# 4x4x4 Method



## dbeyer (Dec 7, 2018)

Greetings,

I am going to start this thread here as I have refined the method since my original proposal.

I want to talk about a Roux-centric method that allows you to quickly solve in a fluid Roux manner.

It is interesting because I question all CFOP preconceived notions that 4x4x4 has to be done a certain way because it best transitions into CFOP.

I would say that I can average 18 seconds with Roux when I practice. So, it isn't world class. However it is well enough.

In this initial post, I shall outline the steps and substeps of the method.


*First 1x3x4 block (FB)*
**
Do take time to plan your first block during inspection. Select a block and focus on that. Do not plan opposite centers like traditional methods may suggest.

*Second 1x3x4 block (SB)*
**
Transition to your second block. You can build half centers and edge pairs on the M slice and build your second block. The pairing can be done intuitively and interchangeably so you can also preserve edge pairs or centers as you insert the others.

*Next 2 Centers (N2C)*
**
Complete the Next 2 Centers on the M slice. Do not solve all 4. Trust me. We use a technique that disturbs the last 2 Centers. Similar to how CmLL and LSE compliment one another. Choosing to only solve 2 Centers at this stage sets up the rest of the solve.

*Last Six Edge Wings (LSEwings)*
**
Utilizing the scrambled state of the Last 2 Centers to apply some short and fast algs to pair the edges for the last six edges. Notice the teal and purple. These color/positional relationships are important.

*Non Matching CmLL*
**
I personally have utilized non matching CmLL for years. I found a way to understand it very well and recognize the cases and relationships. I basically look at my U orientation. And I look at my L/R case hidden within to discern the 40 cases. Being able to recognize nmCmLL allows you to have more options for your first block (Four choices, pick one). Likewise for the second block (Two choices, pick one).

This is an old version from years ago. Maybe I can better explain it as I update this guide.*

*Last Six Edges Roux (LSERoux)*
**
Roux LSE 4a, 4b, 4c. Plus some EOLR tricks.


*Last 2 Centers + Parity (L2C+P)*
So if you transioned smoothly, you'll have at most 2 Centers to fix during this step. It is interesting to note that you can force OLL parity skip. How can OLL parity exist in a Roux method anyway when you don't do OLL? More on this later.

Remember, the end result is this:


I'll follow up with more examples, cases, scrambles, videos, etc to help further breakdown this method.

*The Algorithms*
So, I originally attempted to finish LSE as a mix of commutators and Roux LSE. I also looked to compile the ZBLL of the last 8 wings on the U layer. I realized that the Commutators would be too slow and the latter would be too complex.

So I found some interesting algorithms that started building 5 cycles. I noticed some patterns and also noticed some cause and effect patterns. So, I realized that it was a lot of easy patterns if I went towards a simpler approach.

Next, the algorothims are fast and you can have look ahead as well. The effect that the moves have on the cube are very predictable.

Let's talk about the most basic concept.

Taking ULf and inserting it to FDr.
rU'r'

Taking UBl and inserting it to FDr.
rU2r'

Taking URb and inserting it to FDr.
rUr'

Now all of these algorithms mess up centers. But only the U and F centers. Much like you so not solve the cross for Roux or orient Last Layer Edges before CmLL, these algorithms quickly pair LSEwings and preserve the F2B.

I mentioned how you could basically use this method to pair at the DF slot. What if we were to look at it from another perspective?


Taking FDr and inserting it to URb.
rU'r'

Taking FDr and inserting it to UBl.
rU2r'

Taking FDr and inserting it to ULf.
rUr'

rU'r' and rUr' disturbs quite a lot of other pieces. However, rU2r' has a very measurable and trackable effect on the 4x4.


It pairs the teal at the UB slot. It pairs the purple at the DF slot. It flips the UF slot. UL and UR are preserved and two half center bars are swapped between the U and F faces.

Meanwhile, for l'U2l
It pairs the purple at the UB slot. It pairs the teal at the DF slot. It flips the UF slot. UL and UR are preserved and two half center bars are swapped between the U and F faces.

Now these two algorithms are you bread and butter for LSE wings.

One step I'll do often is place an edge pair at DB. Store a pair at DB with D2 (rUr') D2 or some intuitive variation.
More to come later. Enjoy. Or you could pair up in the U layer and then do MUM', MU'M', or MU2M' to insert to the DB.

