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ProStar

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Possible new Roux-based 4x4 method?

1. First 2 centers
2. First Block on one of the solved centers, but with additional layer (3x4x2 block)
3. Second Block (just outer layer, so 3x4x1)
4. CMLL
5. Solve the rest of the cube using U and the right inner slice (still working on this part)

Essentially, the point of this method is to eliminate the numerous regrips that Lewis/Stadler has when switching between wide slice, left inner slice, and right inner slice moves. Roux's obvious weakness on big cubes is not being able to keep the inner layers together during 3x3 stage, and this is an attempt to solve that as well. There's also probably a way to avoid OLL parity by orienting all the edge-halves during step 5, but I haven't fully fleshed that out yet.
I'm almost certain that this is an existing method, but I can't remember which one it is
 

Etotheipi

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somewhere on the complex plane.
Possible new Roux-based 4x4 method?

1. First 2 centers
2. First Block on one of the solved centers, but with additional layer (3x4x2 block)
3. Second Block (just outer layer, so 3x4x1)
4. CMLL
5. Solve the rest of the cube using U and the right inner slice (still working on this part)

Essentially, the point of this method is to eliminate the numerous regrips that Lewis/Stadler has when switching between wide slice, left inner slice, and right inner slice moves. Roux's obvious weakness on big cubes is not being able to keep the inner layers together during 3x3 stage, and this is an attempt to solve that as well. There's also probably a way to avoid OLL parity by orienting all the edge-halves during step 5, but I haven't fully fleshed that out yet.
This is similar to @dudefaceguy's intuitive 4x4 method, with some variations. His method uses commutators for your 5th step, to stay intuitive, but maybe you can find a faster alg based approach.
 

Alex Shih

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Jun 23, 2020
Messages
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I think step 5 would be too hard to do fast in a solve and you would have to learn a new style of blockbuilding for 4x4 but I think it would be cool if this works.
Personally, I don't think the ergonomics of inner slice + U are significantly worse than the ergonomics of doing outer-layer CFOP. But I could be definitely be convinced otherwise.

This is similar to @dudefaceguy's intuitive 4x4 method, with some variations. His method uses commutators for your 5th step, to stay intuitive, but maybe you can find a faster alg based approach.
After some experimentation, I think the best alg-based approach is probably some variant of this:

5a. Pair up centers (2x1 center piece blocks) while solving ULUR
5b. Solve the rest of the cube using U2's and inner slices (basically an analogue to 4c in normal Roux)

There are only 4 center pairs you need to solve (since the fifth one gets solved automatically). There are also 4 ULUR edges to solve, so you can solve one center pair and one ULUR piece simultaneously and repeat 3 times to reduce # of algs. I ended up dropping the idea of EO as its own step because most 5b cases seem to have misoriented edges anyway.
 
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dudefaceguy

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Feb 17, 2019
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This is similar to @dudefaceguy's intuitive 4x4 method, with some variations. His method uses commutators for your 5th step, to stay intuitive, but maybe you can find a faster alg based approach.
Yup, that's my method! I solve the inner slice after completing both blocks, but you can really do it either way. Hm, maybe I will experiment with switching some of the steps around. Very cool that you remembered :)

Seems to me that it has potential as a speed method, but I don't really know since I'm not a speed solver. The most obvious problem is that it uses completely different skills compared to 3x3, so it's not as easy to leverage your existing skills. I designed it this way on purpose, because I wanted my 4x4 solves to be different than my 3x3 solves.

Recognition is also difficult when pairing opposite wing edges in the inner slice - you need to identify which blue/white edge goes with which blue/yellow edge, even though they have the same colors.

But I am getting good times with this method, i.e. 4x slower than my 3x3 times. This is about what 4x4 times should be for a casual solver. So, a dedicated speed solver who is not an old man could probably get competitive times. Over time, I've come to do some of the steps exactly the same way, effectively making them algorithmic even though I'm technically using commutators. There are certainly some gains to be had by further refining algorthmic steps.

Edit: many of the steps are already used in other speed methods, for example Lewis and Sandwich. The thing that distinguishes it from these two methods is solving 3/4 of one inner slice, and using the other single slice to solve wing edges.
 
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dudefaceguy

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Feb 17, 2019
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5. Solve the rest of the cube using U and the right inner slice (still working on this part)
By the way, I have tried to do this, and you CANNOT solve both centers and edges using only U and r (unless I have really missed something). EDIT: Actually you should be able to, since you can scramble the same pieces with U r. It just seems like the movecount would be very high.

It's either centers first and then edges using commutators (Lewis) or edges first and then centers using commutators (QTPI and Sandwich). You can do some center control while solving edges to get a few extra center pieces solved, but I'm not sure that this is worth it. There are 10 center pieces left if you solve edges first, or 8 if you also solve the two centers in the l slice while solving edges. 1/4 of these will usually be solved by accident, so there are usually 7 or 8 center pieces left, or 6 if you solve the extra 2 center pieces while solving edges. This is the difference between 2 and 3 commutators (or 1 4-move commutator cycling 6 pieces). Center commutators/algs can be really fast, but you have to look at the bottom and back faces to recognize the case.

Anyhow, I am obviously very excited to talk about this method but I will stop now and go to sleep.
 
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Alex Shih

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Jun 23, 2020
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By the way, I have tried to do this, and you CANNOT solve both centers and edges using only U and r (unless I have really missed something). It's either centers first and then edges using commutators (Lewis) or edges first and then centers using commutators (QTPI and Sandwich). You can do some center control while solving edges to get a few extra center pieces solved, but I'm not sure that this is worth it. There are 10 center pieces left if you solve edges first, or 8 if you also solve the two centers in the l slice while solving edges. 1/4 of these will usually be solved by accident, so there are usually 7 or 8 center pieces left, or 6 if you solve the extra 2 center pieces while solving edges. This is the difference between 2 and 3 commutators (or 1 4-move commutator cycling 6 pieces). Center commutators/algs can be really fast, but you have to look at the bottom and back faces to recognize the case.

Anyhow, I am obviously very excited to talk about this method but I will stop now and go to sleep.
Do you know any specific cases where this isn't possible, or the specific reason this isn't possible? There might be a workaround (although I have a feeling that the workaround would probably be algorithmic). Also, if you want to continue this discussion, we should probably move to a different thread.
 
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Skewbed

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Jan 16, 2017
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Here's an idea for finishing Hexagonal Francisco solves using pseudoslotting during the last edge.

Pseudoslotting ZBLL Finish:

1. Hexagon on D
2. Solve 3 E-slice edges like normal (RUru-gen)
3. Insert the last one with the corner by using pseudoslotting
4. Insert DF edge while doing EO (MU-gen)
5. ZBLL or such

Pseudoslotting OLL PLL Finish:

1. Same
2. Same
3. Same
4. Insert DF edge (MU-gen)
5. OLL
6. PLL

Example solve using OLL PLL Finish:

Scramble: U' L' D2 U2 B' D2 B2 L2 B R2 B L2 F2 U L' D R U' R2 B'

y2 // inspection
L D' L' // 3/4 cross, probably inefficient way to build hexagon
U' L' U' L // corner
R2 U' L U L' // corner
(D' U') L' U L // corner
u R U R' r U r' // edge
u r U r' F' U' F // pseudoslot
M' U' M // setup to LL
D' U R U R' U R d' R U' R' F' // OLL
U' L' U R' z R2 U R' U' R2 U D // PLL
R' // AUF (or ARF I guess)
 
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1.) What do you mean by X? an XCross?
2.) You forgot the rest of F2L
3.) There's a thread especially for proposing new methods, which can be found here.
I meant that you would make a literal X. Not practical, but somehow helps with F2L.
Btw for the other people talking about where's f2l, I kind of forgot to say that you did f2l with it, as I've used it so much that it's been pretty much forgotten as a step and more a part of the cross
 

dudefaceguy

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Feb 17, 2019
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Do you know any specific cases where this isn't possible, or the specific reason this isn't possible? There might be a workaround (although I have a feeling that the workaround would probably be algorithmic). Also, if you want to continue this discussion, we should probably move to a different thread.
Yes, let's move to the thread for this method: https://www.speedsolving.com/threads/intuitive-4x4-method-with-parity-avoidance.73049/

I will post a reply there.
 

ProStar

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I meant that you would make a literal X. Not practical, but somehow helps with F2L.
Btw for the other people talking about where's f2l, I kind of forgot to say that you did f2l with it, as I've used it so much that it's been pretty much forgotten as a step and more a part of the cross
By X do you mean inserting all F2L pairs? If so then that's a really bad version of PCMS @CodingCuber
 
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