campos20
Member
I’ve been considering a variant of domino reduction (or HTA) feasible for Fewest Moves. It solves the cube into some steps:
I’ve gotten some good results in training. It’s pretty easy to get some skip during the solve after the double EO.
Additional comments
Scramble: R' U' F L2 U2 B' L2 F' U2 B L2 B R' B2 L U B L2 B' D' F2 R F R' U' F
The next examples were taken from the Facebook Weekly Challenge from Fewest Moves group, week 17.
1. R' U' F L2 D2 B2 U B2 D' B2 U B' D2 R' D L2 B2 R' U' F' R' D2 R' U' F
2.- R' U' F D R2 U B2 D2 U' R2 F' U' F2 L' D R D F' U F' D' U2 R' U' F
3.- R' U' F D2 R U2 F2 L B2 R' D2 B2 F U2 R B' D B R' F2 L' D B2 R' U' F
Example by Anderson Pavia in Weekly FMC
Scramble: R L' D U' F2 B' R2 B R U' B2 F U2 R2 D B2 U' D' R B2
(Almost) Complete example:
Scramble: D2 F2 R2 U B2 F2 D2 R2 B2 R2 F2 L' B' D R F2 U2 F U L2 B'
Comments on the naming
Matěj Grohmann kindly provided more (and very good) examples!
Using his idea, I decided to gather more examples.
- orient edges in multiple axis (let’s say FB and LR);
- solve all edges along with some corners;
- complete the cube with corner commutators.
I’ve gotten some good results in training. It’s pretty easy to get some skip during the solve after the double EO.
Additional comments
- The multiple axis orientation can be done in 2 sub steps: orient axis 1 then axis 2 (you can even orient the third axis if you wish).
- To have a chance to solve a corner, it needs to be oriented when all the edges get oriented.
- You may try double EO in different ways to skip the corner orientation part.
- You can do some stuff between the EOs.
- To build a 2x2x3, we can build a (lower or upper) 1x2x3 (which I call corner line), place 2 corresponding edges, align 2 more edges (edge line), then build the 2x2x3. This preserves EOs.
- To complete edge permutation, we may stumble with 2 permuted edges. We can use Sune to solve this.
- For FM, you may want to avoid the Sune need and finish with AB5C or AB3C.
- As consequence of double EO, the E edges are in the E layer.
- The core of it is to orient in multiple axis.
Scramble: R' U' F L2 U2 B' L2 F' U2 B L2 B R' B2 L U B L2 B' D' F2 R F R' U' F
D' R' U' F // EO FB
L R2 U R // EO LR
D F2 D2 B2 // CORNER LINE+ EDGE LINE
U2 // 123
L2 // LINE FOR 223
D R2 U // AB5C (17)
L R2 U R // EO LR
D F2 D2 B2 // CORNER LINE+ EDGE LINE
U2 // 123
L2 // LINE FOR 223
D R2 U // AB5C (17)
The next examples were taken from the Facebook Weekly Challenge from Fewest Moves group, week 17.
1. R' U' F L2 D2 B2 U B2 D' B2 U B' D2 R' D L2 B2 R' U' F' R' D2 R' U' F
L' U R F // EO FB
(R D R') // EO LR
B2 D' B2 // CORNER LINE
L2 D B2 D U' L2 // EDGE LINE
D' U F2 // BLOCKS
U2 F2 D' F2 // AB3C (23)
(R D R') // EO LR
B2 D' B2 // CORNER LINE
L2 D B2 D U' L2 // EDGE LINE
D' U F2 // BLOCKS
U2 F2 D' F2 // AB3C (23)
2.- R' U' F D R2 U B2 D2 U' R2 F' U' F2 L' D R D F' U F' D' U2 R' U' F
(R B) // EO FB
(D2 L) // EO LR
(D L2 D2 L2) // CORNER LINE
R2 U D2 B2 D2 // EDGE LINE
B2 U' B2
U2 B2 U' // AB5C (19)
(D2 L) // EO LR
(D L2 D2 L2) // CORNER LINE
R2 U D2 B2 D2 // EDGE LINE
B2 U' B2
U2 B2 U' // AB5C (19)
3.- R' U' F D2 R U2 F2 L B2 R' D2 B2 F U2 R B' D B R' F2 L' D B2 R' U' F
(U2 L R F') // EO
(U' L2 R D') // EO
D2 L F2 B2 // 123
L B2 R F2 // EDGE LINE
L' F2 L2 // 223
R' F2 // AB5C (21)
(U' L2 R D') // EO
D2 L F2 B2 // 123
L B2 R F2 // EDGE LINE
L' F2 L2 // 223
R' F2 // AB5C (21)
Example by Anderson Pavia in Weekly FMC
Scramble: R L' D U' F2 B' R2 B R U' B2 F U2 R2 D B2 U' D' R B2
F' L2 D' B' // EO+SQUARE
F2 U' L // EO+PAIR
U2 L2 U // SQUARE
U2 L' R B2 L R D // AB5C (16)
F2 U' L // EO+PAIR
U2 L2 U // SQUARE
U2 L' R B2 L R D // AB5C (16)