Now you have 10 of the LSE wings left to pair. Keep looking at the DFl and FDr, then scan the U layer for their respective matches. You have a 50% chance you can line up your match so they are interchangeable by an l2 or r2.

DFl -> UBl and FDr -> BUr, respectively.

You want to pair up in the UB rather than store down at the DF. Have the right perspective looking at how you can pair the edge pairs.

Now, sometimes the wings are interchangeable by l' and r. Llook
at these cases:



Line the pair up on the same slice at DF and UF. Then apply rU2r' U2 l'U2l or l'U2l U2 rU2r'.

The first algorithm flips the UF edge pair so now the edges are interchangeable at UB and DF, this also disturbs the pair that was at DB. So be sure to not mess up one pair to solve another. Another option may be have the the edge at UR/UL. Then do MUM' or MU'M' to flip the edge. And transion straight to the respective l'U2l or rU2r' algorithm. If you choose MUM', the UL edges will be stored down at DB. Be mindful, if those wings are not yet paired, they will be out of your line of sight. You can't use moves like r'U2r or lU2l' later because the D and B centers are solved.

So, these cases go hand in hand to pairing. In other reduction methods, you'll notice a stage where you are down to only 2 unpaired edge pairs.

You'll see something like
(Uw)' RUR'FR'F'R (Uw') or
L2 (Uw)2 RUR'FR'F'R (Uw)2 L2

So, for our method. You are 90% of the time going to already have one of the edge pairs at DF. DB has already been Paired. So the other edge pair is up in the U layer.

Simply line up the edge pairs at DF and UB, then do rU2r' or l'U2l, if it is that case applies. If the edge is flipped and it lines up interchangeable at UF instead, you can apply this algorithm.

(rU2r') [l'U2 (rU2r'U2) l]
Or you can offset the last edge pair to UL/UR and apply MUM' rU2r'.

So, you should have successfully paired all 12 edge pairs.

The U and F centers are Disturbed. But, look at how easy and intuitive LSEwings was. 

As you get better at LSEwings, you can recognize cases that will even solve the last 3 edge pairs simultaneously. More on this later.

So, the next thing to do is get used to understanding and calculating the impact that your last LSEwing step will have on the L2C. You can do rU2r' or l'U2l algorithm, both will equally finish the LSEwings step. Yet rU2r' swaps the Ur half bar with the Fl. l'U2l swaps the Ul half bar with the Fr. 

Transition to CmLL.

Now, let's hit LSERoux.

You could do Roux 4a, 4b, and 4c then fix and OLL and PLL parities.

I want to share with you a trick that helps you avoid OLL and Double Parity. I am refining this process.

So I did a couple videos. I'll be posting the links below in the next update.

During one of my example solves, I made comment a lot of wing Edge pair already solved. And I was thinking about it earlier today. The wings were not solved after N2C. Rather they became so when I paired my first edge.

So, I visually reconstructed what had happened. I did an rUr' trigger. So follow along on a solved cube.

Actually do rUr'U'. Corners will now be solved and in place. You should notice that several wings are still in place.

So there are multiple ways to pair a single edge. So, what if you could pick the best pairing option to simultaneously solve additional pieces?

This step works best on your 1st or 2nd LSE wing. I'll give examples in a video. More to come soon.


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## pjk (Dec 7, 2018)

Long time no see, Daniel. Good to hear from you. Looking forward to reading more about this. Or a walkthrough video would be interesting.


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## dbeyer (Dec 7, 2018)

pjk said:


> Long time no see, Daniel. Good to hear from you. Looking forward to reading more about this. Or a walkthrough video would be interesting.


Thank you very much. I guess I've been a bit of a silent cuber for a while. I picked up a new 4x4 before Halloween. I am getting a speed cube 4x4 for Christmas.

I've already got some concepts written up on a Facebook group. Plus diagrams to go along with it .


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## FreddyH (Dec 7, 2018)

Sounds promising! Would this also scale to 5x5 or other big odd number cubes (7x7, 9x9, etc)? Or does this only work on even numbered cubes (6x6, 8x8, etc)?


