miotatsu
Member
Here I have documented the method that I use to solve the 3x3x3 Rubik's Cube.
This method could be described as a "belt method". Many of the ideas and algorithms come from another method called LCBM.
I came upon this method while trying to optimize HTA for speed solving.
I hope that these documents will be useful to others interested in this method.
Overview of method:
1. Edge orientation - place edges in the group <F2, B2, L, R, U, D> (or equivilant)
2. Belt - solve 4 edges of the equator (E slice)
3. Parity - create a situation in which corners can be solved with OCLL cases
4. EPOCBL - orient all corners while preserving equator and edge orientation
5. Seperation - permute corners to their correct layers
6. EPPCBL - permute all corners while preserving equator and edge orientation
7. L8E - solve the remaining eight edges
I am no teacher, so I will simply provide links that can explain each step better than myself.
Step 1: Edge Orientation:
This is the same as EOLine without the line.
http://cube.crider.co.uk/zz.php?p=eoline
http://www.youtube.com/watch?v=a6tkUlkjnOE
Step 2: Belt:
Intuitive. Remember not to use single turns on F and B.
Step 3: Parity:
If you do not have OCLL cases on U/D:
Step 4: EPOCBL:
Memorize the algorithms for each case.
Step 5: Seperation:
Intuitive. Use only moves of the group <F2, B2, L2, R2, U, D>. I recommend only using <L2, R2, U, D>.
Do not forget that you must restore the equator after breaking it.
For example instead of bringing 2 U face corners from positions DLF and DLB to the top face with L2 you must do
something that will not destroy the belt such as:
U2 L2 U2 L2 U2
Step 6: EPPCBL:
Memorize the algorithms for each case.
Step 7: L8E:
I solve these using the exact same system used in Roux for LSE minus the edge orientation
http://grrroux.free.fr/method/Step_4.html (4b and 4c)
http://wafflelikescubes.webs.com/rouxmethod.htm (4b and 4c)
http://rouxtorial.webs.com/lse.htm (4b and 4c)
Example solves:
F2 R2 D2 R2 F2 D R2 U B2 L2 F U' R2 B' R' B F2 L2 U L'
EO: R' D R U2 B
Belt: U2 D' R' D' L
Parity: none
EPOCBL: U2 D2 L' U' L' U2 L U' L
Seperation: D' L2 U D L2
EPPCBL: D x2 R U R' F' R U R' U' R' F R2 U' R' x2
L8E: U2 M U2 M' D' M2 D M2 U M U2 M U M2 U x U2 M2 U2 M2
B' U2 B' L' R D2 F L R2 D2 U2 B' U' B' U' R2 F2 R D B U2 R U2 F2 L'
EO: D F' R2 D F2 D F'
Belt: U' D2 R' B2 L2
Parity: none
EPOCBL: D' L' U' L2 U' L' U2 D' L2 U' L'
Seperation: L2 U' L2
EPPCBL: D x2 F' L U L F D2 F' L' U' L' F U D x2
L8E: M2 U M U2 M' D M2 D' M2 U' M U2 M U' M2 U' M' U2 M'
U F2 D F2 U2 F2 L2 U' F2 U' R U' L2 D R U2 B' R2 B' R2 F'
EO: F D' B' D B
Belt: F2 R' U R L' D' L
Parity: L2 U' L2
EPOCBL: f R U R' U' f' F R U R' U' F'
Seperation: U2 L2 D' U2 L2
EPPCBL: U F' L U L F D2 F' L' U' L' F U D2
L8E: M' U2 M D M2 D' U M2 U2 M2 U' M U2 M' U2 M2
Algs:
This method could be described as a "belt method". Many of the ideas and algorithms come from another method called LCBM.
I came upon this method while trying to optimize HTA for speed solving.
I hope that these documents will be useful to others interested in this method.
Overview of method:
1. Edge orientation - place edges in the group <F2, B2, L, R, U, D> (or equivilant)
2. Belt - solve 4 edges of the equator (E slice)
3. Parity - create a situation in which corners can be solved with OCLL cases
4. EPOCBL - orient all corners while preserving equator and edge orientation
5. Seperation - permute corners to their correct layers
6. EPPCBL - permute all corners while preserving equator and edge orientation
7. L8E - solve the remaining eight edges
I am no teacher, so I will simply provide links that can explain each step better than myself.
Step 1: Edge Orientation:
This is the same as EOLine without the line.
http://cube.crider.co.uk/zz.php?p=eoline
http://www.youtube.com/watch?v=a6tkUlkjnOE
Step 2: Belt:
Intuitive. Remember not to use single turns on F and B.
