# 4x4x4 Method

#### dbeyer

##### Member
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

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

#### dbeyer

##### Member
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 .

#### FreddyH

##### Member
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)?

#### dbeyer

##### Member
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.

#### doofnoofer

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

#### dbeyer

##### Member
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?

#### doofnoofer

##### Member
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?

#### dbeyer

##### Member
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.

#### dbeyer

##### Member
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.