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## dbeyer (Dec 7, 2018)

I see it specifically working for the 4x4 and even cubes, to the effect that certain tricks are available because there are not fixed centers.


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## doofnoofer (Dec 7, 2018)

Can you link to the diagrams? I was messing around with this earlier today and I can't get the edge pairing to work.


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## dbeyer (Dec 8, 2018)

I certainly can. Just give me a little bit of time. And just to clarify, you are referring to the LSEwings after the first 2 blocks, correct?


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## doofnoofer (Dec 8, 2018)

dbeyer said:


> I certainly can. Just give me a little bit of time. And just to clarify, you are referring to the LSEwings after the first 2 blocks, correct?


Yes. I'll try again in a few hours. Do you feel like this method will be better than Meyer?


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## dbeyer (Dec 8, 2018)

doofnoofer said:


> Yes. I'll try again in a few hours. Do you feel like this method will be better than Meyer?



I feel that with a speedcube, I can practice and get times down to sub 60.

There are tricks that really empasise the choice to do only 2 centers after F2B.

You really begin to create an understanding of the cube. It reinforces the Roux steps. Also, it is important to do the steps in the most logical order rather than the most natural order. You will find that you have a tendency to want to go back to CFOP-centric pairing methods when you are doing a Roux 4x4 speed solve.

I'm relearning my CmLL algs as I am developing the ins and outs of the method. Also, waiting for a new 4x4 for Christmas. And I am already feeling fast, knowing that my speed cube and rusty CmLL repitoire is holding me back.

I'll be adding examples for the LSEwing step. It is really intuitive, with some extra alg cases that finish LSEwings.


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## dbeyer (Dec 8, 2018)

To my understanding, Meyer transitions into Roux after completing reduction.

However, the steps are different. You have to do Second Block, CMLL, LSE, and parity fix after the reduction method.

Whereas, First and Second block are already done. So you can focus on the LSEwings. Advanced methods allow you to avoid OLL parity and Double Parity. You are also able to influence the L2C+Parity step. That way L2C is fast and as previously mentioned OLL and Double parity are skipped.


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## Filipe Teixeira (Dec 13, 2018)

there is no parity with this method?


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## dbeyer (Dec 13, 2018)

There is. However, you can force odd parity and double parity out.

Your parity fix will be either r2U2r2Uw2r2u2, rU2-rU2F2-rF2-l'U2lU2r2, or l'U2l'U2F2l'F2rU2r'U2l2.


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## dbeyer (Dec 14, 2018)

Hey, so I want to dive into a trick to solve multiple edge pairs during LSE wings.

I'll teach you a 5 cycle that is very intuitive and powerful. Should seem familiar. And you'll build more awareness of the cube and its state as you solve.

These algorithms are mirrors and inverses of one another. I'll go a step deeper in the next post.






It is really powerful because you can choose different ways to pair wings.

Certain edge pairs wind up pairing up whether you you rUr' or rU'r'. You have multiple ways to pair two wings. So, with those different options you have opportunity for additional wings to pair.

Choose rU'r' could pair the wings that are at FUr and UBl and also pair the BUr and URb.

I would say that it is not about recognizing the less common patterns, but recognizing that there are 5 ways to pair an edge pair. It's like CmLL recognition. Sure you can do a 2 look CmLL, but one look is definitely better. And maybe you'll accidentally do the wrong CmLL, but at least you'll have oriented corners.


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## dbeyer (Dec 30, 2018)

Hey guys,

So. I am going to do an overhaul to the steps. I'll be adding some comments to each section and also some videos.

During the development of the method, I questioned each step and substeps of the method. I was critical of the effectiveness of the step. I also evaluated the pros and cons of each step. I looked at how many good cases there were compared to bad cases.

I also did time splits and tried to identify what lead to fast solve times and also was critical of whether it was pauses, mistakes, inefficient excution, or bad methodology that resulted in the times.

I'm going to re-write an overview of the methodology below and highlight tips, common mistakes, and focal points.

