# 2GLL

 2GLL Information Proposer(s): Zbigniew Zborowski, Ron van Bruchem, Timothy Sun, Lars Petrus Proposed: 2005? Alt Names: Step 6+7 (Petrus method) Variants: none Subgroup: No. Algs: 84 Avg Moves: 13.15 Purpose(s): Speedsolving

2GLL (short for 2-Generator Last Layer) is a subset of ZBLL, when all the LL edges are oriented, it solves the LL in 1 of 493 algorithms. 2GLL consists of 85 cases (including solved) that orient the corners and permute the edges, i.e. exactly the ZBLL cases that can be solved by a 2-generator algorithm (using only 2-Gen moves, usually R and U moves).

2GLL is very useful when used with a system that permutes LL corners and orients LL edges before or during the last layer. One CFOP-derived system that achieves this is to do the cross, three F2L pairs, ELS, and lastly CPLS. One can also use specialized algorithms to control edge orientation during F2L. While these are good ways to branch off from CFOP, most cubers agree that 2GLL works better with methods that, like ZZ or Petrus, naturally orient the edges before the final F2L slot. 2GLL may also be used after F2L and CPEOLL which orients edges and permutes corners.

## Learning Approach

Like ZBLL and COLL, 2GLL cases can be divided into eight subsets, typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and EPLL. Each 2GLL case is typically recognized by its COLL followed by the edge cycle (see EPLL). There are up to 12 cases per COLL, or less due to symmetry.

## Recognition

1. Recognize the corner orientation case (one of 7).

1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines. Since a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference. If it helps you to recognize better this way, do so.

2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.

Step 1 should be fairly easy to recognize, as there are only seven possible cases. If you have used another LL technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.

Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy. Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.

Here is one system to recognize these in: - If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.

- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.

- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms. - If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."

If the case does not follow into any of the above, then - For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following: --"Is this cycle going clockwise or anti-clockwise?" --"Where is the edge that is correct?"

Both of these questions can be answered by figuring out the following: --"Where does the FU sticker need to be in respect to the corner permutation?" --"Where does the RU sticker need to be in respect to the corner permutation?"

Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.

As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following: R' U2 R U R' U R U' R' U' R U' R' U2 R

Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now! Next, note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts. Next, note that this is a clockwise U perm - one that does not cycle RU. That's it. Right then, you should be able to apply your alg, AUF, slam your cube down, and stop the timer.

For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.

Before looking too far into 2GLL, it would probably be best to check out CPLS first.