Cride5
Premium Member
This is a method for solving the 3x3x3 cube using the same principles used in the 2x2x2 Guimond method. The idea is to do: orientation, followed by separation, followed by permutation. The method bares some similarities to the Orient-First method and the Human Thistlethwaite algorithm (particularly in the first steps), but there are also a lot of differences. It uses less algorithms, and uses steps which cubers may already be familiar with, including Edge Orientation, Guimond (steps 1 and 2), PLL, and CF/Roux edge permutation.
I'm not sure how appropriate this method would be as a fewest-moves one, since it breaks down the solve into many distinct steps. Possibly, by combining the steps better move counts could be achieved. Because recognition for most steps is fairly straight forward, and the algs can be made quite finger friendly (ie, with M-slice moves), the method may have some potential for speed solving. However, even if not used for any competitive purpose, it can be a fun way to practice many sub-steps including ZZ-style EO, Guimond, PLL etc.
The method broadly goes as follows:
Method Detail
Method Variants
As it stands, the method has a LOT of (simple) sub-steps which can be combined by adding algorithms. For example, the separation steps 4 and 5 combined together would have about 164 cases (less if not counting mirrors/inverses) and have fairly straightforward recognition.
The final three permutation steps could be combined in different ways. For example, new PBL algs which preserve edge separation could be used to solve the corners, and then all edges edges could be solved in one step which would require roughly about 4^3 = 64 algs.
Example Solves
Scramble: B2 D' L2 U B2 R2 B2 L2 D' B2 F D' B U B R' D' R F R2
Solution:
Edge Orientation: B' L R2 U F
Corner Orientation: L D R U' R'
Mid-Edge Grouping: L2 U D2 R E2 R'
Corner Separation: F2 U' F2 U' F2
Edge Separation: M' E2 M'
E-Slice Parity: R2 U2 R2 U2 R2
E-Slice Solve: E L2 E' L2
D-Layer PLL - R(a): x2 y R U2 R' U2 R B' R' U' R U R B R2' U2
U-Layer PLL - E: x z R U' R' D R U R' u2 R' U R D R' U' R
(62 moves STM)
Scramble:L2 F2 D' U R2 U' L2 U2 B2 U' B D L' F' D' U' R D B L U
Solution:
Edge Orientation: B' D2 R F'
Corner Orientation: R d' F E' R y2
Mid-Edge Grouping: B2 R E2 R' y2
Corner Separation: D2 R2 U' L2
Edge Separation: S U2 S' D M U2 M'
E-Slice Solve: E R2 E' R2
PLL Parity: M2 U2 M2
U-Layer PLL - A(b): y2 R B' R F2 R' B R F2 R2 U'
D-Layer PLL - R(a): x2 R U2 R' U2 R B' R' U' R U R B R2' U
(55 moves STM)
I'm not sure how appropriate this method would be as a fewest-moves one, since it breaks down the solve into many distinct steps. Possibly, by combining the steps better move counts could be achieved. Because recognition for most steps is fairly straight forward, and the algs can be made quite finger friendly (ie, with M-slice moves), the method may have some potential for speed solving. However, even if not used for any competitive purpose, it can be a fun way to practice many sub-steps including ZZ-style EO, Guimond, PLL etc.
The method broadly goes as follows:
- Edge Orientation
- Corner Orientation
- Mid-Edge Grouping
- Corner Separation
- U/D Edge Separation
- Solve E-Slice
- U-Layer PLL
- D-Layer PLL
Method Detail
- Edge Orientation
This is exactly the same as the first step of ZZ, but without placement of the line. A fairly detailed outline of how to do this can be found here.
- Corner Orientation
This is exactly the same as the first step of Guimond, but with the restriction of not using any F/B moves. Ensuring there are no F/B moves can be achieved by doing an E-slice quarter turn when ever an alg would require an F/B move. Its also possible to go for an Ortega-style corner orientation, by placing four oriented U/D corners in the D-layer, then using an OCLL alg to orient the U-layer corners.
- Mid-edge Grouping
The goal of this step is to place all the E-slice edges into the E-slice (but not necessarily solved). The basic technique in this step swaps the two E-slice edges (FL and BL) with the two U/D layer edges UR and DR using:
R E2 R'
L E2 L' (mirrored)
To set up for the swap alg, R2/L2/F2/B2 moves can be used to position the mid-slice edges in FL/BL and theh same moves plus U/D can be used to position the mid layer edges in the UR and DR.
Where there are an odd number of U/D layer edges in the E-slice, it will be necessary to swap an even number of mid-edges with an odd number of U/D edges (or visa-versa).
- Corner Separation
This is exactly the same as Guimond corner separation. Because only R2, L2, F2, B2, U and D moves are used, all previous work done on the cube is preserved.
- Edge Separation
This is a very short/easy step. The basic technique for this step is to swap UF and DF using:
M' U2 M
It is also possible to swap four opposite edges at a time using:
M' E2 M'
Finally, all four edges can be swapped using:
M2 S2
- Solve E-Slice
This step is again fairly easy and can be completed using R2/E-slice moves (in a similar manner to the final step of Roux). However, if the E-slice looks like an N-Perm, T-Perm or its solved apart from a single bar which needs to be twisted by 180 degrees, then you have 'parity', which can be solved using:
R2 U2 R2 U2 R2 (the same as SQ-1 parity)
EDIT: qqwref pointed out that when E-Slice parity occurs, one of the U/D layers will be solvable with PLL. Ensuring the solvable U/D layer is positioned in D when mid-layer parity is executed will avoid parity occurring in step 7..
- U and D layer PLL
This will usually be the same PLL cases as expected, however there is again the possibility of parity (which will occur 50% of the time). It's caused by the U and D layer permutations requiring an odd number of swaps to solve individually. It can be fixed by using:
M2 U2 M2
Method Variants
As it stands, the method has a LOT of (simple) sub-steps which can be combined by adding algorithms. For example, the separation steps 4 and 5 combined together would have about 164 cases (less if not counting mirrors/inverses) and have fairly straightforward recognition.
The final three permutation steps could be combined in different ways. For example, new PBL algs which preserve edge separation could be used to solve the corners, and then all edges edges could be solved in one step which would require roughly about 4^3 = 64 algs.
Example Solves
Scramble: B2 D' L2 U B2 R2 B2 L2 D' B2 F D' B U B R' D' R F R2
Solution:
Edge Orientation: B' L R2 U F
Corner Orientation: L D R U' R'
Mid-Edge Grouping: L2 U D2 R E2 R'
Corner Separation: F2 U' F2 U' F2
Edge Separation: M' E2 M'
E-Slice Parity: R2 U2 R2 U2 R2
E-Slice Solve: E L2 E' L2
D-Layer PLL - R(a): x2 y R U2 R' U2 R B' R' U' R U R B R2' U2
U-Layer PLL - E: x z R U' R' D R U R' u2 R' U R D R' U' R
(62 moves STM)
Scramble:L2 F2 D' U R2 U' L2 U2 B2 U' B D L' F' D' U' R D B L U
Solution:
Edge Orientation: B' D2 R F'
Corner Orientation: R d' F E' R y2
Mid-Edge Grouping: B2 R E2 R' y2
Corner Separation: D2 R2 U' L2
Edge Separation: S U2 S' D M U2 M'
E-Slice Solve: E R2 E' R2
PLL Parity: M2 U2 M2
U-Layer PLL - A(b): y2 R B' R F2 R' B R F2 R2 U'
D-Layer PLL - R(a): x2 R U2 R' U2 R B' R' U' R U R B R2' U
(55 moves STM)
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