*First 2 Blocks (F2B)*

*R Centers*
I would recommend planning R Centers First, I feel that transitioning to L Centers and First Block on L has better flow. Then solving second block on R as usual.
*L Centers*
This sub-step of R then L centers should be fast and a low move counts easily planned during inspection.
*First Block*
Sometimes you can forego R centers in favor of an easy First Block. 
*Second Block*
Whether you solved centers first or not, try to quickly and smoothly build the second block. I would recommend pairing an edge pair and attaching it to the centers. Then build the other two edge pairs. Once your other two edge pairs are formed, then solve the Second block. I try limiting my moves to R, Rw, 3R, M, l, r and U. Generally speaking avoinding Uw, Dw, B and For moves.
*Next 2 Centers (N2C)*

*Half Bars*
So it is important to not do CmLL. Also be able to make the 3rd and 4th center in the correct orientation relative to your L/R blocks.
*B first, D next*
I'll solve my Blue/Green Center first (whichever is easier), then take the relative D and complete those centers as well. While solving my D centers, I am normally permuting them do the F face. And once B/D centers are solved, then I do an MRI to finish and transition to LSEwings.
*D then B*
Nothing wrong with this approach either. I just keep the D face on D and push everything from the U and F face to the B Face.
*N2C and Only 2*
Solving the 5th center forces the 6th center to be solved. It is common mistake to either solve all centers (L2C after N2C) or transition from F2B to CmLL. Both of these choices are better left to resolve themselves later. I'll show you why.
*LSEwings*

*Low Move Count*
You are looking at about 20 STM pair the LSEwings
*Efficient*
Sacrificing the unsolved L2C you can keep the move count of Solving LSEwings low.
*Influence L2C*
Quick decisions that may seem inconsequential can make L2C easier and even Force a L2C skip. Doing l'U2l vs rU2r' could be the difference between having 3 unsolved centers or only 1.
*Intuitive*
You build LSEwings very similar to block building of a 3x3x3 F2B. You line up edge pairs with U moves. Arrowhead 4A cases like M'UM, MU'M', and finish LSE wings with a sune 90% of the time (7 moves to pair 3 edge pairs)
*CmLL*

*Solving CMLL post-LSEwings prevents the Sune case for finishing LSE wings from disrupting your CMLL execution.*
*Remember, save your CMLL for after LSEwings*
*LSERoux*

*Odd Parity?*
*Yes*
I would recommend transforming the case into a BLD parity.
You have a chance to influence Even Parity and EO.
*No*
Quickly transition to 4A and 4b.

*Even Parity?*
*Yes*
Attempt to apply the 4c step and Even parity in a manner that they flow together with cancellations and minimal setup moves. As per the Even parity is confined to the M slice, this should be fairly easy.
*No*
Blast through 4c and fix L2C.

*Misoriented Parity*
*Yes??*
So you get Misoriented parity when you encounter odd parity, transform it into a BLD parity and choose to orient your LSE with 2 flipped edges. When you confine the Odd parity to two edge pairs, it is interesting because from the rules defining 4a, you treat those two edge pairs as wildcards. Such that you could have an Arrowhead (3/1) case, or you could have a 2a/0 case. One perspective will result in Even parity and the other will result in no Even Parity. Ultimately you transform your odd parity confined to 1 edge to a BLD parity confined to two edges so that you can influence L2C, Even Parity, and 4A.

I'll talk more on this in a video. I really feel that this is a critical point of the method.
Mastering the ability to manipulate and influence the cube when you have odd parity will define your success with this method.


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## dbeyer (Jan 17, 2019)

awesome, so I put together some videos. And I hope that they help explain the method and show it both in some good cases and some bad cases.


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## dbeyer (Jan 26, 2019)

New example solve

https://alg.cubing.net/?puzzle=4x4x..._U2_m_//_4b
u2_m2_u2_//_4c_swap_&#2b;_centers

enjoy!


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## dbeyer (Feb 7, 2019)

Examples of N2C -> Finish
Scramble 1:
2R' M' U 2L M 2L2 U' M 2R2 U' 2R U M' 2R2 M' 2L M2 2L2 U M' 2R U' 2L U2 2L

Solution 1:
https://alg.cubing.net/?puzzle=4x4x..._//_4a.
Um2U-m-U2m-_//_4b._
x_U2m2U2_//_4c_ez.

Scramble 2:
2R' M U' 2R U2 M2 2L U2 2R U2 M 2L U M 2R U2 2L' U2 2L2 U' 2R2 U 2R2 U' M'

Solution 2:
https://alg.cubing.net/?puzzle=4x4x...c_special_setup.
u2_2R2_u2_2L2_U2_2L2_//_done.


