EOLine for Intermediates - Part 2

by Richard Taylor : 2022-01-28

In the previous article I shared some tools for helping ZZ solvers move towards optimal EOLine solutions. But that is potentially a long road. Are there any stops on the way? I found a few things that might help.

Green-Blue Neutrality

One thing that leaps out quite quickly is that unless you are prepared to spin the cube 180 degrees after EOLine, in about half your solves, then you need to be able to solve with either green on front or blue on front.

If you are always unconsciously trying to find an EOLine that works with green on the front then you are really limiting yourself.

A flip side of this is that you shouldn't worry too much about placing the two line edges in their exact places during EOLine; focus on getting them in opposite slots on the bottom face. As long as they are then you can place them correctly with D, D2 or D'.

For example, if you already have 4 bad edges on the green face like this:

4 bad edges remaining
Opposite line edge

That is already a great position, as you can fix those edges and place the blue-white edge on the line with an F turn. Then you can put the green-white opposite and finish with D2. Alternatively, once you are green-blue neutral, then you can also finish with Uw2 if that gives a better transition into F2L.

EO and Line not EO then Line

This is said in most tutorials but it didn't fully sink in for me. I guess if you start off solving EO first and then thinking about the line, then it is hard to break out of that mental model of always doing the line at the end.

But looking at optimal solutions it is clear that placing a line edge early in the EOLine is often a good idea. In particular if a line edge is bad, then placing it at the same time as fixing its orientation is ideal. Given that you expect at least one of the line edges to be bad in 75% of scrambles, that is something to always bear in mind. You are never going to get better at most EOLine cases if you always leave consideration of the line to the end.

Look again at the 6-bad edge scramble from the previous article:

R U L R U L F2 U B' L U2 F D

Both of the line edges are bad, and the optimal EOLine is 7 moves. What happens if we just concentrate on fixing and placing the green-white edge first?

D U' R' U F

Does the trick. And we are left with B R B' to fix and place the blue-white edge. That's 8 moves, which is only one turn more than the optimal solution.

Also, imagine that you only manage to plan those first 5 moves during inspection. If you execute them on the back using:

y2 D U' L' U B

Or if you do the original moves on the front and then turn the cube round (y2) then you know there are 2 bad edges left, including the blue-white line piece. So you should quickly spot them and know to finish with:

F L F'

This insight helped me build some back-up tactics for when I couldn't plan my whole EOLine in the 15 seconds of inspection. My observation is that if you only get part of the process done in 15 seconds, then it is better to orient some of the edges and place a line piece, than to orient most of the edges but leave the line pieces in limbo. The remaining sections in this article look at some common specific cases.

6 bad with one line bad

The most likely number of bad edges in a scramble is 6 and there is a 50/50 chance that each of the line edges are bad. So the most likely scenario is that you will see 6 bad edges with one of them being a line edge.

If you can orient 4 edges, including the bad line edge, and place that line edge during inspection, then you will be left with 2 bad edges, neither of which will be a line edge.

4 bad edges remaining
4 edges including line

Typically that means putting 4 bad edges on the back face, with the bad line edge in one of the "equator" positions (BL or BR) and executing B or B' to place the line edge.

If you do that and are lucky enough to also have the other line edge in the right place then you will see something like this:

2 bad edges remaining
2 edges remaining = F' U' F

Which solves with F' U' F. Or this:

2 bad edges remaining
2 edges remaining = F' L F

Which solves with F' L F. You will find that these combinations quickly become intuitive, like F2L inserts.

It is more likely that your remaining line edge will not be in the right place. If it isn't, then move it to the FU slot like this:

2 bad edges remaining
2 edges remaining = F U' F

Then you can orient the edges and place the line piece with F U' F. Or you may find the other bad edge is opposite the line edge (in the DF slot) like this:

2 bad edges remaining
2 edges remaining = F L F

Which solves with F L F.

Obviously the edges can be in other positions, but they will either be a symmetry of one of these or a position that can be moved into one of these configurations with one or two additional turns.

6 bad with both lines bad

In about 25% of scrambles with 6 bad edges you will find both of the line edges are bad. If you fix 4 edges including one of the line pieces and place that line piece, then you will be left with 2 bad edges, one of which is the other line piece.

That means you only have 2 pieces to look for and there are fewer different ways to finish off. Basically you need to get the line piece into one of the four slots UL, UR, DL, DR and the other edge into UF or DF. Then there is a 3 move finish.

Here is the line in UL and the edge in UF:

2 bad edges remaining
line + edge = F' L F'

And here is the line in DL and the edge in DF:

2 bad edges remaining
line + edge = F L' F'

All 8 combinations of those slots work, but obviously the ones with edges on the bottom are harder to spot. You can do L2 or R2 rather than rotating the cube if that also helps with the transition to F2L.

6 bad with neither line bad

The remaining 25% of 6 bad edge scrambles will have neither of the line edges badly oriented. You could orient 4 edges, place a line edge and then use the finishes from the "6 bad with one line bad" section above. But I find that a bit clunky. Usually if both line edges are correctly oriented then I find that those are the cases where it does make sense to fix the orientations of the other edges first and then place the line pieces at the end.


Getting lots of +2s and DNFs because you can't plan EOLine in 15 seconds will quickly sap your enthusiasm for the ZZ method as you try to improve. My two main observations that might help you are:

  1. Becoming green-blue neutral is worth the effort
  2. Placing at least one line edge early is often key

Don't give up on finding optimal, or near optimal, EOLine solutions. It does get easier, or at least more intuitive, the more you practise. Hopefully the tips here will show you that you can bridge the gap between intermediate and expert by executing a partial EOLine and then finishing the job with a few simple triggers if you have to - a bit like an extra F2L pair.