View source for KBCM step 5

{{KBCMNAV}}

=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 compeleting 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 1-8. 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:
{|
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 1.jpg]]
|NAME=ELL 1 1-1
|ALGO=
* 1-1 + 2-2 : Solved
* 1-1 + 3-2 : (y' x') r U' R U r' U' R' U
* 1-1 + 4-2 : (y' x') U' R U r U' R' U r'
* 1-1 + 5-2 : (y x') r U L' U' r' U L U'
* 1-1 + 6-2 : (y x') U L' U' r U L U' r'
* 1-1 + 7-2 : (y2 x') l' U L' U' l U L U'
* 1-1 + 8-2 : (x) U2 l2 U L U' l2 U L' U
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 2.jpg]]
|NAME=ELL 1 2-1
|ALGO=
* 2-1 + 1-2 : (x') M' U' R U M U2 M2 U R' U' M2 U2
* 2-1 + 3-2 : r' M D2 l' U l D2 l' U' r2
* 2-1 + 4-2 : l2 U' r' D2 r U r' D2 l' M'
* 2-1 + 5-2 : r' M D2 l' U' l D2 l' U r2
* 2-1 + 6-2 : l2 U r' D2 r U' r' D2 l' M'
* 2-1 + 7-2 : r U2 l D2 l' U2 l D2 l' r'
* 2-1 + 8-2 : r' l' D2 r U2 r' D2 r U2 l
}}
|---
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 3.jpg]]
|NAME=ELL 1 3-1
|ALGO=
* 3-1 + 1-2 : r2 U l D2 l' U' l D2 r M'
* 3-1 + 2-2 : (y x') U L' U' l' U L U' l
* 3-1 + 4-2 : U2 r U r' U r' U' r2 U' r' U r' U r
* 3-1 + 5-2 : (y x') r U L' U' r' l' U L U' l
* 3-1 + 6-2 : (x) R2 F' r2 U2 r2 Uw2 r2 u2 F R2
* 3-1 + 7-2 : (x') l' U' R U l r U' R' U r'
* 3-1 + 8-2 : (y x') L' U' l' U' R U l r U' R' U r' U L
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 4.jpg]]
|NAME=ELL 1 4-1
|ALGO=
* 4-1 + 1-2 : M l D2 r U' r' D2 r U l2
* 4-1 + 2-2 : (y x') l' U L' U' l U L U'
* 4-1 + 3-2 : M' l' U l U l U' l2 U' l U l U l' U2 M
* 4-1 + 5-2 : (y x') M' U L' U' M U L U'
* 4-1 + 6-2 : (y x') l' U L' U' l r U L U' r'
* 4-1 + 7-2 : (y2 x') l' U' R U l r U' R' U r'
* 4-1 + 8-2 : (x') U2 l2 U' L' U M2 U' L U r2 U2
}}
|---
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 5.jpg]]
|NAME=ELL 1 5-1
|ALGO=
* 5-1 + 1-2 : r2 U' l D2 l' U l D2 r M'
* 5-1 + 2-2 : (x') l' U L' U' l U L U'
* 5-1 + 3-2 : (y' x') r U' R U r' l' U' R' U l
* 5-1 + 4-2 : (x) L2 F r2 U2 r2 Uw2 r2 u2 F' L2
* 5-1 + 6-2 : (y2) l' U l U l U' l2 U' l U l U l' U2
* 5-1 + 7-2 : (x') l' U L' U' l r U L U' r'
* 5-1 + 8-2 : (y' x') L' U' r U' R U r' l' U' R' U l U L
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 6.jpg]]
|NAME=ELL 1 6-1
|ALGO=
* 6-1 + 1-2 : l M D2 r U r' D2 r U' l2
* 6-1 + 2-2 : (y' x') l' U' R U l U' R' U
* 6-1 + 3-2 : (y' x') M' U' R U M U' R' U
* 6-1 + 4-2 : (y' x') l' U' R U l r U' R' U r'
* 6-1 + 5-2 : (y' x') U2 r2 U R U' M2 U R' U' l2 U2
* 6-1 + 7-2 : (y2 x') l' U L' U' l r U L U' r'
* 6-1 + 8-2 : (x) U2 l2 U' R' U M2 U' R U r2 U2
}}
|---
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 7.jpg]]
|NAME=ELL 1 7-1
|ALGO=
* 7-1 + 1-2 : r l D2 l' U2 l D2 l' U2 r'
* 7-1 + 2-2 : (x) U2 r2 U' R' U r2 U' R U'
* 7-1 + 3-2 : (x) U2 r2 U' R' U M2 U' R U l2 U2
* 7-1 + 4-2 : (y' x') L' U' l' U' R U l r U' R' U r' U L
* 7-1 + 5-2 : (x) U2 r2 U L U' M2 U L' U' l2 U2
* 7-1 + 6-2 : (y x') R U l' U L' U' l r U L U' r' U' R'
* 7-1 + 8-2 : r2 U2 r2 Uw2 r2 u2
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 8.jpg]]
|NAME=ELL 1 8-1
|ALGO=
* 8-1 + 1-2 : l' U2 r' D2 r U2 r' D2 r l
* 8-1 + 2-2 : (y2 x') r U' R U r' U' R' U
* 8-1 + 3-2 : (y2 x') r U L' U' r' l' U L U' l
* 8-1 + 4-2 : (x') r U L' U' r' l' U L U' l
* 8-1 + 5-2 : (y2 x') r U' R U r' l' U' R' U l
* 8-1 + 6-2 : (x') r U' R U r' l' U' R' U l
* 8-1 + 7-2 : (y2 x') M' U' R U M U' R' U
}}
|}

