This tutorial presumes you already know how to solve a rubik’s cube, if you don’t, please start by learning How to Solve a 3×3 Rubik’s Cube in Under 2 Minutes.

Once you have the basic solution down, you may want to reduce your solve time. There are various ways to do that, but this tutorial will focus on solving the last layer in as little as a quarter of the time.

In How to Solve a 3×3 Rubik’s Cube in Under 2 Minutes you learned how to solve the last layer in 4 steps:
Step 1 – Create a cross – F R U Ri Ui Fi.
Step 2 – Align the centers – R U Ri U R U U Ri Ui.
Step 3 – Position the corners – U R Ui Li U Ri Ui L.
Step 4 – Orient the corners – Ri Di R D.

The algorithms you learned are the minimum amount required to solve the cube, they are not however the most efficient. These algorithms do not take into consideration the state of the cube, and many times you have to repeat an algorithm multiple time to solve each step.

In this tutorial you will learn multiple algorithms for each step, with each algorithm matching a cube state. You will have to memories more algorithms but you will always be able to complete each step in one algorithm with no repetition- 4 algorithms in total to complete the last layer.

We will start by orienting the top face, edges first and then corners.

 

Step 0 – Learn the moves

For reference above are all the move annotations you already know.

In addition to the moves you already know, there are 3 more annotations you need learn:
1) Lower-case letter means turning 2 layers of the corresponding face.
2) B stands for back – the layer facing away from you.
3) M stands for middle – the layer between the front and the back.

 

Step 1 – Orientate the edges

There are 4 possible states in which the top layer edges can be in:

Case 1 – All 4 edges are oriented. You are done, move on to the next step.

Case 2 – 2 oriented edges positioned next to one another. To solve this case rotate the edges to the back of the cube and do:
F (U R Ui Ri) Fi.

Case 3 – 2 oriented opposite edges. Solving this case uses the same old algorithm you have already come to know and love:
F (R U Ri Ui) Fi.

Case 4 – 0 oriented edges.
In this case the algorithm is a combination of both above algorithms:
F (U R Ui Ri) Fi rotate the cube so so the front is parallel to line and do F(R U Ri Ui) Fi.

 
 

Step 2 – Orientate the corners

Now we will orient the corners so at the end of this step the top face will be complete.
There are 8 possible states in which the top face corners can be:

Case 1 – The top face is complete.
You are all done. move on to the next step.

Case 2 – 0 corners facing up, with 2 pairs of corners facing opposite one another. For this case use:
F (R U Ri Ui) (R U Ri Ui) (R U Ri Ui) Fi.

Case 3 – Similar to case 2, but with one pair facing opposite one another and the other pair facing the same direction. For this case use:
R U U R R Ui R R Ui R R U U R.

Case 4 – 1 corner oriented correctly and 3 remaining corners needing to move one position clockwise. For this case use:
R U Ri U R U U Ri.

Case 5 – Similar to case 4, but with 3 remaining corners needing to move one position counter-clockwise. To solve this case use an algorithm that mirrors the algorithm for case 4:
Li Ui L Ui Li U U Li.

Case 6 – 2 solved corners and 2 remaining corners facing the same direction – the headlines case. For this case use:
R R D Ri U U R Di Ri U U Ri.

Case 7 – Similar to case 6, but with remaining corners facing outwards – the chameleon case. For this case use:
r U Ri Ui ri F R Fi.

Case 8 – The last possible case of 2 solved and 2 remaining corners. To solve this case use:
Fi L F Ri Fi Li F R.

 

Step 3 – Position the corners

You now have a complete face, but both the corners and the edges are not necessarily in their correct position. We will start by fixing the corners.
The state of the corners can be one of 3:

Case 1 – All corners are in their place.
You are done, move on to the next step.

Case 2 – 2 corners solved. Rotate the cube so the solved corners are in the back of the cube and do:
Ri F Ri B B R Fi Ri B B R R.

Case 3 – No solved corners. In this case use below algorithm from any direction:
F R Ui Ri Ui R U Ri Fi R U Ri Ui Ri F R Fi.

 

Step 4 – Position the edges

At this point the state of the cube can be one of 5.

Case 1 – The cube is solved.

Case 2 – 1 solved edge and 3 remaining that need to switch positions clockwise.
R R U R U Ri Ui Ri Ui Ri U Ri

Case 3 – Similar to case 2, but with 3 remaining edges needing to switch positions counter-clockwise.
R Ui R U R U R Ui Ri Ui R R

Case 4 – None of the edges are in their placed, with each edge having to switch with opposite edge.
(M M U M M U) (U M M U M M)

Case 5 – Last possible case is where none of the edges are in place and they need to switch with their neighboring corner.
M M U M M U Mi U U M M U U Mi U U

Some more cubes you might enjoy: