U2 R' U2 R U2 L' U2 R' // 10

Diagonal swap:
R U L U' R' U L' (R U R') // 10
(U') (R U R') L U' R U L' U' R' // 10





Spoiler: Corner needs to be twisted clockwise



No swap:
(R U R' U') (R U R') // 7

Right swap:
L' (R U R' U') L (R U R') // 9

Back swap:
(U') R U2 L U' R' U' L' // 7

Left swap:
(U') R U2 L U' R2 U' L' U' R // 9

Front swap:
(U2) L R U' R' U L' (R U2 R') // 9

Diagonal swap:
(U) R U L U' R' U L' (U' R U R') // 11





Spoiler: Corner needs to be twisted counter-clockwise



No swap:
(R U R') (U R U' R') // 7

Right swap:
(U') L' U R U' R U R U' L R' // 10

Back swap:
L R U' R' U L' U2 R U' R' // 10

Left swap:
R U' R' L' (U R U' R') L // 9
R U2 L R' U' R U R' L' // 9
(U) R' U L U' R2 U' L' U2 R' // 9

Front swap:
(U2) L U' R U L' U2 R' // 7

Diagonal swap:
(U) L' U R2 U' L U R' U2 R' // 9
(U) (R U' R' U) L U' R U L' U' R' // 11


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