What Is the ZZ Method? Solve a 3x3 Cube with EOLine

What is ZZ?

The name ZZ comes from the initials of Zbigniew Zborowski, who proposed the method in 2006. Both the SpeedSolving Wiki and Wikipedia say so (SpeedSolving Wiki, Wikipedia).

ZZ has three steps:

1. EOLine: orient all 12 edges and, at the same time, put the two white edges at the front and back of the bottom face in a straight line.
2. First two layers (F2L): build a 1x2x3 block on the left and one on the right, using only R, U and L.
3. Last layer: solve the yellow layer. Because the edges are already oriented, the yellow cross is already there.

According to the SpeedSolving Wiki, the hardest part of ZZ is the first step. The other two are much easier to get the hang of (SpeedSolving Wiki).

How to read the pictures

• Yellow on top, white on the bottom, green at the front. The left face is red and the right face is orange.
• Each picture shows two cubes: the left one is before the move sequence, the right one is after.
• Pieces you do not need to worry about in that step are grey.

Every move sequence in this post has been tested on EasyRubic's Rubik's Cube simulator. If R, U and R' are new to you, see Rubik's Cube notation for beginners.

What is edge orientation?

This is the most important idea in ZZ. An edge is oriented (good) if you can bring it home using only the R, L, U and D faces. An edge that can only get back into place with an F or B turn is misoriented (bad).

A quick way to spot them, holding the cube with green at the front:

• An edge with yellow or white on it: it is good when its yellow or white sticker is on the top or bottom face. If the edge is in the middle layer, its yellow or white sticker must be on the front or back face.
• An edge with no yellow or white: look at its green or blue sticker and use the same rule.

Why this rule helps: R, L, U and D never change an edge's orientation. Only F and B (quarter turns) flip it, and each one flips exactly the four edges on that face. That is why the number of bad edges is always even.

The picture below: all four edges on the front face are bad. One F turn flips all four back to good.

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

Step 1: EOLine

EOLine does two jobs at once: it fixes every bad edge, and it puts the white-green edge and the white-blue edge on the bottom face, at the front and the back. These two edges make the "line" that the two blocks in the next step are built on.

How to do it as a beginner:

1. Count the bad edges.
2. Use R, L, U and D to move the bad edges to the front or back face, four on each face, then turn F or B to flip them.
3. After that, use only R, L and D to place the two line edges, so you do not break the edges you just fixed.

The picture below has four bad edges, all on the front face, and the line is not done yet:

F R' D'

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

F flips the four bad edges. R' and D' put the two white edges in place on the bottom face.

In a competition, you get 15 seconds of inspection before you start solving. ZZ solvers use that time to plan the whole EOLine in advance. The SpeedSolving Wiki says that getting EOLine planned within the 15-second inspection can take a few months of practice, and that ZZ depends a lot on inspection time (SpeedSolving Wiki).

Step 2: The first two layers with only R, U and L

After EOLine, every edge is oriented. You do not need F or B any more, and you do not need to turn the whole cube. Your left hand looks after the left block and your right hand looks after the right block. Both the SpeedSolving Wiki and Wikipedia point this out (SpeedSolving Wiki, Wikipedia).

The left block

The left block is made of the bottom-left edge and the two corner-edge pairs for the two left slots. The picture below: the corner-edge pair for the front-left slot is in the top layer.

U' L' U L

The back-left slot works the same way, just the other way round:

U L U' L'

The right block

The right block is exactly the same, but with R. This is the most familiar part if you already know the beginner's method. A pair going into the front-right slot:

U R U' R'

A pair going into the back-right slot:

U' R' U R

All four sequences above use only R, U and L, so they never make an edge bad. The SpeedSolving Wiki also notes one tricky point: ZZ's F2L has 10 pieces to solve, more than the 8 in CFOP, and switching between L and R feels a bit awkward at first (SpeedSolving Wiki).

Step 3: The last layer

Once the first two layers are done, the top face always has a yellow cross, because the edges have been oriented since step 1. You skip the cross part of OLL completely. Wikipedia says the last layer can be solved with CFOP techniques (Wikipedia).

Two-look: OCLL then PLL

First look (OCLL): turn the yellow stickers of the four corners to face up. OCLL has only 7 algorithms (SpeedSolving Wiki). The two you will see most often are Sune and Antisune.

Sune:

R U R' U R U2 R'

Antisune:

R U2 R' U' R U' R'

Second look (PLL): move the top-layer pieces into place. If the four corners are already in place and only three edges need to cycle, use one of the two U perms. Both use only R and U, which suits ZZ perfectly.

Three edges cycling one way:

R U' R U R U R U' R' U' R2

Three edges cycling the other way:

R2 U R U R' U' R' U' R' U R'

The other PLL cases are exactly the same as in CFOP. According to the SpeedSolving Wiki, OCLL then PLL needs about 20 algorithms if you count the mirror versions (SpeedSolving Wiki).

ZBLL: the whole last layer in one look

Because the yellow cross is always there, strong ZZ solvers can solve the whole last layer in one go with ZBLL. The catch is that ZBLL has 493 cases. Wikipedia says a ZBLL algorithm is, on average, a little over 12 moves long (Wikipedia, SpeedSolving Wiki).

Beginners do not need to think about ZBLL. Two-look is plenty until you can solve consistently under 30 seconds.

What is good about ZZ, and what is hard?

Pros:

• Fewer moves. The SpeedSolving Wiki gives an average of about 45 moves with EOLine. Wikipedia gives ZZ an average of about 53.5 moves, compared with 55 to 60 moves for CFOP (SpeedSolving Wiki, Wikipedia).
• No turning the whole cube in the first two layers, and only R, U and L. According to the SpeedSolving Wiki, this also makes ZZ a good fit for one-handed solving.
• Easier look-ahead. With the edges already oriented, finding and pairing up pieces is easier.
• A flexible last layer, from a simple two-look up to ZBLL.

Cons:

• EOLine is hard. Counting and fixing bad edges during inspection takes months of practice.
• It depends on inspection time. Without the 15 seconds of inspection, the first step is much harder.
• F2L has more pieces than CFOP, and you have to get used to using both hands for L and R.

Where to start with the ZZ method

1. First, be able to solve the cube with the beginner's method. If you cannot solve it yet, start with the 7-step guide.
2. Practise spotting bad edges. Scramble the cube, count the bad edges, then check by fixing them. Do not worry about the line yet.
3. Add the line. Once you can count edges quickly, practise doing the full EOLine, without a timer at first.
4. Practise F2L with only R, U and L. You will notice that the corner-edge pairs never end up "flipped the wrong way".
5. Last layer: use OCLL and PLL. If you already know CFOP, you have this part covered.

To compare ZZ with other methods, see What is CFOP?.

Video

Want to see it in motion? The short video below from the Việt Roux channel on YouTube shows more of what this post covers. The video belongs to that channel and is embedded directly from YouTube.

Sources

• ZZ method (SpeedSolving.com Wiki)
• OCLL (SpeedSolving.com Wiki)
• Speedcubing – Wikipedia