Step 3: Parity:
If you do not have OCLL cases on U/D:
qqwref said:The idea is this: R2 U' R2 basically replaces DRF with ULF.
So what you want to do is replace one corner on D with a differently-oriented one, fixing the corner parity.
If you want to rotate a bottom corner clockwise, for instance, you could replace solved with clockwise,
or clockwise with counterclockwise, or counterclockwise with solved.
Another option (if you're willing to have the belt be either solved or an R2 off, which might be worthwhile for corner separation)
is to simply do an R2, moving two corners to the bottom layer.
I am not sure this can always create a solvable parity case, but it seems to work most of the time,
so it's probably still useful (and hey, one move is better than 3 or 7, eh?).
I guess, yeah, if you're going to separate later, it wouldn't hurt to leave the belt up to an R2 off -
no point wasting moves keeping it that way when you're just going to intuitively mess it up later.
Step 4: EPOCBL:
Memorize the algorithms for each case.
Step 5: Seperation:
Intuitive. Use only moves of the group <F2, B2, L2, R2, U, D>. I recommend only using <L2, R2, U, D>.
Do not forget that you must restore the equator after breaking it.
For example instead of bringing 2 U face corners from positions DLF and DLB to the top face with L2 you must do
something that will not destroy the belt such as:
U2 L2 U2 L2 U2
Step 6: EPPCBL:
Memorize the algorithms for each case.
Step 7: L8E:
I solve these using the exact same system used in Roux for LSE minus the edge orientation
http://grrroux.free.fr/method/Step_4.html (4b and 4c)
http://wafflelikescubes.webs.com/rouxmethod.htm (4b and 4c)
http://rouxtorial.webs.com/lse.htm (4b and 4c)
Example solves:
F2 R2 D2 R2 F2 D R2 U B2 L2 F U' R2 B' R' B F2 L2 U L'
EO: R' D R U2 B
Belt: U2 D' R' D' L
Parity: none
EPOCBL: U2 D2 L' U' L' U2 L U' L
Seperation: D' L2 U D L2
EPPCBL: D x2 R U R' F' R U R' U' R' F R2 U' R' x2
L8E: U2 M U2 M' D' M2 D M2 U M U2 M U M2 U x U2 M2 U2 M2
B' U2 B' L' R D2 F L R2 D2 U2 B' U' B' U' R2 F2 R D B U2 R U2 F2 L'
EO: D F' R2 D F2 D F'
Belt: U' D2 R' B2 L2
Parity: none
EPOCBL: D' L' U' L2 U' L' U2 D' L2 U' L'
Seperation: L2 U' L2
EPPCBL: D x2 F' L U L F D2 F' L' U' L' F U D x2
L8E: M2 U M U2 M' D M2 D' M2 U' M U2 M U' M2 U' M' U2 M'
U F2 D F2 U2 F2 L2 U' F2 U' R U' L2 D R U2 B' R2 B' R2 F'
EO: F D' B' D B
Belt: F2 R' U R L' D' L
Parity: L2 U' L2
EPOCBL: f R U R' U' f' F R U R' U' F'
Seperation: U2 L2 D' U2 L2
EPPCBL: U F' L U L F D2 F' L' U' L' F U D2
L8E: M' U2 M D M2 D' U M2 U2 M2 U' M U2 M' U2 M2
Algs:
EPOCBL Beginner (2-look) - 7 cases:
====================================================
Sune: on U: R U R' U R U2 R'
antiSune: on U: L' U' L U' L' U2 L
H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
U: on U: R2 D' R U2 R' D R U2 R
T: on U: r U R' U' r' F R F'
L: on U: y' F' r U R' U' r' F R
Pi: on U: f (R U R' U') f' F (R U R' U') F'
EPPCBL Beginner (2-look) - 2 cases:
====================================================
Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
J: R U R' F' R U R' U' R' F R2 U' R' U'
EPOCBL Intermediate (1-look) - 25 cases:
====================================================
Sune: R U R' U R U2 R'
H: y F (R U R' U') (R U R' U') (R U R' U') F'
U: R2 D' R U2 R' D R U2 R
T: r U R' U' r' F R F'
L: y' F' r U R' U' r' F R
Pi: f (R U R' U') f' F (R U R' U') F'
sune/sune: R' U' R' U R U2 D R' D' R
anti/sune: R' U' R U2 R (U' D) R2 U R'
H/sune: U' R (U' D) M2 U' r2 U R'
U/sune: R' U2 R' U D R2 U2 R' U' R
T/sune: L D' L' U' r2 U2 L' U' L'
L/sune: R D r2 R' U R U2 r2 R'
Pi/sune: L U D L' U D2 L' U2 D L'
H/H: R2 (U' D) L (U D') M2 (U D') L
U/H: R D R' U D2 l2 U2 R' U' R'
T/H: L D L' U' D2 r2 U2 L' U' L'
L/H: L U' L2 R2 U' L' l2 D U2 L
Pi/H: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
L/U: D' L' U' L' U2 L U' L
Pi/U: L' U R U2 R' U L R U R'
L/T: U R U D2 R' U' D2 R'
Pi/T: L' U' L l2 U' l2 U' L' U2 L
L/L: L U' D' L U D L'
Pi/L: L' U' L2 U' L' U2 D' L2 U' L'
Pi/Pi: L U D L' U2 D2 L U D L'
EPPCBL Intermediate (1-look) - 5 cases:
====================================================
Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
J: R U R' F' R U R' U' R' F R2 U' R' U'
J/J: F2 U' R2 U D R2 D' F2
J/Y: F' L U L F D2 F' L' U' L' F
Y/Y: F2 U2 R2 U2 R2 U2 F2
EPOCBL Advanced (1-look) - 70 cases
====================================================
One case:
Sune: on U: R U R' U R U2 R'
Sune: on B:
antiSune: on U: L' U' L U' L' U2 L
antiSune: on B:
H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
H: on B:
U: on U: R2 D' R U2 R' D R U2 R
U: on B:
T: on U: r U R' U' r' F R F'
T: on B:
L: on U: y' F' r U R' U' r' F R
L: on B:
Pi: on U: f (R U R' U') f' F (R U R' U') F'
Pi: on B:
Two cases:
Sune: on B:
Sune: R' U' R' U R U2 D R' D' R
antiSune: R' U' R U2 R (U' D) R2 U R'
H/Double Sune: U' R (U' D) r2 R2 U' r2 U R'
U/Headlights: R' U2 R' U D R2 U2 R' U' R
T/Chameleon: L D' L' U' r2 U2 L' U' L'
L/Bowtie: R D r2 R' U R U2 r2 R'
Pi/Wheel: L U D L' U D2 L' U2 D L'
antiSune: on B:
Sune: L U L' U2 L' (U D') L2 U' L
antiSune: L' U L U' L U' D2 L U L'
H/Double Sune: U' L' (U D') l2 L2 U l2 U' L
U/Headlights: U R U' R2' D2 R U2 R U' R'
T/Chameleon: R' (U2 D2) R' D R2 U2 D R
L/Bowtie: L U R U' L U2 L2 U' R'
Pi/Wheel: R U2 L2 U R U D r2' R U R
H: on B:
Sune: D R (U D') L2 R2 U' r2 U R'
antiSune: D' L' (U' D) L2 R2 U l2 U' L
H/Double Sune: R2 (U' D) L (U D') L2 l2 (U D') L
U/Headlights: R D R' U D2 l2 U2 R' U' R'
T/Chameleon: L D L' U' D2 r2 U2 L' U' L'
L/Bowtie: L U' L2 R2 U' L' l2 D U2 L
Pi/Wheel: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
U: on B:
Sune: R U' R2 D L' R2 U R' U' L
antiSune: L' U R U' L l2 U l2 U R'
H/Double Sune: R U R' U2 D R2 U2 R' U' R'
U/Headlights: U2 L' U L' U' r2 U' L U L'
T/Chameleon: R (U' D) R U' R' U2 D' R'
L/Bowtie: D' L' U' L' U2 L U' L
Pi/Wheel: L' U R U2 R' U L R U R'
T: on B:
Sune: L U' L' D' L2 U2 L' U' L'
antiSune: R' (U2 D2) R' U R2 U D2 R
H/Double Sune: L U L' U2 D' L2 U2 L' U' L'
