# Rubik's Cube

There are several ways to solve a Rubik's Cube; this is just one way. I've split these instructions into seven basic steps. The basic algorithms (sets of moves) are given in the menu here. Click on the links for further explanation in the sections below.

1. First layer cross (edges).
2. First layer corners. B L B' L' or B' R' B R (mirror images).
3. Middle layer edges. D L D' L' TT' R' D R or D' R' D R TT L D' L' (mirror images).
4. Final layer cross (edges).
1. Edges orientation. F R T R' T' F' (repeat if required).
2. Edges location. R T R' T R T2 R'.
5. Final layer corners.
1. Corners location. T R T' L' T R' T' L.
2. Corners orientation. R' D' R D repeat.

The algorithms for the final layer each have two versions, normally for clockwise and anti-clockwise moves. It is possible to solve the cube using just one of these versions (the ones stated in bold in the menu here), although it will take a little longer.

### Definitions

F (Front): the face of the cube currently facing the solver.
T (Top): the face above or on top of the front face (often referred to as U, Up).
TT (Top two): the top two layers. (One algorithm involves turning the top two layers, equivalent to turning the bottom layer in the other direction while turning the whole cube in the given direction.)
L (Left): the face directly to the left of the front.
R (Right): the face directly to the right of the front.
D (Down): the face opposite the top, underneath the cube.

When just a letter appears in an algorithm (with no ' after it), it means turn the face clockwise if looking at the face. If the letter appears in an algorithm with a ' after it, it means turn face anti-clockwise if looking at the face. For example, R' D' R D means turn the right face anti-clockwise, the bottom face anti-clockwise, the right face clockwise, and the bottom face clockwise (in that order).

Centre: The centre pieces on each face determine the colours of the faces. The centres are attached to the cube so they are free to rotate but not change position relative to each other.

Cubie: One of the mechanically independent pieces that make up a cube. The cubies do not include fixed centres, or the central hardware to which they are attached. When used here cubie normally refers to the particular cubie intended to be moved to a new location.

Corner: One of the 8 cubies at the corners of the cube. Corners have three colours on them.

Edge: One of the 12 cubies on the edges of the cube in between the corners. Edges have two colours on them.

Orient: To manoeuver a cubie so that the colours on its faces point in the correct directions. The cubie is not necessarily positioned correctly.

Position (verb): To manoeuver a cubie to its correct location. It is not necessarily oriented correctly.

Position (noun): The location of a cubie, without regard to its orientation.

### 1. First layer cross

Choose a colour to solve first. Many people choose white. To keep these instructions generic I'll call this the top face colour. Hold the cube so this colour is on top.

Line up each of the four edges with your chosen top face colour so that the top face colour on each edge faces up, and each edge's other colour (the side colour) lines up with the colour of the centre of the side faces.

When complete the top side will have a central cross.

### 2. First layer corners

Now the corners in the first layer will be put in place. There are several positions these corners can have.

Top layer in the wrong location with the top face colour facing up. Hold cube so the cubie is at top right: R' D R (or R' D' R).

After doing this move the cubie will be on the bottom layer facing sideways. Now choose an appropriate move for it from further down this section.

Top layer with the top face colour facing sideways. Hold cube so cubie is either at front left with the top colour facing left, or at the top right with the top face colour facing right.

• Cubie at top left: L D L'.
• Cubie at top right: R' D' R.

After doing this move the cubie will be on the bottom layer facing sideways. Now choose an appropriate move for it from further down this section.

Bottom layer with the top face colour facing sideways (including forward or back). Rotate the bottom layer to move the cubie underneath where you want it to go, then hold the cube so the cubie is on the front face with its top face colour facing forward.

 Easiest to remember: Cubie at bottom left: B L B' L'. Cubie at bottom right: B' R' B R. Faster: Cubie at bottom left: F' D' F. Cubie at bottom right: F D F'.

Bottom layer with the top face colour facing down. Rotate the bottom layer to move the cubie underneath where you want it to go, then hold the cube so cubie is at front right: R' D R F D2 F'.

