Roux Method

The Magic Cube is the world's most popular toy, with over 350 million having been sold world-wide. (This includes both the original Rubik's-brand cube and similar puzzles with or without an improved internal mechanism.)

Over the years, there have been a number of approaches to solving the cube, but currently my favourite is Giles Roux's eponymous method based on block-building. My times are currently averaging around 40 seconds, with a current PB of 27.77s (Not great when the world record is 5.55s but I am improving.)

Step1 diagram

Step 1: Block 1

Create a 3x2x1 block on the Left slice. Following the example from Roux, I've been using Red on the Down face and Yellow on the Left. So this means solving the block consisting of the Yellow centre, the Yellow/Red edge, the Yellow/Blue edge, the Yellow/Green edge, the Yellow/Red/Green corner and the Yellow/Red/Blue corner. (Diagram looking at the L-face)

Hint for speed: Try to plan out the whole of this step in the inspection phase and to execute the moves without looking.

Step2 diagram

Step 2: Block 2

Create the corresponding 3x2x1 block, opposite the first, on the Right slice (W centre, W/R, W/B, W/G edges, W/R/G and W/R/B corners). This should be done without disturbing the block built in step 1, using only R, r, M and U moves. (Diagram looking at the R-face)

Step 3: Corners Last Layer (CMLL)

This step is known as CMLL because (a) other methods have similar corner methods with other CxLL abbreviations and (b) we are free to disturb the M-slice.

Initially I found Roux's corners page quite confusing and it put me off his method for some time. But I'll use his system for classifying the CMLL algs, because (almost) everyone else does.

There are 8 orientations (A-H) with up to 6 permutations within each. Each permutation involves swapping a pair of corners (other than 1 which is no swap). The 6 permutations are:

  1. No swap
  2. Swap back
  3. Swap right
  4. Swap front
  5. Swap left
  6. Swap diagonal

Aside: Two-look CMLL

Waffle-Jim (who has built a great guide to the Roux method) recommends learning two-look CMLL at first. Learn (initially) one alg for each orientation possibility, and then use one of the two "A"-cases to permute if necessary. So that's what I have done. I've highlighted the CMLL algs I've learned for two-look in green and other algs in yellow.

NB These are just the algs I use. Other Roux users use other algs. If you're trying to learn, I recommend checking out as many algs as you can, and using the ones that feel best to you.

The algs of doom

All diagrams are as if looking down on the U-face, with the colours of the edge tiles also shown. NB This is still very much a work in progress.

A-generic diagram

A: Skip

Recognition: look at the edges of the U-layer corners

A1: All edges are paired up correctly
A1 diagram

Nothing to do

A2, A3, A4, A5: These cases are all equivalent. One correct pair. Adjust U-face to get this pair in the L-face.
A2 diagram

R U2 R' U' R U2 L' U R' U' L

A6: No correct pairs, all edges are pairs of opposite colours.
A6 diagram

(R' U L' U2 R U' L)2

B-generic diagram

B: Antisune

Recognition: look for a pair of opposite colours in the U-face, and examine the tile on the F-edge of the UFR corner to see which tile in the U-face (if any) it matches.

B1: Opposite pair diagonal, F-edge UFR matches U-face UBR
B1 diagram

R' U' R U' R' U2 R

B2: Opposite pair column, F-edge UFR not in U-face
B2 diagram

U2 R2 D R' U R D' R' U R' U' R U' R'

B3: Opposite pair row, F-edge UFR not in U-face
B3 diagram

R' L U' R U L' U2 R' U2 R

B4: Opposite pair column, F-edge UFR matches U-face UFL
B4 diagram

U2 R U2 R' U2 R' F R F'

B5: Opposite pair row, F-edge UFR matches U-face UBR
B5 diagram

R' U L U' R U L'

B6: Opposite pair diagonal, F-edge UFR matches U-face UFL
B6 diagram

U2 R' U' R U' L U' R' U L' U2 R

C-generic diagram

C: Sune

Recognition: look for a pair of opposite colours in the U-face, and examine the tile on the R-edge of the UFR corner to see which tile in the U-face (if any) it matches.

C1: Opposite pair diagonal, R-edge UFR not in U-face
C1 diagram

R U R' U R U2 R'

C2: Opposite pair column, R-edge UFR not in U-face
C2 diagram

R' F2 R U2 R U' L' U x'

C3: Opposite pair row, R-edge UFR matches U-face UBR
C3 diagram

x U R' U' L U2 R U2 R'

C4: Opposite pair column, R-edge UFR matches U-face UBL
C4 diagram

U' R U R' U R U' R D R' U' R D' R2

C5: Opposite pair row, R-edge UFR matches U-face UBL
C5 diagram

R U' L' U R' U' L

C6: Opposite pair diagonal, R-edge UFR matches U-face UBR
C6 diagram

U2 R U R' U L' U R U' L U2 R'

D-generic diagram

D: Bowtie

Recognition: Examine U-face diagonal: is it matching, opposite or other? Then compare F-edge of UFR with U-face of UBR

D1: U-diagonal other, F-edge of UFR opposite U-face of UBR
D1 diagram

U2 R U2 R' U' R U R' U' R U R' U' R U' R'

Also:

sune U antisune

D2: U-diagonal pair, F-edge of UFR not in U-face
D2 diagram

R U2 R D R' U2 R D' R2

D3: U-diagonal opposite, F-edge of UFR matches U-face of UBR
D3 diagram

F R' F' R U R U' R'

D4: U-diagonal opposite, F-edge of UFR not in U-face
D4 diagram

R' F R U F U' F'

D5: U-diagonal pair, F-edge of UFR opposite U-face of UBR
D5 diagram

U' R' U2 R' D' R U2 R' D R2

D6: U-diagonal other, F-edge of UFR matches U-face of UBR
D6 diagram

U2 L' U2 R U' R' U2 R L U' R'

E-generic diagram

E: Headlights

Recognition: look at the pair of tiles on the B-row corners of the U-face, and the pair on the U-row corners of the F-face.