(Almost) Complete example:
Scramble: D2 F2 R2 U B2 F2 D2 R2 B2 R2 F2 L' B' D R F2 U2 F U L2 B'
U B R F2 D F // EO
R B2 D L // EO
L' D' L D' L' D2 L // Sune for corner orientation
L2 F2 B2 // 1x2x3
R2 D2 U F2 // Align edges+Edge Line
D' B2 D2 // 2x2x3
B2 U2 B2 U2 B2 U' // Permuted edges case
U2 B U B' U B U2 B' // Sune to fix this
U' // AB6C
R B2 D L // EO
L' D' L D' L' D2 L // Sune for corner orientation
L2 F2 B2 // 1x2x3
R2 D2 U F2 // Align edges+Edge Line
D' B2 D2 // 2x2x3
B2 U2 B2 U2 B2 U' // Permuted edges case
U2 B U B' U B U2 B' // Sune to fix this
U' // AB6C
Comments on the naming
Why didn't I call it Double EO and name the steps EO1 / EO2 or EO / new EO
1: When you do the 2nd EO, you must not disturb EO1, thus you must avoid 2 moves. This is not true when you are doing pure EO.
2: In a solve, you can do EO1, EO2 in such a way that EO2 destroys EO1 and still have a good solution. Changing the name, this would never be the case.
3: Domino reduction is already out there, but is basically found with brute force these days, not very human friendly. I was quite inspired by domino reduction when I thought about this new method, so naming after it seemed right.
4: In this new method, the number of oriented corners is very, very important. If you have 3 good corners after EO2, the best skeleton you can get is AB5C without breaking any of the EO. If you have 4 good corners, you can end up with AB4C (or AB5C). If you have 5, 6 good corners, AB3C. 8 good corners is full domino reduction. Less than 3 good corners is usually not worth it (although we can have good AB6C with 2 good corners, but it cancels badly). In my point of view, this is a new way of thinking and it's not true for traditional EO (we usually don't care about the numbers of good corners). That's the main reason why I decided to name it some way else.
So, I don't use
moves // EO
stuff // EO
I prefer
moves // EO
stuff // Partial Domino Reduction or PDR.
Sometimes I even indicate the number of good corners after PDR.
I'm not saying everyone should name like that, I'm just saying my point of view.
1: When you do the 2nd EO, you must not disturb EO1, thus you must avoid 2 moves. This is not true when you are doing pure EO.
2: In a solve, you can do EO1, EO2 in such a way that EO2 destroys EO1 and still have a good solution. Changing the name, this would never be the case.
3: Domino reduction is already out there, but is basically found with brute force these days, not very human friendly. I was quite inspired by domino reduction when I thought about this new method, so naming after it seemed right.
4: In this new method, the number of oriented corners is very, very important. If you have 3 good corners after EO2, the best skeleton you can get is AB5C without breaking any of the EO. If you have 4 good corners, you can end up with AB4C (or AB5C). If you have 5, 6 good corners, AB3C. 8 good corners is full domino reduction. Less than 3 good corners is usually not worth it (although we can have good AB6C with 2 good corners, but it cancels badly). In my point of view, this is a new way of thinking and it's not true for traditional EO (we usually don't care about the numbers of good corners). That's the main reason why I decided to name it some way else.
So, I don't use
moves // EO
stuff // EO
I prefer
moves // EO
stuff // Partial Domino Reduction or PDR.
Sometimes I even indicate the number of good corners after PDR.
I'm not saying everyone should name like that, I'm just saying my point of view.
Matěj Grohmann kindly provided more (and very good) examples!
Using his idea, I decided to gather more examples.
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