The basic solution involves 4 sub steps to solve the last layer:

- Orient the last layer edges
- Orient the last layer corners
- Position the last layer corners
- Position the last layer edges

#### Orient the Last Layer Edges

The purpose of this step is to orient the last layer edges. We are not concerned with the positioning of the edges but rather the orientation. Also we are not concerned with any of the corner pieces in this step so you can ignore them. When the edges are oriented correctly, the upper face of your cube will look like the following diagram.Now after you have solved the first 2 layers there are 4 possible states of the upper face of your cube. One of the states is with the edges correctly oriented as above. If this is the case then you can move onto the next step. Otherwise, identify the state from the following diagrams and perform the relevant algorithm.

F R U R' U' F'

F U R U' R' F'

(F R U R' U' F') U2 (F U R U' R' F')

If no edges are oriented correctly, then simply perform one of the algorithms to orient two edges, align the upper layer and perform the other algorithm to orient the other two edges.

Your cube should now look like the following diagram:

#### Orient the Last Layer Corners

This step is very similar to orienting the edges but we are working with the corners instead. Again, there are two basic moves to remember. One algorithm twists 3 corners clockwise, and the other twists three corners anti-clockwise.After orienting the edges, there are 7 possible states of your cube. Two cases will be solved directly by using one of the algorithms you are about to learn. The other 5 states can be solved by first performing one of the algorithms to bring your cube into one of the first two states, and then by performing the appropriate algorithm to orient the last layer corners. Notice in the diagrams below that the yellow lines on the side of the diagram represent where the yellow sticker is positioned on the corner cube. This is important as you need to decide whether the cubes need to be rotated clockwise or anti-clockwise.

Here are the first two cases that can be solved by using only one algorithm:

R' U2 R U R' U R

R' U' R U' R' U2 R

Notice that the second algorithm is simply the inverse of the first. Now if your cube is not in one of these states, then look at the diagrams below to determine what sequence of the above algorithms to perform.

(R' U2 R U R' U R) (R' U2 R U R' U R)

If your cube looks like this then perform the first algorithm twice to orient the last layer corners.

(R' U2 R U R' U R) U (R' U2 R U R' U R)

This case is very similar to the one above. It is important to note the positioning of the yellow sticker on the corner piece to decide which sequence of moves to use.

(R' U2 R U R' U R) U (R' U' R U' R' U2 R)

(R' U2 R U R' U R) U2 (R' U' R U' R' U2 R)

(R' U2 R U R' U R) U' (R' U' R U' R' U2 R)

Once you have completed the correct algorithms your cube should now look like the following diagram:

#### Position the Last Layer Corners

For this step there is another two algorithms to remember. These algorithms move the three corners clockwise and anti-clockwise respectively. The algorithms do not change the orientation of the pieces and hence leave our work performed in the last step intact. The trick here is to move the Upper layer until just one corner position is in itâ€™s final solved place, leaving three corners unsolved. Once you have done this you simply look at the corners to see if they need to moved clockwise or anti-clockwise and use the relevant algorithm. If you cannot move the Upper layer so that only one corner is solved, then simply perform either of the algorithms and then you will have a situation where you can move the upper layer so that only one corner is solved.For these moves there is an extra move that needs to be described. A lower x in an algorithm means to rotate the whole cube so that the Down face becomes the Front face. If you have solved the cross with the white face as the Down face, then after performing the x move, white will now be the Front face.

x R' U R' D2 RU' R' D2 R2 x'

x R2 D2 R U R' D2 R U' R x'

Your cube should now look like the following diagram:

#### Position the Last Layer Edges

All that is left is to position the last layer edges. This step is very similar to the one above. You will learn two algorithms to move 3 edges clockwise and anti-clockwise. If your cube has all 4 edges in the wrong place, you will need to perform either of the algorithms once to end up with one correctly solved edge and 3 unsolved edges.R2 U R U R' U' R' U' R' U R'

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

And that is it, you now know how to solve the cube.