# 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.)

## 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.

## 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: Skip

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

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.

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

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

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

#### 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

R' U' R U' R' U2 R

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

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

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

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

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

R' U L U' R U L'

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

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

#### 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.

R U R' U R U2 R'

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

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

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

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

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

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

R U' L' U R' U' L

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

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

#### 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

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

R U2 R D R' U2 R D' R2

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

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

R' F R U F U' F'

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

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

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

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

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

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

Actually is:

antisune sune

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

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

##### E3: Forward Slash

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

##### E4: Double Slash

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

##### E5: Back Slash

R2 D' R U2 R' D R U2 R

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

U' F R U R' U' F'

U' F sexy-move F'

#### 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

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

R' U r U2 R2 F R F' r

##### F3: Right column

U R' F R U2 F U2 F'

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

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

##### F5: Left column

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

##### F6: Double columns

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

#### G: Superman

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

##### G1: Right column

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

Also:

U sune U sune

##### G2: Back slash

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

##### G3: Double slash

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

##### G4: Forward slash

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

##### G5: Two columns

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

##### G6: Left column

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

#### 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

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

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

##### H5: One pair, right column

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

##### H6: Two pairs, rows

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.

### 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!

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

M' U M' U2 M' U M'

##### 2 bad edges in U layer, opposite

M' U M U' M' U M'

Again, just some example cases.

##### 2 bad edges in U layer, 2 bad edges in D layer

M U2 M' U2 M' U M'

##### 4 bad edges in U layer

M' U2 M' U2 M' U M'

M' U M'

M U M

There's obviously only one possibility: