F2L Pair Solutions

By yoruba


At the highest level, you want to make sure that you're using speed-optimal solutions for the majority of the F2L cases you're going to solve. This will cut down your movecount by a significant margin and make the solve much simpler and faster.

Here you will learn how to implement such solutions and incorporate them into your solving.

Main resource: ZZF2L doc

ZZF2L doc (opens in a new tab)

This is the resource you would want to use, it covers every single possible pair you can get in ZZ, as well as alternative solutions to different combinations of open slots. A fantastic resource, it's all you need to optimize your pair solutions. An "open slot" is a slot with unsolved pieces.

To accompany you, you can also use ZZ example solves. High level CFOP recons are OK too, but make sure that the solutions they do preserve EO.

How to use it?

You can learn F2L pair solutions by going through F2L untimed, and whenever you feel like you solved an F2L pair inefficiently, just check the doc. This is a completely viable way to learn, as you learn these solutions on the fly as they appear in your solves. You do not need to try to memorize all cases at once like you might with last layer algs.

Each tab of the spreadsheet has solutions for all 4 slots. The FR tab has all cases for the front-right slot, so most solutions are simply mirrors of the FL (front-left slot) tab.

Last Slot

The last slot (LS) where you want to optimize solutions first, as they are the least intuitive, so you want to get them out of the way first.

Use the doc and check the LS solutions for all 4 slots to see if you could use a better solution.

For the majority of the pairs, they will usually have 1 solution that is speed optimal and considered best. For the worse LS cases, there are typically 2-3 that you can choose from, although they vary in speed by 0.1 seconds at most, so it doesn't matter which one you choose.

Tip: it's good to know all of them later, as they can help in forcing better OCLLs.

Free slots

When optimizing efficiency more, take note of the alternative solutions that prioritize free slots. For example, R U2 R2 U' R2 U' R'. The last 3 moves are just there to restore the FR pair.

But with the FR slot open, there's no need for that. This mean the case could now be solved with just R U2 R2 U' R:

One example of these free slot solutions is keyhole: when you have a slot with only one solved piece, you can leverage an open slot to insert the other piece.

  1. Bring the other piece to the U layer if it's not there already.
  2. Do a certain D move.
  3. Insert the other piece.
  4. Undo the D move.

Edge keyhole

When inserting an edge, the D move in Step 2 should be to move the solved corner out of the way, replacing it with an unsolved corner from the open slot. In Step 3, insert the edge into the slot that it belongs to. Here's an example:

Moves: D' R U' R' D

We take advantage of the open BR slot. The edge we want to insert is already on the U layer. So we can do D' to move the solved corner out of the way. Then R U' R' to insert the edge to the slot it belongs to, and D to undo the first D move.

Corner keyhole

When inserting a corner, the D move in Step 2 should be to move the spot the corner belongs to into the open slot. In step 3, insert the corner into that open slot. Press ▶️ to see an example:

Moves: D' L' U L D

We take advantage of the open FR slot. The corner we want to insert is already on the U layer. So we can do D' to move the spot that it belongs to into the open FR slot. Then L' U L to insert the corner into FR, and D to undo the first D move.

Other cases

After going through LS, you could then check the cases where one of the pieces is in the U layer, and the other in the F2L slots. A lot of these cases are also easy (just 2 RU/LU triggers), although some might have really strange solutions, like the infamous example being R' F2 R F2.

So the only cases left are the ones with both pieces in the F2L slots, what about those? Bar a few good cases, it's not recommended to learn them. Why? Because when these cases appear in a solve, there's a very high chance that there will be another F2L pair on the cube that's more efficient and faster to solve, so we could just choose that pair instead. This is called Pair Choice.