==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:
{|
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL2 1.jpg]]
|NAME=ELL 2 1-1
|ALGO=
* 1-1 + 2-2 : Solved
* 1-1 + 3-2 : (y' x') r U' R U r' U' R' U
* 1-1 + 4-2 : (y' x') U' R U r U' R' U r'
* 1-1 + 5-2 : (y x') r U L' U' r' U L U'
* 1-1 + 6-2 : (y x') U L' U' r U L U' r'
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL2 2.jpg]]
|NAME=ELL 2 2-1
|ALGO=
* 2-1 + 1-2 : (x') M' U' R U M U2 M2 U R' U' M2 U2
* 2-1 + 3-2 : r' M D2 l' U l D2 l' U' r2
* 2-1 + 4-2 : l2 U' r' D2 r U r' D2 l' M'
* 2-1 + 5-2 : r' M D2 l' U' l D2 l' U r2
* 2-1 + 6-2 : l2 U r' D2 r U' r' D2 l' M'
}}
|---
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL2 3.jpg]]
|NAME=ELL 2 3-1
|ALGO=
* 3-1 + 1-2 : r2 U l D2 l' U' l D2 r M'
* 3-1 + 2-2 : (y x') U L' U' l' U L U' l
* 3-1 + 4-2 : U2 r U r' U r' U' r2 U' r' U r' U r
* 3-1 + 5-2 : (y x') r U L' U' r' l' U L U' l
* 3-1 + 6-2 : (x) R2 F' r2 U2 r2 Uw2 r2 u2 F R2
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL2 4.jpg]]
|NAME=ELL 2 4-1
|ALGO=
* 4-1 + 1-2 : M l D2 r U' r' D2 r U l2
* 4-1 + 2-2 : (y x') l' U L' U' l U L U'
* 4-1 + 3-2 : M' l' U l U l U' l2 U' l U l U l' U2 M
* 4-1 + 5-2 : (y x') M' U L' U' M U L U'
* 4-1 + 6-2 : (y x') l' U L' U' l r U L U' r'
}}
|---
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL1 5.jpg]]
|NAME=ELL 2 5-1
|ALGO=
* 5-1 + 1-2 : r2 U' l D2 l' U l D2 r M'
* 5-1 + 2-2 : (y' x') U' R U l' U' R' U l
* 5-1 + 3-2 : (y' x') r U' R U r' l' U' R' U l
* 5-1 + 4-2 : (x) L2 F r2 U2 r2 Uw2 r2 u2 F' L2
* 5-1 + 6-2 : (y2) l' U l U l U' l2 U' l U l U l' U2
}}
| valign="top"|
{{Casebox4
|IMAGE=[[Image:BCELL2 6.jpg]]
|NAME=ELL 2 6-1
|ALGO=
* 6-1 + 1-2 : l M D2 r U r' D2 r U' l2
* 6-1 + 2-2 : (y' x') l' U' R U l U' R' U
* 6-1 + 3-2 : (y' x') M' U' R U M U' R' U
* 6-1 + 4-2 : (y' x') l' U' R U l r U' R' U r'
* 6-1 + 5-2 : (y' x') U2 r2 U R U' M2 U R' U' l2 U2
}}
|}

==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:
{| border="1"
| colspan="2"|Group 1; Solve as a 3x3x3.
|---
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 4312.jpg|60px|]]
|NAME=Solved
|ALGO=Stop the timer!
}}
{{Casebox3
|IMAGE=[[Image:BCELL 2134.jpg|60px|]]
|NAME=PLL-parity|ALGO=r2 U2 r2 Uw2 r2 u2
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 4321.jpg|60px|]]
|NAME=OLL-parity
|ALGO=F2 l2 F2 U2 l' U2 l U2 l2 F2 r' F2 r U2 l'
}}
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 3421.jpg|60px|]]
|NAME=Orientation only
|ALGO=M' U M' U M' U2 M U M U M U2
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 1243.jpg|60px|]]
|NAME=Orientation + PLL-parity
|ALGO=x' U 3Rw' U x' (PLL-parity) x U' 3Rw U' x
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 2143.jpg|60px|]]
|NAME=O+P (both paritys)
|ALGO=r U2 r' E2 F2 l F2 l' F2 r F2 r' D2 l
}}
|---
| colspan="2"|Group 2; 3-cycle commutators.
|---
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 4123.jpg|60px|]]
|NAME=UBl solved
|ALGO=r l D2 l' U2 l D2 l' U2 r'
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 4231.jpg|60px|]]
|NAME=UBl inverse
|ALGO=r U2 l D2 l' U2 l D2 l' r'
}}
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 2341.jpg|60px|]]
|NAME=UBr solved
|ALGO=l' r' D2 r U2 r' D2 r U2 l
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 1324.jpg|60px|]]
|NAME=UBr inverse
|ALGO=l' U2 r' D2 r U2 r' D2 r l
}}
|---
| colspan="2"|Group 3; Odd paritys.
|---
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 1423.jpg|60px|]]
|NAME=Checkers
|ALGO=r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r'
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 3241.jpg|60px|]]
|NAME=Mirror checkers
|ALGO=l U2 l2 U2 l' U2 l U2 l' U2 l2 U2 l
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 4213.jpg|60px|]]
|NAME=Swap opposites
|ALGO=r2 D2 r' D2 l D2 l' D2 B2 l' B2 r'
}}
| valign="top"|
{{Casebox3
|IMAGE=[[Image:BCELL3 2314.jpg|60px|]]
|NAME=Swap R diagonals
|ALGO=l' S2 U2 l U2 l' U2 r U2 r' F2 l B2 r
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 4132.jpg|60px|]]
|NAME=Swap L diagonals
|ALGO=r S2 U2 r' U2 r U2 l' U2 l F2 r' B2 l'
}}
{{Casebox3
|IMAGE=[[Image:BCELL3 3124.jpg|60px|]]
|NAME=Swap opposites + deges
|ALGO=F2 l2 F2 l F2 l' F2 r U2 l U2 r' U2 l U2 l'
}}
|}

'''See also:''' my set of ELL 3 algs that I use for the [http://sites.google.com/site/rectangularcuboids/double-domino-3x3x4/Roux 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.


[[Category:4x4x4 substeps]]