Dr Phill’s Science Made Simple

First of all get one face of the cube, I chose the white face, with all of its eight movable cubelets in the correct position. The white face will be described as the botton face from now on. The bottom face cubelets will remain in position for the rest of the solution.

The face opposite the bottom face, in my case the yellow face, will be described as the top face from now on.

The cube will need to be rotated at each step of the solution. At each step, the cube will be rotated so that the cubelets to be moved are in the correct position. The other four faces will be designated as N, S, E, and W at each step.

Each step involves a sequence of 90° rotations of of the six faces T, B, N, S, E, and W. In a sequence, a T means a clockwise rotation of the top face when looking down at it. A \(T^{-1}\) means an anti-clockwise roation of the top face when looking don on it.

Figure 1 shown the top face and the top two rows of the North, South, East, and West faces after a randomky scrambled cube has its bottom white face cublets put in the correct positions.

The next step is to get the four cornet cubelets of the top face in the correct position and orientation. Start by rotating the top face so that the north west corner cubelet is in the correct position. A \(T^{-1}\) rotation will achieve this.

Figure 2 shows the cube after the top face rotation. The North West and North East cubelets are now in the correct position and orientation.

The sequence \(E^{-1}BESBS^{-1}TSB^{-1}S^{-1}E^{-1}B^{-1}ET^{-1}\) changes the orientation of the North East and South East cublets in opposite directions without changing any cubelet position.

The sequence $WBENE^{-1}S{-1}EN^{-1}E{-1}SB^{-1}W{-1}$ performs this rotation.

The next step is to get all four middle layer edge cubelets and all four top layer edge cubelets in the correct position and orientation. For this we need to rotate the cube so that the West face is the white face that was previously the bottom. We then need to select sequences that rotate the now North, South, and East middle cublets.

Applying an $N$ rotation puts the three middle cubelets in position where an anti-clockwise rotation will put two of them in the correct position and orientation.

The sequence $EET^{-1}SN{-1}EENS^{-1}T{-1}EE$ rotates the North, South, and East middle cubelets anti-clockwise preserving orientation.

Now apply an $N^{-1}$ rotation to undo the initial rotation.

Reorient the cube with the white face at West and the green face South.

Reorient the cube with the white face at Bottom and the green face South.

The inverse sequence $EETSN^{-1}EENS{-1}TEE$ rotates the North, South, and East middle cubelets clockwise preserving orientation.

Now apply an $E^{-1}$ rotation to undo the initial rotation.

Apply the sequence $EET^{-1}SN{-1}EENS^{-1}T{-1}EE$ to rotate the cubelets anti-clockwise.

The cube has now been solved!

There are a number of sequences that rotate the corner cubelets of the top face in various ways without changing any other cubelets. For any cube solve, one of the sequences or its inverse may be sufficient to put the corner cubelet is the correct position and orientation. A pair of sequences can be used to correct the corner cubelets of any cube solve though one of the sequences may have to be used twice.

The sequence $E^{-1}BESBS{-1}TSB^{-1}S{-1}E^{-1}B{-1}ET^{-1}$ changes the orientation of the North East and South East cublets in opposite directions without changing any cubelet position.

There are a number of sequences that rotate the middle edge cubelets of the top face in various ways without changing any other cubelets.

Figure 5.0 shows the initial cube top face subsequent diagrams will show the effect of a sequence on the initial top face.

The sequence $EET^{-1}SN{-1}EENS^{-1}T{-1}EE$ rotates the North, South, and East middle cubelets anti-clockwise preserving orientation.