### 3. Middle layer edges

Look for an edge on the bottom layer with the right colours to move up to the middle layer. In its present postion, that edge has a side colour and a bottom colour. Turn the bottom layer so the edge's side colour is aligned with the colour in the centre of a side face. Hold that face at the front.

If there are no edges available on the bottom layer then all the edges are already in the middle layer, but in the wrong positions. If so, just do this algorithm to move another edge from the bottom layer into the middle layer.

• If you want to move the edge up to the left: D L D' L' TT' R' D R.
• If you want to move the edge up to the right: D' R' D R TT L D' L'.

Note that turn of the top two layers in the middle of that algorithm instead of turning the bottom layer. This makes it easier to see what you're doing with the top face's colour, and it's easier not to have to turn the front face.

### 4a. Orient last layer edges – FART

The memorable name of this algorithm comes from the letters in the algorithm. This algorithm orients the final layer edges so they show the correct colour on the final face. (Ignore the position of the edges for now – putting the edges in the correct positions is the next algorithm.)

Turn the cube over. The final layer is now the top, and the two bottom slices are solved.

If none of the correct coloured edges are showing on the final face do either of the versions below then the other, turning the cube as indicated.

• Two edges oriented correctly in L shape. Hold cube with correct edges at left and back: F T R T' R' F'.
• Two edges oriented correctly in straight line. Hold cube with correct edges at left and right: F R T R' T' F'.

You can use just the second version, which will need to be done up to three times.

### 4b. Position last layer edges – RT

This algorithm repositions three of the final face edges either clockwise or anti-clockwise. The edge at the front does not move, so hold the cube with that edge at the front.

Turn the top layer so that (if possible) one and only one edge lines up with the side face colour. If you have two adjacent edges correct, turn the top layer so only one edge is in the correct position. If two opposite edges are correct, do either version then choose one to repeat.

The three edges not ot the front will need to be repositioned clockwise or anti-clockwise (when looking down on the top face).

• Exchange back three edges clockwise: L' T' L T' L' T2 L.
• Exchange back three edges anticlockwise: R T R' T R T2 R'.

Note that in each version the top layer always turns in the same direction.

You can use just the second version, which may need to be done up to three times (possibly turning the cube after the first time).

### 5a. Position last layer corners – TURTLE

This name comes from the letters in the anti-clockwise version of this algorithm. I remember what it's for by considering a turtle has four legs – one on each corner. This algorithm repositions three of the corners either clockwise or anti-clockwise.

If none of the corners are in the correct position do either version, then choose one version to repeat.

• For clockwise, hold the cube so the correct corner is at the front left: T' L' T R T' L T R'.
• For anti-clockwise, hold the cube so the correct corner is at the front right: T R T' L' T R' T' L.

Note that in this algorithm the top layer turns back and forth, interspersed with the left and right alternately moving up and down. Note what is happening to the columns of the bottom face colour made on the front face as you turn the top layer back and forth.

You can just use the second version, which may need to be done twice.

Named for the similarly sounding algorithm letters for one version of this algorithm.

Each corner can be reoriented three times before getting back to its original orientation. Changing the orientation of a corner changes other parts of the cube, but these also end up back in their original state after three corner rotations. This means that the corners will be rotated from their correct positions in combinations of threes (or sixes). For example, three corners can be rotated once each, or one corner is rotated clockwise once and one corner is rotated clockwise twice (equal to anti-clockwise once).

• Orient front left corner clockwise: L D L' D' repeat.
• Orient front right corner anticlockwise: R' D' R D repeat.

The set of 4 moves needs to be repeated (8 moves) to complete a single reorientation of the top left or right corner. Don't forget the last rotation of the bottom layer (D' or D) when finishing each group of 8.

After each group of 8 moves, if the corner cubie is correctly oriented, rotate the top layer only so another cubie in at the top left or right ready to be reoriented.

Stick with just one of these algorithms until all three corners have been reorientated. Don't worry if the cube looks messed up after just one or two reorientations.

You can use just the second version, but the whole thing (24 turns plus top layer turns) may need to be repeated.

After all the reorienting is done, turn the top layer if required.

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