This section shows an appropriate way of numbering the cube, the few simple algorithms required, and how to use the algorithms to solve a cube blindfold. Try to follow the example and relate it to this method page and it should become a lot clearer. It is possible to use shorter algorithms, but avoid them until the basic algorithms are under the fingers. At first it may be difficult to do the stages without making mistakes, or to plan the solution, so I would recommend doing it with eyes open and only planning the next stage until you can do the cube without much mental expenditure, working gradually to the point where the whole cube can be done in the head.
To understand the method you will need to know how the cube is numbered, what pieces the algorithms used affect and the stages in the solution. I recommend reading the theory first.
I recommend that you actually understand the basic method and can apply each stage. After you have done that I recommend going to the simplification section and seeing simple shortcuts which make the actual method much easier without having to learn many more algorithms.
An appropriate numbering of the edges and corners is required. The following numbering scheme will be used in the examples:
I number the corners clockwise on the top layer starting at the near lefthand side from 1-4, and on the bottom layer starting at the back righthand side anticlockwise as seen from above from 5-8. Using this organisation, if you turn the cube forwards through 180 degrees the corners 5-8 would be ordered clockwise starting at the near lefthand side. This picture shows what I mean.
The edges I number in 3 different bands; the top layer I number from 1-4 in a clockwise fashion starting at the front top edge. The middle band I number from 5-8 clockwise as seen from above starting from the edge on the near left. The edges in the bottom layer I number from 9-12 starting from the front bottom edge going in a clockwise manner as seen from above. Look at this picture.
You need to be familiar with algorithms to achieve 5 distinct objectives; 2 algorithms are required for the corners only - one to orient and one to permute, 2 algorithms are required for the edges only - one to orient and one to permute, and one algorithm is required that affects both edges and corners - this one needs to swap a pair of corners and swap a pair of edges. The following algorithms are chosen to be easy to remember and easy to apply when blindfold.
The algorithms described are used in the solving by placing the pieces that are to be affected in the appropriate slots/layer, doing the algorithm, and then doing the reverse of the moves that placed the pieces in the appropriate slots/layer.
ALG 1: corner orientation (Ux)(LD2L'F'D2F)(Ux')(Uy)(F'D2FLD2L')(Uy')
This will rotate the corner in the FLU position after Ux clockwise, and the corner in the FLU position after Uy counter-clockwise. Replace Ux/Ux' and Uy/Uy' with U/U', U'/U, U2/U2 or nothing to affect the appropriate corners. The example will show how to use the algorithm if the corners aren't all in the U layer to start with.
ALG 2 (video): corner permutation Ux(R2D' R2D2 R2D R2D' R2D2 R2D R2)Ux' Uy(R2D' R2D2 R2D R2D' R2D2 R2D R2)Uy'
This will swap the corners that are in the FRU and BRU position after Ux, and the corners that are in those same positions after Uy. Replace Ux/Ux' and Uy/Uy' with U/U', U'/U, U2/U2 or nothing to affect the appropriate corners in the U layer.
First of all, I had better clarify notation since it has been brought to my attention (thanks Pejave!) that my use of M is opposite to that used on www.speedcubing.com - having spoken to Ron I am informed that the majority of books use his notation, but a small minority (including that by world champion Minh Thai) use my notation. So for the purposes of this site M is as shown in the following before and after picture:
ALG 3: edge orientation (MUMUMU2M'UM'UM'U2)
The above algorithm will flip 2 edges FU and BU on the U layer. Incase you are wondering, the move M changes the cube in the same manner as doing LR' and then rotating the whole cube so that F becomes U.
The following algorithm will swap a pair of edges and then swap a pair of edges with all the edges involved being in the D layer. This can be used to provide a variety of effects. If one of the edges in the first pair swapped is one of the edges in the second pair being swapped then the whole sequence will be a 3-cycle.
ALG 4: edge permutation ((Uw)(M'DM)(Uw')) ((Ux)(M'D'M)(Ux)) ((Uw)(M'DM)(Uw')) ((Uy)(M'D'M)(Uy')) ((Uz)(M'DM)(Uz)) ((Uy)(M'D'M)(Uy'))
The edge in the FU position after Uw will be swapped with the edge in the FU position after Ux, and the edge in the FU position after Uy will be swapped with the edge in the FU position after Uz. Replace Uw/Uw', Ux/Ux', Uy/Uy' and Uz/Uz' with U/U', U'/U, U2/U2 or nothing to affect the appropriate edges in the U layer. The undoing of the U moves adds to the length of the algorithm, but makes it easier to perform since you only need to know where the edges were before the start of the algorithm, and not where they are during the performance of the algorithm.
