# ZBLL

**ZBLL** (short for *Zborowski-Bruchem Last Layer*) is a step of a method which involves solving the entire last layer in one step, assuming that the edges are already oriented. This is part of the ZB method, but it can be useful for any other method which leaves the edges of the last layer oriented after F2L is solved (such as the Petrus method).

ZBLL indeed sounds like a very useful step to learn, but the main reason that it is not in wide use is that it involves a massive 177 algorithms (counting inverses and mirrors are the same), or a total of 493 cases. Only a handful of people have ever learned this step in its entirety. If you wish to learn it, it is useful to start by learning either OCLL/PLL or COLL/EPLL, so that you will always be able to finish the cube relatively quickly even if you do not yet know the ZBLL case.

### Learning Approach

The ZBLL cases are divided into 7 sets: T, U, L, Pi, Sune, Anti-sune, H, and the Pll cases, in which all pieces are oriented. The sets are then divided further into 40 subsets. They are recognized by their COLL case as well as a corresponding edge cycle. Every subset contains 12 cases, which are all different edge cycles possible with the COLL case of that set. Many people recognize ZBLL by looking at the UFR corner, and its neighboring stickers. Whether the stickers are adjacent, or opposite allows for a quick recognition. However, this method only works for the T, U and L subsets of ZBLL, because in the other cases the UFR corner is not correctly oriented. Another way to recognize is through blocks of colour or simply the edge cycle.

### Edge recognition

For the T, U and L cases (there are 3*6*12=216 algorithms in this set) recognition goes as follows:

1. Recognize the orientation case.

2. Recognize the COLL case.

3. Recognize the edge cycle by looking at the UFR corner and the edge stickers around it.

4. Apply the corresponding algorithm.

Step 3 may look a little complicated, but it's actually not too bad. In total there are 12 cases, but those are recognized by 2 minor sub-cases, of which there are 3:

C: If the FU sticker is the same as the FRU sticker, and if the RU sticker is the same as the RUF sticker.

A: If the FU sticker is an adjacent color to the FRU sticker, and if the RU sticker is an adjacent color to the RUF sticker.

O: If FU and FRU are opposite, and if RU and RUF are opposite.

A case is recognized by the combination of those. First comes the FU/FRU relation, then the RU/RUF relation, divided by a slash. That means there are 9 possibilities with these cases: C/C, C/A, C/O, A/C, A/A, A/O, O/C, O/A, O/O. However, there are 12 cases. That's because the A case can mean 2 stickers. That's why the last 3 cases are known as C/OX, O/CX and OppX. This means that you don't look for the relation between FU/FRU and RU/RUF, but between FU/RUF and RU/FRU. In the C/OX case, FU and RUF are the same, and RU and FRU are opposite to each other. The same goes for the O/CX case, but vice versa. In the OppX case, both FU/RUF and RU/FRU are opposite. This looks like a Z-permutation. Note that all of these cases can be seen as A/A cases at first, but whenever you have an A/A case, you should always look if it isn't the other one.