Notes for EOLine Solving

by Richard Taylor


The ZZ method for solving a Rubik's Cube has a first step called EOLine, where edges are oriented and a line is made across the bottom face. After this step the cube can be solved with only R, U and L turns. This can be very fast, especially for one-handed solving.

Check out Conrad Rider's excellent tutorial to get you started.

Which is great. Except that EOLine is hard. Which means that most people start by solving edge orientation (EO) first and then solving the line as a second step.

As you get more experienced you want to start solving EO and the Line in one step. But that can be a big leap to make; because you have to stop thinking of just good and bad edges and realise that the 2 line edge pieces are special.

This page is a collection of examples that helped me improve my EOLine. If I get time I will also make some YouTube videos to match.

I scramble with yellow on the top and green on the front; but I will try and refer to slots (e.g. UF for up-front) rather than colours.

2 bad edges

Quite rare (3%) and fairly easy.

4 bad edges

Common (24%) and not too hard.

4.1 Simple case

This example shows that the most obvious edge orientation moves can sometimes place the line nicely. Initially one line edge is good and the other is bad.

scramble: U B2 D2 B U2 F U2 L' B2 L2 F D2 F' U2 R2 F' R2 D2 F' U'

eoline: U R' L' F D2 (video)

The U R' puts the bad edges in UB and UR onto the front face without disturbing the good line edge in DB. The L' places the last bad edge on the front face; and the F then makes all 4 bad edges good. Finally the D2 puts the line the right way round.

Things to note here:

  1. Putting a bad line edge into the FL or FR position allows it to be oriented and placed into the line with one turn.
  2. If it is easier to place the line edges on the opposite face to where they end up, then go for it, because you only need one D2 to swap them at the end.
  3. This is not the only way... D2 U' L' R' B is the same number of turns but maybe a bit slower to execute.

6 bad edges

Most likely (45%); can be tricky; lots of options.

6.1 Simple case

In this example both line edges are good and placed on the bottom face.

scramble: U2 R' U2 R' D2 U2 L' F2 D2 F2 L2 D' B D2 B2 D F' R' F' D

eoline: R' F R U2 B D' (video)

Since the line pieces are already on the bottom we want to keep them there if possible. There are 3 bad edges conveniently on the back face, and 2 on the front face. We can start with R' F R to reduce the front face to one bad edge without damaging the line. Then U2 B places all the bad edges on the back face and fixes them; leaving just D' to swing the line into place.

Things to note here:

  1. If line edges are already good then you probably have to place them (or leave them) in the DL and DR slots, because they will get in the way on the front and back faces.

6.2 Hard case

Normally with 6 bad edges you would either fix 4 + 2, or 3 + 3. But sometimes it might be better to add 2 bad edges and then fix 4 + 4. It sounds mad; but when you are trying to place the line at the same time it can work out nicely.

scramble: F' U2 B D2 B L2 F' D2 F' R2 D2 U R F' L F2 D' B' D' R' U

eoline: F B2 R F B U' F2 (video)

This is hard to spot quickly. Especially since B' looks like a good start.

The initial F B2 takes us from 6 bad edges to 8. But crucially those 8 edges are much better balanced between the left and right side of the cube. And so from there we only need a single R turn to place all 8 edges onto the front and back faces. Which leaves just F B to fix all the edges (and place one of the line pieces) followed by U' F2 to place the final line piece.

Things to note here:

  1. Where the bad edges are is as important as how many there are. In some cases like this, it is worth increasing the number of bad edges to get a better distribution of bad edges.
  2. You can use B2 (or F2) to move edges between the left and right side of the cube and the top and bottom, without changing any edge orientation.

8 bad edges

Common (24%) can be hard if the line pieces are awkward.

8.1 Simple case

Here the bad edges are nicely spread, with 4 already on the front face and 2 on the back. One line piece is good and the other is bad.

scramble: R B2 L2 B2 U R2 D2 F2 U' B2 R2 U' R' U2 R2 B' U2 R U F R

eoline: F' R U F2 B' (video)

The initial F' is better than F because it allows us to then move the line piece onto the top of the cube while we put the other 2 bad edges onto the back with R U. We then simply place that line piece with F2 and fix the last 4 edges with B' which also places the back line piece.

Things to note here:

  1. Having 8 bad edges is not necessarily harder than 4.

10 bad edges

Quite rare (3%) can be hard if the line pieces are awkward.