E1: U-face opposites, F-face same
E1 diagram

R' U' R U' R' U2 R2 U R' U R U2 R'

Actually is:

antisune sune

E2: U-face same, F-face same
E2 diagram

U R U' r' F R' F2 U' F U r

E3: Forward Slash
E3 diagram

U2 R2 D R' U2 R D' R' U2 R'

E4: Double Slash
E4 diagram

U2 R' F U' R F R' U R F'

E5: Back Slash
E5 diagram

R2 D' R U2 R' D R U2 R

E6: U-face same, F-face opposites
E6 diagram

U' F R U R' U' F'

U' F sexy-move F'

F-generic diagram

F: Chameleon

Recognition: As case E: look at the pair of tiles on the B-row corners of the U-face, and the pair on the U-row corners of the F-face.

F1: U-face same, F-face same
F1 diagram

F R' F R2 U' R' U' R U R' F2

Also:

U' antisune U2 sune

Or:

U' sune U2 antisune

F2: U-face opposites, F-face same
F2 diagram

R' U r U2 R2 F R F' r

F3: Right column
F3 diagram

U R' F R U2 F U2 F'

F4: U-face same, F-face opposites
F4 diagram

F U' L' U R2 U' L U R2 F'

F5: Left column
F5 diagram

U' R U R' U' R' F R F'

F6: Double columns
F6 diagram

R2 U' R F R' U R2 U' R' F' R

G-generic diagram

G: Superman

Recognition: Look for matching pair(s) in the U-face

G1: Right column
G1 diagram

F (R U R' U')2 F'

Also:

U sune U sune

G2: Back slash
G2 diagram

R' U' R U' R' U2 R U' L' U R U' L U R'

G3: Double slash
G3 diagram

U' R' F R U F U' R U R' U' F'

G4: Forward slash
G4 diagram

R U2 R' U2 R' F R2 U R' U' F'

G5: Two columns
G5 diagram

U2 L' U R U' L U' R' U' R U' R'

G6: Left column
G6 diagram

U2 R' U' R U' R' U F' U F R

H-generic diagram

H: H

Recognition: Start with the U colour on the F and B faces. Look for orientation of any pairs on the U-face. (There are only four cases, as H2 and H4 are interchangeable with U2, as are H3 and H5.)

H1: Two pairs, columns
H1 diagram

R U2 R' U' R U R' U' R U' R'

Also:

U sune sune

H2: One pair, back row

(U2 to convert to H4)

H3: One pair, left column

(U2 to convert to H5)

H4: One pair, front row
H4 diagram

U' R U R' U R U L' U R' U' L

H5: One pair, right column
H5 diagram

U R U2 R2 F R F' U2 R' F R F'

H6: Two pairs, rows
H6 diagram

F (R U R' U')3 F'

F (sexy-move x 3) F'

Step 4: Last 6 edges

After orienting the M slice so the centres are in the correct faces, (if necessary; it's a step I usually perform before the corners) all that remains to be solved are the four U edges and the front and back edges in the D layer.

edge-all6 diagram

Step 4a: Orientation

An edge-piece is correctly oriented if the U- or D-face colour is in the U- or D-face. In other words, in this case where we have the Orange centre on the U-face and Red on the D-face, an edge in the U-layer is correctly oriented if it is Orange-up or Red-up, and one in the D-layer is correct if it is Orange-down or Red-down.

It is only possible for an even number of the 6 remaining edges to be incorrectly oriented. (None, 2, 4 or 6, obviously.) Therefore it is possible to infer the state of the invisible DB edge from the four U edges and the DF edge that you can see.

In the diagrams for this step, we are still looking at the U face, with F and R for perspective. The (possibly) incorrectly oriented pieces will be in grey, and the rest of the cube (all of which is now correct) in pink.

It should go without saying that no bad edges is a skip!

2 bad edges

There are a number of possible configurations but I'll just give two examples. Other cases can be reduced to these two with a combination of M2 and U moves

2 bad edges in U layer, adjacent
edge-2-u-adj diagram

M' U M' U2 M' U M'

2 bad edges in U layer, opposite
edge-2-u-opp diagram

M' U M U' M' U M'

4 bad edges

Again, just some example cases.

2 bad edges in U layer, 2 bad edges in D layer
edge-2-u-2-d diagram

M U2 M' U2 M' U M'

4 bad edges in U layer
edge-4-u diagram

M' U2 M' U2 M' U M'

3 bad edges in U layer, DF bad
edge-3-u-df diagram

M' U M'

3 bad edges in U layer, DB bad
edge-3-u-db diagram

M U M

6 bad edges

There's obviously only one possibility:

All six edges bad
edge-all6 diagram

R U' r' U' M' U r U r'

Step 4b: UL and UR edges

  1. If the pieces for UL and UR (in this case the Y/O edge and the W/O edge) are not in the same layer, adjust the U slice until they are diagonally opposite each other (i.e. at UF & DB or at UB & DF), then M' U2 M' to put them in the same layer.
  2. Use M2 to put the edges into the D-layer.
  3. Adjust U so that an M2 puts the edges between their matching corners, then adjust U again to complete this sub-step. Your L and R layers should now be solved.

Step 4c: Final permutation of M-slice

Largely intuitive. Use a combination of E2, M2 and U2 moves.