Orientate Last Corners

We can have the following cases:

• Four yellow corner stickers are on the roof, the roof is completely yellow. We go to the next lesson.

• No yellow corner stickers are on the roof. All yellow corners need to be orientated (as in the example).

• One yellow corner sticker is on the roof. The other three corners need orientation.

• Two yellow stickers are on the roof. The other two corners need orientation

The nature of the Rubik’s Cube does not allow a situation where three corners are correct and only one needs orientation!

What do we mean by “orientation”?

If we imagine, we could twist a corner around its tip, we want to twist a incorrectly orientated corners either clockwise or anticlockwise to get its yellow sticker to the roof.

Please, have a look at the green/yellow/orange corner at UFR. If we could twist it anticlockwise on its place, the yellow sticker would go to the roof, the green sticker to the F wall and the orange sticker to the R wall. Another case is the yellow/green/red corner at FRB (in the R wall back). This one needs a clockwise twist. Because we cannot twist them really on place, we need an algorithm!

Here it is R, F', R', F, R, F', R', F, (algorithm IV-clockwise)

We analyze it and see

• We count eight moves.

• The first four moves are exactly repeated by the second four moves. The usual notation for this would be

• (R, F', R', F)*2. The four moves inside the brackets are repeated.

• Only the R and F walls are turned.

Here are the 8 moves executed on a solved Rubik’s Cube:

Please, note that a single execution of this algorithm produces an intermediate result, only. The lower two layers are very much scrambled. The roof is almost unchanged, only the yellow/green/red corner got twisted clockwise. The interesting thing is: If we just repeat the algorithm twice more, the cube will be solved again, completely.

This can be used to turn three corner cubies clockwise, if we turn U in between the three executions of the algorithm!

How do we memorize this best?

Be warned that this is a dangerous part of the solution. We may not turn the whole cube and we may not do a single wrong move.

We have to repeat this algorithm of 8 moves several times. Before we go on we need the brother sequence (which is the sequence above reversed): F', R, F, R', F', R, F, R', or (F', R, F, R')*2 (algorithm IV-anticlockwise)

(Please, rest assured that we will not need further algorithms to learn. The next lesson describes a method without anymore new algorithm.)

Here are the 8 moves executed on a solved Rubik’s Cube:

As in the clockwise variant of this algorithm, the lower two layers of the cube are pretty much scrambled. On the roof, a single anticlockwise twist of the yellow/green/red corner has happened.

The memorizing sequence remains the same: away, away, to, to, away, away, to, to

In the “anticlockwise” case, we just start with the F wall by F’.

Now, when do we do what and how do we apply the two algorithms?

We turn the whole cube that the first corner cubie that needs to be twisted in the F wall at our right (at UFR).

As I have said this is the twisting place. If the yellow sticker is in the F wall, we start by a R turn and do the 8 moves using our memorizing sentence away, away, to, to, away, away, to, to.

If the yellow sticker is in the R wall, the first move is F’.

We recognize a rule: The first turn moves the yellow sticker to the roof!

Let’s go back to our example

The first corner is twisted correctly; the roof is completely unchanged except of this single twist, the cellar (the white layer) and the second layer are pretty much scrambled. Do not worry; the first two layers will be OK at the end. We just go on and turn by U the second corner (the yellow/red/green) to the twisting place

The complete sequence has been: F', R, F, R', F', R, F, R' U R, F', R', F, R, F', R', F

If we leave out the U in the middle, nothing happens. By the U we move the first corner (twisted anticlockwise) away and the second arrives at the twisting place and gets a clockwise twist as necessary.