#### cubacca1972

##### Member

- Joined
- Jan 3, 2009

- Messages
- 147

I revisited an old solution method I came up with for corners first solves, which would work with the Roux method. After using cube explorer 5.0 to search out the algorithms, I found several shorter algorithms than the ones I found a few years ago.

First, solve up to step 3 in Roux (i.e., everything solved except the M slice edges, and UL and UR).

Step 1

Solve UL and place the UR cubie in UR, but flipped. This is relatively easy, but takes a bit of getting used to, as you have to resist the urge to solve UR.

Step 2

Use 1 of 24 algorithms to flip UR, and solve the M slice (9.583 moves on average). With UR flipped, one of two orientation patterns are forced in the M slice: 3 edges flipped, or 1 edge flipped. Park the odd edge (the single flipped edge, or the single oriented edge) at UF, and apply the appropriate algorithm. If you are solving corners first, this would be a handy place to align the L face with the R face.

Identify which edge is at UF and UD to determine which algorithm to use. There is no need to identify if it is a 3-cycle, double edge swap, etc. For a lot of the cases, you can deduce which edge is at DF without peeking at its D facelet.

Here are the algorithms. The first column shows which edge is at UF. The second shows which edge is at DF. The first 12 algorithms are the cases where there are 3 flipped edges in the M slice, and the last 12 are the cases where there is 1 flipped edge in the M slice.

UF Oriented, Remaining M Edges Flipped

UF-DF--M' U' M' U' M' U' M' U' (8s*)

UF-DB--M' U M U2 M' U M' U' M' U (10,11)

UF-UB--U' M' U2 M U' M U M U' (9s*)

DF-UF--U M U' M2 U2 M U' M' U' (9s*)

DF-DB--U' M' U M U2 M2 U M U (9s*)

DF-UB--U M U M U M U' M U2 (9s*)

DB-UF--M' U M U' M U' M U (8s*)

DB-DF--U' M' U M' U M' U' (7s*)

DB-UB--U' M' U M' U M' U' M2 U2 M U2 (11,14)

UB-UF--U' M' U M' U M' U M2 U2 (9s*)

UB-DF--U M U2 M' U' M' U M' U (9s*)

UB-DB--U' M' U M' U M' U M U2 (9s*)

UF Flipped, Remaining M Edges Oriented

UF-DF--F R' F' M2 F2 M' F' R F M F2 (11s*)

UF-DB--F R' F' M2 F2 M' F' R F M2 F2 (11s)

UF-UB--F R' F' M' F2 M2 F' R F M F2 (11s)

DF-UF--F R' F M2 F2 M F R F' (9f*)

DF-DB--M F' R' F M2 F2 M F R F (10f*)

DF-UB--F R' F M F2 M2 F R F' (9f*)

DB-UF--B2 M' B' R B' M' B2 M2 B' R' B' (11f*)

DB-DF--F R' F M2 F2 M F R F M F2 (11f*)

DB-UB--F R' F M F2 M2 F R F M F2 (11f*)

UB-UF--M' B' R B' M' B2 M2 B' R' B (10f*)

UB-DF--F R' F' M2 F2 M' F' R F' (9f*)

UB-DB--F R' F' M' F2 M2 F' R F' (9f*)

Align the M slice.

Special Cases

Occasionally, at the end of Step 3 in Roux, or the corners first equivalent, the UL and UR edges will be accidentally placed at UL and UF, in some configuration other than what we want for the method outlined as above. Here's how to handle these cases.

Case 1: UL is in the correct place but flipped, UR is solved.

Do y2 and proceed to Step 2 as above.

Case 2: UL and UR are in the correct place, but both are flipped.

2 M edges flipped, adjacent, and at UF and UB--U M2 F2 M' F2 U' (6f*)

2 M edges flipped diagonal, at DF and UB--U2 M' U F2 M F2 M2 U (8f*)

4 M edges flipped--R U' r' U' M' U2 M2 U' r U R' (11f*)

0 M edges flipped--U M2 U M' U M' U' M U M' U (11f*)

The M slice is now oriented, and can be solved with the usual algorithms.

Case 3: UL and UR are solved.

2 M edges flipped, adjacent, and at DB and UB--U2 F M F' U2 F M' F'

2 M edges flipped, diagonal, and at DB and UF--F M F' U2 F M' F' U2

4 M edges flipped--U M' U2 M' U' M U' M' U2 M' U

The M slice is now oriented, and can be solved with the usual algorithms.

