Advanced 2x2 Methods: A Roadmap from Ortega to CLL and EG

The roadmap at a glance

The time goals below come from the advanced 2x2 guide by J Perm. They are suggested milestones that tell you when it might be time for the next level, not strict rules.

You do not have to go all the way. Lots of people stop at Ortega or CLL and still solve the 2x2 really fast.

Level 0: get solid with the beginner method

Before adding anything new, make sure you can solve the 2x2 without having to think, using the 2x2 beginner guide. That method has three steps: make the white layer, make the top face yellow with Sune, then swap the yellow corners into place.

The two best-known algorithms at this level are Sune, which makes the top face yellow:

R U R′ U R U2 R′

and the algorithm that swaps two yellow corners, used when the two back corners already show the same colour on the back face:

R′ F R′ B2 R F′ R′ B2 R2

The downside of this method: you often have to do Sune several times, and the last step sometimes needs its algorithm twice. The next levels replace each step with one algorithm.

Level 1: Ortega, 12 algorithms

According to the SpeedSolving Wiki, Ortega is a popular intermediate method for the 2x2. It has three steps:

1. Make one white face, without matching the colours on the sides.
2. OLL: make the whole top face yellow with one algorithm (7 cases).
3. PBL: put all 8 corners in place on both layers at the same time (5 cases).

The biggest change is step 1: you only need the white stickers on the bottom face, and any corners in the wrong place get fixed in the PBL step. That makes the first step much shorter.

An example OLL case: the two right corners have their yellow sticker on top, the front-left corner has its yellow sticker facing the front, and the back-left corner has it facing the back.

R U R′ U′ R′ F R F′

An example PBL case: look at the four sides, and none of them has two matching stickers in the same layer, on either the top layer or the bottom layer. This is the shortest algorithm in Ortega:

R2 F2 R2

1. You start with (input)
3. After the formula

All 12 algorithms, with a picture for every case, are in the Ortega 2x2 method post.

When to move on: when you know all 12 algorithms by heart, spot each case straight away without turning the cube to look for it, and your times start to level off.

Level 2: CLL, 42 algorithms

CLL solves the whole yellow layer with one algorithm once the white layer is done. According to the SpeedSolving Wiki, CLL has 42 algorithms that average about 9.8 moves, and it was already used at the 1982 World Championship.

Unlike Ortega, the first step in CLL has to be the whole white layer: the white face is done and the white corners are in place, which means the two bottom-layer stickers on each side match. So the first step takes a bit longer, but you combine OLL and PBL into one step.

Good news: according to J Perm, 9 of the 42 CLL algorithms are the same as in Ortega, and many others come from 3x3 OLL. You are not starting from scratch.

Example: one yellow sticker on top, in the front-left spot, and the front-right corner has its yellow sticker facing the front. This is the Sune shape, but the corners are in different places than in the normal Sune case, so CLL uses a different algorithm that solves the whole cube in one go:

R U′ R′ F R′ F′ R

How to recognise each case from the colours on the sides, plus all 42 pictures, is in the CLL 2x2 algorithms post.

When to move on: when you can plan the white layer neatly during inspection and spot the CLL case without stopping.

Level 3: EG, solve the whole cube after one face

EG was put forward by Erik Akkersdijk and Gunnar Krig in 2006 (SpeedSolving Wiki). The idea: just like Ortega, you only make one white face, and the white corners do not need to be in place. Then one algorithm solves the whole cube.

Which algorithm you use depends on the white layer at the bottom, split up the way J Perm does it:

• Bottom layer already solved: use CLL (42 algorithms, which you already have from level 2).
• Two side-by-side corners on the bottom layer need swapping: EG-1 (43 algorithms).
• Two diagonal corners on the bottom layer need swapping: EG-2 (43 algorithms). There is also a shortcut called Anti-CLL that needs no new algorithms but is a little slower.

If you already know CLL, you have about a third of EG. The SpeedSolving Wiki counts the full set as 128 algorithms, PBL included.

When the yellow face is already done, the EG case is exactly an Ortega PBL case, so you already know a few EG algorithms. EG-1 example: each layer has exactly one side where the two stickers of that layer match. Turn U and D so both matching pairs are on the front face, then do:

R2 U′ B2 U2 R2 U′ R2

1. You start with (input)
3. After the formula

EG-2 example: the bottom layer has no side with two matching stickers (two diagonal corners need swapping), and the top layer has exactly one such side. Turn U so that side is at the front, then do:

R U′ R F2 R′ U R′

1. You start with (input)
3. After the formula

Add EG in this order: CLL first, then EG-1, then EG-2. According to the SpeedSolving Wiki, EG-1 needs more U turns before and after the algorithm than CLL, because the first turn has to line up the two bottom corners that need swapping. Practise spotting that position until it is second nature.

Level 4: planning the whole solve

Once you know EG, the next step is not more algorithms but how you use your inspection time. According to J Perm, fast 2x2 solvers usually:

• Find the shortest white face (or a face of another colour), usually 4 to 6 moves.
• Track the corners to predict which EG case will come up.
• Predict the final U turn as well.

Start by predicting what the yellow face will look like, and only then move on to the full EG case. J Perm recommends getting EG down before practising planning the whole solve, because tracking the corners is harder with CLL. There are also optional algorithm sets such as TCLL and LEG-1 for anyone who wants to go even further.

How to practise and level up faster

• Add a few algorithms at a time. Scramble the cube, solve up to the step where you need it, and only use the new algorithm when you get the right case. Repeat until your hands do it on their own.
• Practise the first step on its own. On the 2x2, making the white face or layer takes up most of your inspection time. Spend a few minutes each day just finding the shortest white face.
• Try faces of other colours. Once you are comfortable, pick whichever face takes the fewest moves instead of always making white.
• Time yourself. Use the EasyRubic timer and look at your average of 5 solves, not just your fastest one.
• Do not rush to the next level. A level you have mastered is always faster than a new one you still have to think about.

Sources

• 2x2 Advanced Methods – J Perm
• EG Method – SpeedSolving Wiki
• CLL – SpeedSolving Wiki
• Ortega Method – SpeedSolving Wiki