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Noah's CP Block Method 2.0

Noahaha

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As some of you may remember, I proposed a Petrus based CP-block method a while back. The problem with it was that it made Petrus even more inefficient than it already was just in order to have a 1LLL.

I never dropped the idea of CP-blocks, however...

...and today I bring you my NEW AND IMPROVED CP-block method. Unlike the last one, it is its own method. It shares characteristics with Petrus, Roux and OBLBL, but the end result is definitely something entirely different and hopefully new. I say hopefully, because all "new" methods must come with the disclaimer that someone may have discovered them before.

Onto the method:

Step 1: CP (Roux) Block

The goal of this step is to reach a state where there is a Roux block solved on the left and the corners are permuted.

It can be divided into three parts:

1a - SOLVE A ROUX BLOCK on the left (note that you can mirror the entire method) just like the first step of Roux. I recommend doing the same block every time.

1b - PLACE, but do NOT orient the FDR and BDR corners. This should take 4 moves at most.

1c - CP.

Recognition: figure out which two U-layer corners need to be swapped.
If no corners need to be swapped, you're done!
If two adjacent corners need to be swapped, place them at UFR and UBR, and do F' U F or y R U' R' y'.
If two diagonal corners need to be swapped, make them adjacent and then do what's above.

Cases:
- UFL UFR = F' U' F
- UFR UBR = F' U F
- UBR UBL = F' U2 F
- UBR UFL = U' F' U' F
- UFL UBR = R' F' U' F
- UBL UFR = R F' U2 F


Ideally, 1a and 1b would both be planned in inspection, or at the very least the positions of the last two D-layer corners would be noted.


Step 2: EDGES!

This step has two parts, although ideally they should merge into one step. Step 2 is where this method has a LOT of freedom.

Step 2 brings the cube to a state where the bottom left 2x2x3 is solved, the edges are oriented and the corners are permuted. As long as you only use U, R and r moves during this step, the corners will remain permuted from the CP-block.

2a - ORIENT ALL EDGES

I haven't found a way to break this down yet, so people who are not familiar with Roux might struggle a little bit here. A Roux approach seems best to me, using moves like M' U M to orient 4 edges at a time. If you have two edges left, just put them at UB and UL and do M' U M U2 M' U M. Note that an M/M' move changes the orientation of all edges on the M-slice. You should start by placing your U/D centers into place or opposite places because in the end you have to have them oriented along with the edges.

As qq pointed out, there are 5-move 2-flips:
DR and UF: r U R U' r'
FR and UF: M' U R U' r'
etc. they all follow the trend of slice, replace an edge, slice back.


2b - FINISH THE 2x2x3 by placing the DF and DB edges.

This is extremely easy and should only require 3-6 moves depending on where your edges are at the end of 2a. A good strategy is to connect them at UL and UR, and then insert them between the correct two centers. Remember, you can only do double turns involving the M-slice in order to preserve EO, so other than M U2 M' type things, the moves you can make are: R, R2, R', M2 and r2.

NOTE: you can start step 3 before finishing 2a if it's convenient.

Step 3: Right Block

This is the same as the right block in ZZ and step 4 of Petrus. Just use R and U to finish F2L.

Step 4: 2GLL

Yay! We have finally reached our 1LLL, and it only requires 85 algs. That's not much more than CFOP :)


Summary

Step 1 - CP block
-1a = Roux Block
-1b = Place last two D-layer corners
-1c = CP in 0, 3, or 4 moves
Step 2 - EDGES
-2a = EO
-2b = Finish Petrus Block
Step 3 - Right Block
Step 4 - 2GLL


Analysis

Pros:
- REALLY fingertrick friendly (only uses M, U, R and r after step 1)
- Practically rotationless
- Many substeps can be solved in very few moves
- 1LLL
- Lots of freedom
- It's really fun!!!


Cons:
- A lot needs to be planned in inspection
- Lots of sub-steps
- Potentially really high movecount
- 85 algs to learn
- Although there are often really quick solutions, they are not always easy to see in a speedsolve.

Feel free to give me more pros and cons to add :)


Example Solve

Scramble (in solving orientation): B2 U2 L2 R2 D' R2 D' B2 D' B2 U2 L B F2 L2 D' L' F2 R' D F2

1a: U2 L' U L2 D F U' L2 (8)
1b: U' R' U R (4)
1c: U2 B U' B' (4)
2a: R' U2 M' U M (5)
2b: R2 U' r' U2 r (5)
3: R U2 R' U2 R' U R U2 R' U R (11)
4: U2 R' U R' U' R' U' R' U R U R2 (12)

Move count: 49


Conclusion

I don't think anyone will end up using this to speedsolve because it is pretty complicated, but I hope people enjoy the method and use it for fun sometimes. If you like it, please post an example solve. A lot of the fun of this method is finding shortcuts and ways to accomplish two things at once.

Sorry for the long read, and sorry if this has been thought of already!
 
Last edited:

ottozing

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

x' y'
D' F r U x' U r U r' B (1x2x3)
U' R r (Place corners)
(CP skip)
R U R r U2 M' U2 M' U r (EO)
U2 r' U2 r' (DF DB)
R U2 R U' R' U' R' U R U2' R' U R U' R' (Finish F2L)
U R' U2 R2 U2 R U2' R' U2 R U2 R2' U2' R' (2GLL)

Not very efficient, but that's probably my fault XD Cool method :tu
 

qqwref

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It's interesting! I like it. Definitely worth playing around with, although I don't exactly plan to learn 2GLL. There are going to be a lot of steps no matter what you do, but it should be sub-15-able.
 

erikoui

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

UR'U'RU DRDR'L (FB)
U'R'U'R (2Corners)
U2 BU'B (CP)
I might have messed up.
 

Smiles

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i came up with a really inefficient method once, and it included the roux block + <R,r,M,U> for EO. a big problem was recognition for bad edges since the centers move around so much, as well as just locating all of them and orienting them since it's pretty much impossible to find them during inspection.

and i like the whole 2-gen thing including LL, and <M,U> (+R?) is also a great restriction imo. however, i think 2 gen LL is probably a bit much even though it's 1LLL, cause not all the algs are that great anyway. this method could be interesting for OH since almost the whole thing is RrU with table abuse for M.
 

CubicNL

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For the CP part it would be really much better if you would fix CP when you finish the block, without having to place FDR and BDR first.
And I can assure you it's possible, I have worked out half a system so far, but I would loook into that, for that would improve the method a lot.

And for the CP fixes, I would like to add some :)
Given that the two pieces that need to be swapped are adjacent:
UFL UFR : F'U'F
UFR UBR : F'UF
UBR UBL : F'U2F

These can be done with B moves too, but I prefer them with F in a solve.
 
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aznanimedude

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Not bad. Kinda reminds me of what porkynator tried to do with zz-rainbow. His step is kinda similar to your first step except if came after eoline. Still pretty interesting
 

Noahaha

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For the CP part it would be really much better if you would fix CP when you finish the block, without having to place FDR and BDR first.
And I can assure you it's possible, I have worked out half a system so far, but I would loook into that, for that would improve the method a lot.

And for the CP fixes, I would like to add some :)
Given that the two pieces that need to be swapped are adjacent:
UFL UFR : F'U'F
UFR UBR : F'UF
UBR UBL : F'U2F

These can be done with B moves too, but I prefer them with F in a solve.
Thanks for those! I updated the section on 1c, and now the longest case is 4 moves. I'd be interested to see how you'd solve CP without placing DFR and DBR.


P.S. I'm going to start calling it NCPB because it sounds good :p
 

A Leman

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Cool!This is better than The last one. I have also been developing a method, but I'm too lazy/busy to document it.
 

CubicNL

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Thanks for those! I updated the section on 1c, and now the longest case is 4 moves. I'd be interested to see how you'd solve CP without placing DFR and DBR.


P.S. I'm going to start calling it NCPB because it sounds good :p
No problem ;) I'm planning on releasing it someday, but it is not quite ready yet as if now. I'd be much more interested in other people looking into it as well, with unspoiled eyes xD
 

Kirjava

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You just need to fix that nasty CP step for actual viability. :c

Having to place two corners is ugly. Placing one results in 15 cases + AUF (if my math is right).

This is only a minor improvement (maybe) and still doesn't fix the issue. I was looking for something nice for this when CPLS was all the rage, but I'll take another look tonight when I have a cube on me. Maybe something flowcharty could be useful.
 
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Kirjava

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What are your thoughts on 2a? I have a lot of trouble with it, but I imagine it's easier as a Roux user. Do you think it's worth breaking down?
Yeah, it's crazy easy. Here's my 8flip; r'UR'U2r2U2RU'r

If it gets decent, I'd enumerate all the cases for you - CP is the worry for now though.
 

Noahaha

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CP is the worry for now though.
If someone can do 1a and 1b in one look though, won't it not add that many moves and make CP pretty easy? The only better approach I can think of would be predicting CP from inspection. Is that what you're thinking of? Recognition seems really bad for a CPLS kind of thing.
 

Noahaha

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New step 1 approach:

1a: Solve DBL and DFL while permuting the corners, place DL with a slice move when convenient.
1b: Place BL and FL along with the left center.

I have very little 2x2 experience, but I imagine that 15 second inspection is enough time figure out which two corners need to be swapped to solve CP. Does that sound reasonable?

I don't know if you mentioned this, but there's an easier way to flip two edges. You can just do something like r U R U' r', or M' U' R' U M, or whatever. You can also use r U r' to flip four edges.
I'll add those. Thanks!
 
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Pros and cons of 2gll:

Pros:

-1LLL
-most cases are only R and U
-lots of cases are sune+anti sune combos

Cons:

-crappy recog on some cases
-most cases are only R and U (can be crappy for 2H)
-algs are either long, or super long and RU or okay length and super crappy

judging by my experience with them
 
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