I don't know how this compares to other finishes as far as move count goes, but it does guarantee a 2 look finish every time (there is a slim chance of a skip in special cases 2 and 3), and there are fewer algorithms to know compared to solving DF and DB, then O and P of the LL edges.

First, solve up to step 3 in Roux (i.e., everything solved except the M slice edges, and UL and UR).

Step 1

Solve UL and place the UR cubie in UR, but flipped. This is relatively easy, but takes a bit of getting used to, as you have to resist the urge to solve UR.

Step 2

Use 1 of 24 algorithms to flip UR, and solve the M slice (9.583 moves on average). With UR flipped, one of two orientation patterns are forced in the M slice: 3 edges flipped, or 1 edge flipped. Park the odd edge (the single flipped edge, or the single oriented edge) at UF, and apply the appropriate algorithm. If you are solving corners first, this would be a handy place to align the L face with the R face.

Identify which edge is at UF and UD to determine which algorithm to use. There is no need to identify if it is a 3-cycle, double edge swap, etc. For a lot of the cases, you can deduce which edge is at DF without peeking at its D facelet.

Here are the algorithms. The first column shows which edge is at UF. The second shows which edge is at DF. The first 12 algorithms are the cases where there are 3 flipped edges in the M slice, and the last 12 are the cases where there is 1 flipped edge in the M slice.

UF Oriented, Remaining M Edges Flipped

UF-DF--M' U' M' U' M' U' M' U' (8s*)

UF-DB--M' U M U2 M' U M' U' M' U (10,11)

UF-UB--U' M' U2 M U' M U M U' (9s*)

DF-UF--U M U' M2 U2 M U' M' U' (9s*)

DF-DB--U' M' U M U2 M2 U M U (9s*)

DF-UB--U M U M U M U' M U2 (9s*)

DB-UF--M' U M U' M U' M U (8s*)

DB-DF--U' M' U M' U M' U' (7s*)

DB-UB--U' M' U M' U M' U' M2 U2 M U2 (11,14)

UB-UF--U' M' U M' U M' U M2 U2 (9s*)

UB-DF--U M U2 M' U' M' U M' U (9s*)

UB-DB--U' M' U M' U M' U M U2 (9s*)

UF Flipped, Remaining M Edges Oriented

UF-DF--F R' F' M2 F2 M' F' R F M F2 (11s*)

UF-DB--F R' F' M2 F2 M' F' R F M2 F2 (11s)

UF-UB--F R' F' M' F2 M2 F' R F M F2 (11s)

DF-UF--F R' F M2 F2 M F R F' (9f*)

DF-DB--M F' R' F M2 F2 M F R F (10f*)

DF-UB--F R' F M F2 M2 F R F' (9f*)

DB-UF--B2 M' B' R B' M' B2 M2 B' R' B' (11f*)

DB-DF--F R' F M2 F2 M F R F M F2 (11f*)

DB-UB--F R' F M F2 M2 F R F M F2 (11f*)

UB-UF--M' B' R B' M' B2 M2 B' R' B (10f*)

UB-DF--F R' F' M2 F2 M' F' R F' (9f*)

UB-DB--F R' F' M' F2 M2 F' R F' (9f*)

Align the M slice.

Special Cases

Occasionally, at the end of Step 3 in Roux, or the corners first equivalent, the UL and UR edges will be accidentally placed at UL and UF, in some configuration other than what we want for the method outlined as above. Here's how to handle these cases.

Case 1: UL is in the correct place but flipped, UR is solved.

Do y2 and proceed to Step 2 as above.

Case 2: UL and UR are in the correct place, but both are flipped.

2 M edges flipped, adjacent, and at UF and UB--U M2 F2 M' F2 U' (6f*)

2 M edges flipped diagonal, at DF and UB--U2 M' U F2 M F2 M2 U (8f*)

4 M edges flipped--R U' r' U' M' U2 M2 U' r U R' (11f*)

0 M edges flipped--U M2 U M' U M' U' M U M' U (11f*)

The M slice is now oriented, and can be solved with the usual algorithms.

Case 3: UL and UR are solved.

2 M edges flipped, adjacent, and at DB and UB--U2 F M F' U2 F M' F'

2 M edges flipped, diagonal, and at DB and UF--F M F' U2 F M' F' U2

4 M edges flipped--U M' U2 M' U' M U' M' U2 M' U

The M slice is now oriented, and can be solved with the usual algorithms.

I don't know how this compares to other finishes as far as move count goes, but it does guarantee a 2 look finish every time (there is a slim chance of a skip in special cases 2 and 3), and there are fewer algorithms to know compared to solving DF and DB, then O and P of the LL edges.

Last edited: Sep 11, 2010