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## dbeyer (Feb 7, 2019)

[15:17] <nibblrjr> LSEWings scramble #11: M' U' M' U 2R' M2 U' M 2R2 U2 2R2 M U2 M U' M2 2R2 M' U' 2L' U 2L U2 2R U'
https://alg.cubing.net/?puzzle=4x4x...-_m_U2_m_//_4ab
U-_m_U2_m-_U2_m2_U2_m2_//_4c


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## dbeyer (Feb 8, 2019)

Scramble:
2R' U2 M' 2R2 U2 M2 U 2R M' 2L2 M2 2L2 M2 U2 2R M2 2R' U' 2R2 U2 M U M 2R U2

Solution:
https://alg.cubing.net/?puzzle=4x4x..._U2_m2_U2_2R2_U2_2R2_u2_2R2_u2_m2_//_4b&#45;c.


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## dbeyer (Feb 9, 2019)

After a lot of thought.

I have discovered a way to permute the LSEwings and resolve any odd parity issues. The concept is relatively simple.

Recognize it sooner and and influence another step of the solvee with a parity insertion to negate parity.

The cube is bound to finite permutations. Due to the mathematical calculations, there are. a lot of 3x3x3 states, let alone for 4x4x4. It would be overwhelming to approach it from such a large scale view. However, we solve the cube with simple steps.

I would really strongly recommend this method to a Roux solver, because you are constantly using your understanding of building blocks and LSE EO to analyze the cube.

We understand the 2/4/6 rule of LSE for 3x3x3. It has to be even.

If there is parity, you will see 1/3/5 good/bad wings.

So, now you need to understand the effect of wing edge pairs being paired, false barred, or bow tied.

pairs can be can be counted correctly, either as good or bad.

The best point to analyze this situation is with 3 pairs and a combo of bowties and false bars.

Certain combinations of pairs, false bars, and bowties result in parity or not.

We consider parity to be an odd number of flipped edges. Since we like even 2, 4, 6. So if we have 3 pairs and a combo of 3 bow ties and false bars. How do we tell if we have even. Can we just count the solved pairs?

No.
You can have 3 good pairs and have parity or not have parity. Likewise, you could have 2, 1, and even 0 good pairs and still be able to have either parity of not.

You need it be able to evaluate the state of the unsolved wings (which although not paired, are still confined by rules even though parity seems to happen 50% of the time).

Similar to Boolean Logic and Digital Circuits analysis, your false bars and now ties give different signals based on their order or other relative data.

You could get 3 false bars and have parity ...

The next solve you could have 3 false bars and not have parity. You need to evaluate the number of pairs and false bars. They can match.

So, you have 3 and 3. Fortunately for LSEwings, the False Bars will have U/D colors grouped together so it is easy to recognize this EO. Count the number of good and bad edges. In this case you can treat the false bars just like the pairs. Count how many good edges there are and bad. Even = no parity. Finish with a wide sune. Odd = odd parity. Stay tuned to fix this with a cool little trick.




https://alg.cubing.net/?puzzle=4x4x...;_U2M2U2.
U_2L-_U-_2R_U_2L_U-_2R-_//_L2C.____


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## dbeyer (Feb 9, 2019)

In the event that you identify parity during LSEwing pairing and I will propose a recognition system later.

For now, I'll provide some algorithms that can easily pair 3 edge pair (therefore preserve the other 3) and it is N2C safe. L2C effects are predictable.

It is important that you understand how to execute the proper algorithms for the case. 

If you apply a parity insertion, and there wasn't parity, you have created parity. If you apply a left handed version, when you should have done a right handed version, you'll wind up without having the LSEwings finished after this step.

I am attaching a variety of short simple sequences (you'll setup these cases with a quick MU trigger). Then if done correctly, you can proceed to CmLL, LSE 4abc, and a commutator to resolve the L2C inserted where you see fit.

These algs disrupt the U/F centers and cycle wings about 3 positions on the M slice. 

Enjoy.


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## dbeyer (Feb 9, 2019)

pair 3 pair and resolve parity at the same time. Setup with the appropriate MU trigger.


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