Commonly Proposed Methods

Steps:

1. Solve the four edges of a slice, with or without orienting all remaining edges.

2. Solve the rest of the cube.

This may be the most thought of and proposed method of them all.

Steps:

1. Build a 2x2x3 block.

2. Add a 1x2x2 block on the right.

3. Solve the last slot and last layer.

This can be seen as Petrus without early edge orientation

Steps:

1. Solve three of the four cross edges.

2. Finish the first two layers, leaving out the missing cross edge.

3. Complete the solve using one of a few variants. DF + EO > ZBLL, CLL > L5E, etc.

The thought process behind the proposal of this method is that leaving out a cross edge shortens the move count and provides more freedom of movement for the first step of CFOP or CFCE and also the rest of the first two layers.

Steps:

1. Place the cross edges in any orientation and permutation.

2. Solve the four F2L pairs.

3. Complete the last layer while correcting the cross.

This method is likely so often proposed because the idea is that there is a move count reduction and a lot of freedom in placing the cross edges in any order. Then the idea, or hope, is that the correction algorithms at the end maintain the same move count and ergonomics as the last layer algorithms that are used when the cross is solved normally.

Steps:

1. Build a 1x2x3 block on the left.

2. Solve the three bottom layer edges and all centers.

3. Place the last two F2L pairs.

4. Solve the last layer

This is another way of combining Roux and CFOP that is commonly proposed, though not nearly as often as RouxFOP. Sometimes there are variants suggested such as manipulating the LL pieces in some way during the last two pairs and or having a finish that isn't always LL. EO is also sometimes suggested to be combined with the first two steps.