ALG 5: swap 2 edges and swap 2 corners RBU'B'RDB'L'B'LB2D'R2
Which algorithm you use for swapping 2 edges and 2 corners is up to you, merely choose one from the permutation phase of the Jessica LL method and make sure that you know what it affects and that you can do it whilst blindfold. Be careful that the algorithm doesn't leave the layer rotated - you will need to end it with appropriate turns of U if that is the case.
Incase you don't have a list of the appropriate algorithms, simply choose one of the following and get familiar with it: L2DF2D'L2B2D'R2DB2U', FLUL'FLU'FUFU'F'L'F2, B2LUL'B2RD'RDR2, RBU'B'RDB'L'B'LB2D'R2 or LD'BL'D2RF'R'D2L2B'L'DL'.
Basically that means the corner pieces should be orientated so that the colour showing on the top and bottom face is the same as either the centre-piece of the top or bottom. To do this you will apply ALG 1.
There are 8 corners to rotate, 4 of which are in the D layer, and 4 of which are in the U layer. The total twist of the corners is 0. If the total twist for the U (or D) layer is 0 (see theory section) then corner rotation of corners just in the U layer will correctly orient the corners in the U, and then flipping the cube through 180 degrees just rotating corners in the new U layer will correctly orient all those, and finally the cube can be flipped through 180 degrees to make the U layer the original U layer.
The tricky situation occurs when the twist in each layer is non-zero. In that case, most of the corners can be correctly orientated by using the procedure in the previous paragraph, but you will be left with one corner in the U layer and one corner in the D layer that need rotating. To solve this final pair of corners, do any moves that move the corner in the D layer to the U layer whilst leaving the corner already in the U layer still in the U layer. Now do ALG 1 on the appropriate corners, and then do the reverse of the moves that you used to place the corner from the D layer into the U layer.
For each edge determine if use of L2R2FBUD moves to place the edge puts the edge in place flipped. If so then the edge needs flipping. Difficult to determine quickly at first, with practise it becomes easier to work out.
Note: moves U and D do not affect the parity of the edges, hence alg 5 later does not affect the parity of the edges.
For each pair of edges that needs flipping do any moves that place the edges in the FU and BU position and then do ALG 3, and finally undo the moves that you used to place the edges in those positions.
Determine the corner moves in terms of cycles as described in the theory section. Decide whether the parity is odd or even. If the parity is odd then you will perform the move that swaps 2 corners and 2 edges (alg 5). If this is required it will affect what you need to do in step 4 and 5.
To place corners, do any moves in the L2R2F2B2UD group to put all the corners that you want to move in the U layer, do ALG 2, and then do the reverse of the moves that put those corners into the U layer. Use the representation of the corners in terms of cycles from step 3 to work out what you need to do. If you do single turns of L, R,F or B when placing the corners in the layer you will rotate corners, so make sure that you only use allowable face turns for this phase.
Shortened allowable manoeuvres that step out of the group and back into it include:
3 cycle clockwise on top/bottom face 3 cycle anti-clockwise on top/bottom face double-pair swap on top/bottom face
Note that if alg 5 was performed in step three then you have already swapped a pair of corners. In practise I almost always permute the corners and then fix the parity with algorithm, but the fixing of the parity can be done at any point during the corners if convenient, it is just easier to leave it until the end everytime.
Write the edges in terms of cycles, as you did for the corners. Remember that if you did algorithm 5 in step 3 then two edges will already have been swapped.
For this phase, use moves from the L2R2FBUD group to place all the edges that you want to affect in the U layer, do ALG 4, and then undo the moves used to place the edges in the U layer. Remember to avoid using single turns of L or R or you will end up flipping edges.
The three cycles R2UFB'R2F'BUR2 and R2UFB'R2F'BUR2 are within the group. Also allowable are diagonal edge swaps and opposite edge swaps. All these moves are from the LL permutation phase of the Jessica method. As with ALG 5 mentioned earlier, you need to make sure that if you use those algorithms that you don't end with U or D rotated.
The cube will now be solved.