User:Kenneth/Kenneth's Big Cubes Method

Contents
Introduction
First thing, if you don't know CLL you are in trouble. If you don't and still want to try out this method, then it's recommended to use the 2step variation. Algorithms can be found at the CxLL pages, grey fileds but any CO + CP set of algs will do.
When I started to use this method in 2006 I averaged about 150 moves, now it is less than 130. The improvement comes from better algs in some cases but most of it comes from experience, I do not spam turns as much as I did initially. If you try this and can't reach my figures, then think I used it for several years now, I had time to find the tricks I use in the intuitive parts.
Example solve
Scramble :
 R' U Fw' F2 R U B2 Fw' Rw R' Fw2 F' L2 B2 D' Uw2 R Fw' Uw L' U Rw U2 Fw F Uw F' D' U' Fw L' R2 Fw' Rw2 F2 L' Uw' Rw2 B2 F2
Step 1, First two centres and dedges:
 F Rw' (z') U' Lw U Lw' U2 Rw U' Rw' (10)
The yellow was three pieces but that's my D colour, I only use red/orange or blue/green for the first step.
Add two dedges:
 First: R' (y) Rw' D (13)
 Second: B' U' r' B Lw' (18)
Step 2, complete F2B (4 corner columns)
 1: U' l2 F2 R U' Rw' (24)
 2: U' r' U Rw' U2 Rw (30)
 3: l U' r' U' L' M2 U' Lw (38)
 4: Lw U' Lw' U2 l' U' (L M) U' Lw' (48)
Step 3, CMLL
 Two twist: U Rw U2 Rw' U' R U' Rw2 U2 Rw U R' U Rw (62)
Step 4, complete first layers
 Two centres: r U' r U' r' l' U r2 l' U2 l' U l r U2 l (78)
 add the dedge: r' U' r l U l U M' U' M (88)
(y2) .. because I solved F instead of B I have to turn it around to ease up recognition.
 Fside triplets: U M' U2 M U' r U2 r' ... l' U l U l' U' l (103)
Step 5, ELL
 ELL 1: U (y2 x') M' U' R U M U' R' U (x) (112)
 ELL 2: (y x') r U' R U r' U' R' U (x) (120)
 ELL 3: (y2) Rw U2 l D2 l' U2 l D2 l Rw' (130)
Step 1 (R and L columns)
I use three different ways to complete this step, the most basic is to just form the centres and then pair up and place the dedges. The problem with this is that the pieces for the the dedges are slow to find because they may be spread all over. To avoid this I often pair up at least one of them and put it in the middle layers before I do the centres, this way I can use some of the inspection time to find the pieces, the centres I have time to see anyway (or if the first centre is easy, try to track where the edges for that side will go and do them after the centre).
The third way to complete step 1 is to form four columns of two centres and one edge, this is a little slow so I only do it when I have a good start for it.
Step 2 (corner columns)
This step I do in much the same way as I solve the first step of my 3x3x3 columns first method but I only use the Mslice and x rotations (if the F or B sides are still empty).
Sometimes, if there is a nice pair to start from and I can quickly see one more in the inspection I do this as the first step. Not really Akimoto columns because I fill in the rest of F2B after this.
I'm usually not strict in the solving order for F2B, sometimes I even solve the whole first block before I do anything to the second, trying to use already paired pieces I see in the inspection or on the fly.
Step 3 (CLL)
Any set of CxLL will solve this step but I use CMLL and have a few algs that are unique for the 4x4x4 in my set, the rest are a mixture of 2x2x2 CLL (but double layers (triple really) at some points), CLL and COLL.
Step 4 (M slice)
 Scramblers (step 4 and 5) for both 4x4x4 and 5x5x5: 4xRoux.zip (DOS.EXE program)
Solve D and B edges (1x2 blocks, store in the r and l slices), add the BD dedge (in parts with the centre blocks if there are good cases) and then form two 1x3 blocks of 2 centres and one edge to solve the F side (1x2 centres keyholed on the Bside using r or l').
Example 1
 Scramble : r2 l U' r2 U M U2 r l2 U2 r2 l' U r l2 U r2 l U' r l U r l2 U' r' l2 U2 M U2 M
 Centres : l U' r2 ... U2 l' U l' r' U' l2 r
 Dedge : U' r' U' r U' M' U M
 Side swap : y2
 First Ftriplet : U' M' U l
 Second : r' U' r U r'
Example 2
 Scramble : U r l2 U r2 l U r2 U M' U2 l U2 r U' r U' r' U2 M' U r l U2 M2 U
 Centres : U' l ... M' U r U2 r U r' U2 r l
 Dedge : r U l' U' l U r' M U2 M'
 First Ftriplet : U' M' U' M
 Second : U' l' U l U2 l' U2 l
Example 3
 Scramble : l2 U2 M2 U r2 l' U' l U' r2 l U M U' l' U' r2 U2 r l U2 M2 U M' U2 r
 Centres : r2 U' r' U l' U r2 ... l U' l' U2 l2
 Dedge : U l' U' l U M U2 M'
 First Ftriplet : M' U l
 Second : U2 r' ... l' D2 r U2 r' D2 r U2 M (last is 3cycle edges)
This is the most effective way I tried so far but mastering this style takes a lot of practice and it is, like most effective methods, a bit slow.
Another method, that uses a little more turns but are having quicker look ahead and is easier to master, is to just solve the four centres, add one half of BD and one half of FD using 3x3 MUM moves and then do the last two using a commutator.
The commutator is just 'one alg' but comes in variations:
 (y') r' U' R2 U r U' R2 ... Solves FDl if it is oriented
 (y') l U' R2 U l' U' R2 ... Solves FDr if it is oriented
 (y') R2 U r' U' R2 U r ... Solves FDl if it is unoriented
 (y') R2 U l U' R2 U l' ... Solves FDr if it is unoriented
Mirrors to solve the Bside, reflect to avoid y2's or U2's, a total of 16 variations! :P
In some (two + mirrors) cases both edges left are sitting in FD and BD but swapped; use a dummy commu first to get one out and then as normally from there (or find the algs to solve optimally ^^ )
Same scramble as 'example 1' above:
 Centres : M2 U2 M U l' U l' U2 l' ... U' r' U2 M' U' l
 3x3 edges : solved on both sides!
 FDr : (y') U R2 U l U' R2 U l'
 BDr : U L2 U' r' U L2 U' r
Example 2:
 Centres : U' l' M' U r' U M U2 r' U r U2l' U2 l
 3x3 edges : M' U2 M2 U M'
 BDl : (y') U l U L2 U' l' U L2
 FDr : U2 R2 U l U' R2 U l'
Example 3:
 Centres : r U' l' U' l2 ... r U2 r U' M' U l ... U' r U' r' U2 r U2 r' ... U' r' U r
 3x3 edges : M' U' M U' M U M'
 FDr : (y') U2 R2 U l U' R2 U l'
 BDr : U' L2 U' r' U L2 U' r
Step 5 (ELL)
Edges of the last layer I solve in 3 looks and less than 30 moves on average (forcing some skips if possible makes it lower than it looks if you calculate the move count, that is ~30). It looks like a load of algos but most are single or double Niklas and variations of these.
 Most basic double Niklas: (x') l' U' R U l r U' R' U r' (x)
 Is the same as 2 commutators: (x') l' U' R U l U' R' U (x) + (x') U' R U r U' R' U r' (x) and as many cancellations you can ask for =)
5x5 and larger:
5x5 as 4x4, leave the mid edges for last and do 3x3 ELL but single layer m slices. Some algs destroys the +edges in m, often both on two opposite sides. To avoid that it is often enough to just use double layer moves for two U2, F2, B2 or D2 moves in sequence. This ZPLL shows that : m2 U' B2 m2 B2 m2 U m2  change the two B2 for Bw2 and it will work. Test your set of ELL's and change the ones that are troublesome for better ones.
6x6 as 4x4 but two times, one for each pair of edges of each side.
7x7 as 6x6 and end as 5x5
A.S.O.
Try to use double, triple... layers if it solves more than one group for each side (force!).
ELL Algorithms
Yes, there are some case description images missing but I lost the originals while I was working on this page (my computer broke down, this is also the reason for me not completing this method description, I had no computer for like 2 months after the breakdown and in the mean time I moved to other projects). But all algs are present and from the images that are here you can easily figure the rest of the cases from the numbers preceding the algs.
ELL 1:
The image for the first case shows the way the edges are labeled; they are initially placed at positions 1 through 8. This step solves the first two (edges number 1 and 2). These edges initially are placed at positions 18. Note that even edges (such as #2) are 'oriented' if they are in even positions, and similarly odd edges (such as #1) are 'oriented' if they are in odd positions.
The cases:

 

 

 


ELL 2:
This step solves the opposite edges (numbered 7 and 8 in the first step). Do a y2 and then you can use the same cases as in ELL 1, except that the cases containing a 7 or 8 are not possible since those positions are solved.
The cases:

 

 


ELL 3:
Finally we must solve two opposite edges. The images show the stickers of the U layer (assuming white is on top and green is on front); a gray piece means it is already solved. The arrows in the images show where the pieces need to go, although in many cases they are not necessary because many of the cases can be recognized just by looking at the patterns of the stickers.
The cases:
See also: my set of ELL 3 algs that I use for the 3x3x4 Tower 'Roux' method (many are the same as here but some are optimised).
Faster turns
To improve the speed of the method, it is possible to use double layer turns in some of the algorithms, instead of having only slice turns. Take for example the case with UBl solved from ELL 3, which can be tweaked like this:
 r l D2 l' U2 l D2 l' U2 r' ... original
 (Rw l) D2 l' U2 l D2 l' U2 Rw' ... tweaked
With a little bit of skill it is possible to do the first two turns at once and directly trigger in the D2 turn. Doing the algorithm like that it is almost twice as fast as doing it all as separate turns, so, as you can see, examining the algorithms to find possibilities for double layer turns can lead to some interesting improvements.
5x5x5 Example
Bw2 F2 Dw' U' L Bw2 F' Lw' Uw U2 L' D2 B' Uw' U Bw2 Rw' Dw' Uw' L2 Dw2 U' Fw2 U' L Lw2 Dw2 U Fw' F' U Bw2 Fw2 F Rw' Dw2 Uw' Fw' Uw U2 F' Dw2 B' F Rw B' Bw' R2 B' Dw L' Fw2 R2 Dw2 R' U Rw' R Uw U2
(yes, yellow centre, but I never use yellow or white, only side colours, not U or D)
Step 1, centres :
 U' m ' (z) U l R2 f
 L' s2 U Lw' U2 m (y') Rw U2 Rw'
 m2 u m (y) U' r2 s'
 (x2) r' U r U (y) U m' U m
Add tredges:
 L U (y') r' L2 U Lw2 D
 L U' r2 B' m2 U L2
29 + 14 moves, 43 total, a little above normal.
Step 2:
 p1 : l' U2 r2 L U' M2 R U' R2 (x) (9)
 p2 : lm B2 m2 B M2 L U' L' (8, 'lm' is double inner slice at the Lside)
 p3 : m U l U2 m' B U2 B' (8)
 p4 : L' U' m U2 L U M2 U L' U2 L (11)
9+8+8+11=36 moves, normal pairs. Total moves is 79, still a little high.
Step 3, CMLL :
 (y2) L' U2 R (y) U' R' U2 R U (y') R' U2 L (11, conjugate, maybe not optimal but pretty fast)
90 moves.
Step 4: Rows of centres :
 U r2 U' M2 m' U m U'
 M U r U m' U' l2 U2 l'
 M' U' rm' (rm' = double inner rslice)
 Keyhole some mid rows : U' l m2 U' m' U' m2
 Keyhole and place BD tredge : U2 l' U' l U l' U l U' ... M2 U2 M' U2 M'
 Keyhole and place FD : U l' U l u2 M' U2 r' l U2 m
 Lost centre : U r U m' U' r' U m
60 in this step, total 150
Step 5, ELL :
 ELL 1 : is skipped =)
 ELL 2 : (y) r2 l D2 l' U l D2 l' U' r2
 ELL 3 : (y') Lw' r' D2 r U2 r' D2 r U2 Lw'
Mid edges I solve like 3x3 L5C
 Solve last F2L and orient LL : (y') U' m U' R2 Um' U' R2
 Last centres : (y) m' U r l' U' m U r' l
 EPLL : R2 (y') U' m' U2 m U' F2
 AUF : U
20 for ELL, a little lucky, (average is about 28) and 24 for L5C + last centres (I normally leave these for last), gives 44 and a total of 194, that is about the average, I was behind at first but the lucky ELL fixed it for me)
Phew, I messed a bit, it can be done better but I won't make another try wth a new scramble atm... :P