1. Solving a 2x2x3
For simplicity purposes, this tutorial will explain the method using white on the bottom face, even though at a higher level, solvers should be able to solve with either white or yellow on the bottom.
Introduction
The first step of the APB method is building a 2x2x3 block on the bottom-left side of the cube. This can be achieved through various ways and it is ultimately up to the solver to decide on which option to choose for a particular scramble. Since this is by far the step with the most freedom, there are a lot of techniques required to consistently achieve a good movecount. Below I will show some of the most useful and consistent methods of creating the 2x2x3.
Unlike in regular Petrus, the 2x2x3 in APB is always solved on the bottom-left.
When explaining methods making use of blockbuilding, Block Referencing is very useful to name a certain set of pieces. In block referencing, a combination of layers, for example DF, refers to those pieces that are in all of those layers, in this case the DFL, DF, and DFR pieces. This can be done with wide moves and slices as well. dM would therefore refer to the DF and DB edges and the B, D, and F centers. See more on Athefre’s website
1x2x3 → 2x2x3
First creating a Roux-style 1x2x3 block and then adding the DF and DB edges is probably the most consistent way of solving the 2x2x3. On most scrambles, this way of making your 2x2x3 leads to an efficient solution.
Creating the 1x2x3
Like with the whole 2x2x3, the 1x2x3 can also be created through various techniques. To figure out new techniques, it is recommended you experiment a little on your own as well. Below are some possible methods to create the 1x2x3.
General Blockbuilding
Various blockbuilding techniques can be used to build the 1x2x3. If the scramble, for example, already provides the block at Db, the solver could first solve the Eb edge and center in relation to each other and then insert them. Finally, they would create and solve the pair belonging in dF. On many scrambles, such blockbuilding techniques lead to the best solutions.
Example Solution
Solving the DFDB Edges
After having created the 1x2x3 block in dL, you can extend it to a 2x2x3 by solving the edges at DF and DB. This can be achieved in two main ways: You can either solve each of them seperately by placing them in the U-layer an then inserting them by doing r U' r', r U2 r', r' U r, or r' U2 r depending on the situation. The other option is creating a line consisting of the two edges and the white center in the U-layer and then inserting it by doing an r2-move. This method often is more efficient, especially when the edges are oriented (e.g. have their white side on the U-face, front-right, back-right or D-face).
Examples
Instead of creating the 1x2x3 in dL and then solving the DF and DB edges, you can also create the 1x2x3 in Dl and then solve the FL and BL edges.
2x2x2 → 2x2x3
An alternative way to solve the 2x2x3 is first creating a 2x2x2 in dbl or dlf and then extending it by attaching a second 1x1x2 block in dlF or dBl. This is a very versatile technique too, but it sometimes leads to awkward fingertricks with F2- or B2-moves.
Creating the 2x2x2
One way of creating a 2x2x2 block is by creating a 1x2x2 block in Dbl or Dlf. You can then add an edge with the correct two center pieces, creating a 2x2x2. Of course it is also possible to first create a block in Ebl or Elf and then adding the other block. As there is a lot of freedom, we recommend you experiment a bit on your own.
Extending to a 2x2x3
To then add another 1x2x2, you can again make use of multiple strategies. Often, you would connect one of the two edges to the center and then attach a corner-edge pair using a sequence like R' F R or L F' L'. You might even solve the two edges first and then solve the corner using a keyhole-style insert like D R U R' D'.
Three Cross Pieces + 2 F2L Pairs
Even though you might be tempted to always solve your 2x2x3 like this, this is NOT the most efficient method and is only useful on very specific scrambles.
On some scrambles, solving the 2x2x3 like F2L in CFOP, except without any of the pieces in the R-layer, is the fastest method. Even though the movecount might not be too low, this method does allow for high TPS. Keep in mind this is really only recommended if:
- at least two cross pieces are solved or solvable in one move and
- at least one of the two edges belonging into FL and BL is oriented (e.g. has its front/back color on the U-face, D-face if it is in those layers or the front/back face if it is in the E-layer).