U/Headlights: L2 U2 L' U' L U2 L' U' L'
T/Chameleon: R (U2 D2) R' (U2 D2) R'
L/Bowtie: U R U D2 R' U' D2 R'
Pi/Wheel: L' U' L l2 U' l2 U' L' U2 L
L: on B:
Sune: R U L2 U2 L' U R' U' L'
antiSune: x2 L U R U' L U2 L2 U' R'
L D R D' L D2 L2 D' R'
H/Double Sune: L U L2 U' L U' D2 L U2 L
U/Headlights: U' L' D' L' D2 L D' L
T/Chameleon: D R U2 D R' U2 D' R'
L/Bowtie: L U' D' L U D L'
Pi/Wheel: L' U' L2 U' L' U2 D' L2 U' L'
Pi: on B:
Sune: L U D L' U2 D L' U D2 L'
antiSune: D R U L2 U D R U2 r2 U' R'
H/Double Sune: R' U L2 U' R2 (U D') L2 R (U' D) R'
U/Headlights: R' U' r2 D2 U' R' U r2 U' R
T/Chameleon: L' U' L2 D2 L U2 D' L U' L
L/Bowtie: D L' U' D' L D R2 U L R2
Pi/Wheel: L U D L' U2 D2 L U D L'
EPPCBL Advanced (1-look) - 35 cases
====================================================
Case J/:
L: R U R' F' R U R' U' R' F R2 U' R' U'
R: (y) R' U L' U2 R U' R' U2 L R U'
F: R' U L' U2 R U' R' U2 L R U'
B: R U' L U2 R' U R U2 L' R'
Case Y/:
F R U' R' U' R U R' F' R U R' U' R' F R F'
Case /J:
L:
R:
F:
B:
Case /Y:
Case J/J:
L/L: F2 U' R2 U D R2 D' F2
L/R:
L/F:
L/B:
R/L:
R/R:
R/F:
R/B:
F/L:
F/R:
F/F:
F/B:
B/L:
B/R:
B/F:
B/B:
Case Y/Y:
F2 U2 R2 U2 R2 U2 F2
R2 U2 R2 U2 y' R2 U D' R2
R2 U2 R2 U2 F2 dD' R2
R2 U2 R2 U2 F2 E R2
U' R2 U2 R2 D2 F2 E' L2
Case J/Y:
L: F' L U L F D2 F' L' U' L' F
R:
F:
B:
Case Y/J:
L:
R:
F:
B:
====================================================
Sune: on U: R U R' U R U2 R'
antiSune: on U: L' U' L U' L' U2 L
H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
U: on U: R2 D' R U2 R' D R U2 R
T: on U: r U R' U' r' F R F'
L: on U: y' F' r U R' U' r' F R
Pi: on U: f (R U R' U') f' F (R U R' U') F'
EPPCBL Beginner (2-look) - 2 cases:
====================================================
Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
J: R U R' F' R U R' U' R' F R2 U' R' U'
EPOCBL Intermediate (1-look) - 25 cases:
====================================================
Sune: R U R' U R U2 R'
H: y F (R U R' U') (R U R' U') (R U R' U') F'
U: R2 D' R U2 R' D R U2 R
T: r U R' U' r' F R F'
L: y' F' r U R' U' r' F R
Pi: f (R U R' U') f' F (R U R' U') F'
sune/sune: R' U' R' U R U2 D R' D' R
anti/sune: R' U' R U2 R (U' D) R2 U R'
H/sune: U' R (U' D) M2 U' r2 U R'
U/sune: R' U2 R' U D R2 U2 R' U' R
T/sune: L D' L' U' r2 U2 L' U' L'
L/sune: R D r2 R' U R U2 r2 R'
Pi/sune: L U D L' U D2 L' U2 D L'
H/H: R2 (U' D) L (U D') M2 (U D') L
U/H: R D R' U D2 l2 U2 R' U' R'
T/H: L D L' U' D2 r2 U2 L' U' L'
L/H: L U' L2 R2 U' L' l2 D U2 L
Pi/H: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
L/U: D' L' U' L' U2 L U' L
Pi/U: L' U R U2 R' U L R U R'
L/T: U R U D2 R' U' D2 R'
Pi/T: L' U' L l2 U' l2 U' L' U2 L
L/L: L U' D' L U D L'
Pi/L: L' U' L2 U' L' U2 D' L2 U' L'
Pi/Pi: L U D L' U2 D2 L U D L'
EPPCBL Intermediate (1-look) - 5 cases:
====================================================
Y: F R U' R' U' R U R' F' R U R' U' R' F R F'
J: R U R' F' R U R' U' R' F R2 U' R' U'
J/J: F2 U' R2 U D R2 D' F2
J/Y: F' L U L F D2 F' L' U' L' F
Y/Y: F2 U2 R2 U2 R2 U2 F2
EPOCBL Advanced (1-look) - 70 cases
====================================================
One case:
Sune: on U: R U R' U R U2 R'
Sune: on B:
antiSune: on U: L' U' L U' L' U2 L
antiSune: on B:
H: on U: y F (R U R' U') (R U R' U') (R U R' U') F'
H: on B:
U: on U: R2 D' R U2 R' D R U2 R
U: on B:
T: on U: r U R' U' r' F R F'
T: on B:
L: on U: y' F' r U R' U' r' F R
L: on B:
Pi: on U: f (R U R' U') f' F (R U R' U') F'
Pi: on B:
Two cases:
Sune: on B:
Sune: R' U' R' U R U2 D R' D' R
antiSune: R' U' R U2 R (U' D) R2 U R'
H/Double Sune: U' R (U' D) r2 R2 U' r2 U R'
U/Headlights: R' U2 R' U D R2 U2 R' U' R
T/Chameleon: L D' L' U' r2 U2 L' U' L'
L/Bowtie: R D r2 R' U R U2 r2 R'
Pi/Wheel: L U D L' U D2 L' U2 D L'
antiSune: on B:
Sune: L U L' U2 L' (U D') L2 U' L
antiSune: L' U L U' L U' D2 L U L'
H/Double Sune: U' L' (U D') l2 L2 U l2 U' L
U/Headlights: U R U' R2' D2 R U2 R U' R'
T/Chameleon: R' (U2 D2) R' D R2 U2 D R
L/Bowtie: L U R U' L U2 L2 U' R'
Pi/Wheel: R U2 L2 U R U D r2' R U R
H: on B:
Sune: D R (U D') L2 R2 U' r2 U R'
antiSune: D' L' (U' D) L2 R2 U l2 U' L
H/Double Sune: R2 (U' D) L (U D') L2 l2 (U D') L
U/Headlights: R D R' U D2 l2 U2 R' U' R'
T/Chameleon: L D L' U' D2 r2 U2 L' U' L'
L/Bowtie: L U' L2 R2 U' L' l2 D U2 L
Pi/Wheel: R' U' L2 U R2 (U' D) r2 R' (U' D) R'
U: on B:
Sune: R U' R2 D L' R2 U R' U' L
antiSune: L' U R U' L l2 U l2 U R'
H/Double Sune: R U R' U2 D R2 U2 R' U' R'
U/Headlights: U2 L' U L' U' r2 U' L U L'
T/Chameleon: R (U' D) R U' R' U2 D' R'
L/Bowtie: D' L' U' L' U2 L U' L
Pi/Wheel: L' U R U2 R' U L R U R'
T: on B:
Sune: L U' L' D' L2 U2 L' U' L'
antiSune: R' (U2 D2) R' U R2 U D2 R
H/Double Sune: L U L' U2 D' L2 U2 L' U' L'
U/Headlights: L2 U2 L' U' L U2 L' U' L'
T/Chameleon: R (U2 D2) R' (U2 D2) R'
L/Bowtie: U R U D2 R' U' D2 R'
Pi/Wheel: L' U' L l2 U' l2 U' L' U2 L
L: on B:
Sune: R U L2 U2 L' U R' U' L'
antiSune: x2 L U R U' L U2 L2 U' R'
L D R D' L D2 L2 D' R'
H/Double Sune: L U L2 U' L U' D2 L U2 L
U/Headlights: U' L' D' L' D2 L D' L
T/Chameleon: D R U2 D R' U2 D' R'
L/Bowtie: L U' D' L U D L'
Pi/Wheel: L' U' L2 U' L' U2 D' L2 U' L'
Pi: on B:
Sune: L U D L' U2 D L' U D2 L'
antiSune: D R U L2 U D R U2 r2 U' R'
H/Double Sune: R' U L2 U' R2 (U D') L2 R (U' D) R'
U/Headlights: R' U' r2 D2 U' R' U r2 U' R
T/Chameleon: L' U' L2 D2 L U2 D' L U' L
L/Bowtie: D L' U' D' L D R2 U L R2
Pi/Wheel: L U D L' U2 D2 L U D L'
EPPCBL Advanced (1-look) - 35 cases
====================================================
Case J/:
L: R U R' F' R U R' U' R' F R2 U' R' U'
R: (y) R' U L' U2 R U' R' U2 L R U'
F: R' U L' U2 R U' R' U2 L R U'
B: R U' L U2 R' U R U2 L' R'
Case Y/:
F R U' R' U' R U R' F' R U R' U' R' F R F'
Case /J:
L:
R:
F:
B:
Case /Y:
Case J/J:
L/L: F2 U' R2 U D R2 D' F2
L/R:
L/F:
L/B:
R/L:
R/R:
R/F:
R/B:
F/L:
F/R:
F/F:
F/B:
B/L:
B/R:
B/F:
B/B:
Case Y/Y:
F2 U2 R2 U2 R2 U2 F2
R2 U2 R2 U2 y' R2 U D' R2
R2 U2 R2 U2 F2 dD' R2
R2 U2 R2 U2 F2 E R2
U' R2 U2 R2 D2 F2 E' L2
Case J/Y:
L: F' L U L F D2 F' L' U' L' F
R:
F:
B:
Case Y/J:
L:
R:
F:
B: