Intuitive F2L: Solve F2L Without Memorising Algorithms

What is F2L?

F2L stands for First Two Layers. In CFOP, once the cross (the white cross) is done, you have four "slots" left. Each slot is one white corner on the bottom layer and one edge in the middle layer sitting right above it.

The beginner method puts in the four white corners first, then the four middle-layer edges. F2L does it differently: it joins a corner with its matching edge into a pair on the top layer, then puts the whole pair into the slot in one go. Do that four times and the first two layers are finished, just like the goal picture of step 3 in our guide:

According to the SpeedSolving Wiki, the idea of pairing four corners and edges was put forward by John Conway, David Benson and David Seal back in 1979, before CFOP even had a name (SpeedSolving Wiki).

Why go for intuitive F2L?

The last F2L slot alone has 41 cases, and every one of them has an algorithm (SpeedSolving Wiki). But the SpeedSolving Wiki recommends solving F2L intuitively and only using algorithms for the few cases where working it out yourself is slow. Ruwix also says all 41 cases can be solved intuitively (Ruwix).

J Perm recommends getting the hang of F2L by understanding why each step works, rather than remembering every case, and practising until the steps feel natural (J Perm). J Perm's page also calls F2L the most important part of a solve, and usually the part with the most room to get better.

There are three clear benefits:

• Less to remember. You only need two ways to insert a pair and a few setup tricks.
• You never get stuck. When you meet an odd case, you still know what to do.
• Easier to move on. Once you understand it, the full F2L algorithms are just shorter versions of what you already do.

You already know half of F2L

If you have followed how to solve a 3x3 Rubik's Cube for beginners, you have already used most of the move sequences in this post. The three-move sequence that brings a white corner down to layer 1 is the first F2L insert. The first half of the algorithm for the layer 2 edges is the second insert.

The only difference: in F2L, the corner and the edge go down together.

How to hold the cube and read the pictures

Throughout this post, hold the cube like this:

• White face on the bottom, with the cross already done.
• Green face at the front, orange on the right, red on the left.
• The slot to solve is the front right slot. Its pair is the white, green and orange corner and the green and orange edge.

Each picture has two cubes. The left cube is the case you have. Only the cross, the F2L pairs and the centres are coloured; the top layer is left grey so you can focus on the pair you are solving. The right cube is the result, flipped so the white face is on top so you can see the two finished layers. When you solve for real, you don't need to flip the cube.

If R, U, F and the apostrophe are new to you, see the post Rubik's Cube notation for beginners.

The one rule to remember

Ruwix sums up F2L in one sentence: never break the pieces you have already solved (Ruwix). Every move sequence in this post follows one pattern:

1. Open the slot with an R move (or F). The slot is lifted up to the top layer.
2. Turn U so the corner and the edge meet exactly where the slot was lifted to.
3. Close the slot with the opposite move, R' (or F'). The pair goes down and the cross is back as it was.

Because the slot is closed straight away, the cross and the finished slots are not lost. Understand this pattern and you understand intuitive F2L.

Case 1: the three-move insert

This is the nicest case. The corner and the edge are apart on the top layer:

• Corner on the top layer, right above the slot (front right corner). The white sticker faces right, the orange sticker faces up.
• Edge on the back edge of the top layer, with the green sticker facing up.

How to spot it: the corner's white sticker is on the side, the colour on top of the corner (orange) is different from the colour on top of the edge (green), and the two pieces don't touch.

The solution is R U R':

1. R: open the slot. The corner moves to the back right corner.
2. U: the corner comes back right above the slot, and the edge moves from the back to the right. Now they meet as a pair.
3. R': close the slot and the pair goes down. Done.

The mirror version uses the F face: the corner is in the same spot but the white sticker faces the front and the green sticker faces up, and the edge is on the left edge of the top layer with the orange sticker facing up. The solution is F' U' F, following the same open the slot, turn U, close the slot pattern.

Case 2: pair already joined, the four-move insert

In this case the corner and the edge are already stuck together as a small block:

• Corner in the front right corner of the top layer, with the white sticker facing the front.
• Edge on the right edge of the top layer, right next to the corner.
• Both green stickers face up and both orange stickers face right. The pair is joined correctly.

You can't open the slot right away, because the R move would drag the pair along with it. So you move the pair out of the way first. The solution is U R U' R':

1. U: move the pair to the front, off the right face. Now the R move doesn't touch it.
2. R: open the slot.
3. U': bring the pair back to exactly where the slot was lifted to.
4. R': close the slot and the pair goes down.

The mirror version: the corner is in the same spot but the white sticker faces right, the edge is on the front edge of the top layer, both orange stickers face up and both green stickers face the front. The solution is U' F' U F.

Put these two sequences together and you get the layer 2 algorithm from the beginner method.

Case 3: white sticker facing up

When the corner's white sticker points straight up, there is no three-move or four-move insert. For example:

• Corner in the front right corner of the top layer, with the white sticker facing up.
• Edge on the right edge of the top layer, with the green sticker facing up.

The idea: first turn things so the white sticker ends up on the side, then turn it into case 1. The solution is R U2 R' U' R U R':

1. R U2 R': open the slot, turn the top layer half a turn, close the slot. These three moves turn the corner's white sticker to the side and split the corner from the edge. The cross stays in one piece.
2. U': line the two pieces up exactly as in case 1: the corner above the slot with the white sticker facing right, the edge at the back with the green sticker facing up.
3. R U R': the three-move insert from case 1.

Our simulator found no solution shorter than 7 moves for this case using only R, U and F. So "turning it into case 1" here doesn't cost a single extra move.

Every other case: turn it into case 1 or 2

Most of the remaining cases are solved the same way: use one open the slot, turn U, close the slot sequence to rearrange the two pieces, then insert them with case 1 or 2. Here are three common examples.

Corner and edge touching but with the wrong colours

• Corner in the back right corner of the top layer, with the white sticker facing the back and the orange sticker facing up.
• Edge on the back edge of the top layer, right next to the corner, with the green sticker facing up.

The two pieces touch, but the colours on top don't match (orange next to green), so they are not a pair. You have to split them first.

The solution is R U' R' U R U R': R U' R' splits the corner from the edge, U lines them up exactly as in case 1, then R U R' inserts the pair.

Corner in the slot but twisted

• Corner already in the front right slot, but its white sticker faces the front instead of down.
• Edge on the right edge of the top layer, with the green sticker facing up.

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

The solution is R U' R' U R U' R': R U' R' brings the corner up to the top layer, and it joins the edge straight away as the joined pair from case 2. Then U R U' R' inserts the pair.

If the corner in the slot has its white sticker facing right, and the edge is still on the right edge of the top layer with the green sticker facing up, then R U R' U' brings the corner up and makes case 1, and R U R' inserts it. The whole sequence is R U R' U' R U R'.

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

Edge stuck in the slot

If the green and orange edge is in the front right slot but the wrong way round (flipped), or another edge is sitting in that slot, do R U R' to bring that edge up to the top layer. This sequence only touches the front right slot: the cross and the other three slots stay as they are. Then look again and solve it like the cases above.

Example: the edge is in the slot but flipped (green sticker facing right, orange sticker facing the front), and the corner is in the back right corner of the top layer with the white sticker facing right.

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

The solution is R U R' U F' U' F: R U R' brings the edge up to the top layer without touching the corner, U lines the two pieces up exactly as in the mirror version of case 1, then F' U' F inserts the pair.

If your pair is stuck in a different slot, it works the same way: turn the whole cube so that slot is at the front right, do R U R' to push the piece up to the top layer, then carry on.

When the slot is not at the front right

This post uses the front right slot because it is easy to follow. When you solve for real, there are two ways:

• Turn the whole cube so the slot you want is at the front right, then do the same as above. Easiest for beginners.
• Use a different face. The front left slot uses L and F, the back slots use B. The open the slot, turn U, close the slot pattern stays the same.

J Perm recommends turning the whole cube as little as possible and avoiding extra moves (J Perm). When you are just starting, go ahead and turn the cube. Once you are used to it, slowly practise using the other faces.

Summary table of the basic F2L cases

A picture for each row, in the same order as the table:

R U R'

F' U' F

U R U' R'

U' F' U F

R U2 R' U' R U R'

R U' R' U R U R'

R U' R' U R U' R'

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

R U R' U' R U R'

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

R U R' U F' U' F

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

Tips for faster intuitive F2L

• Use empty slots. While several slots are still unsolved, you can open any empty slot to park a piece for a moment without losing anything.
• Pick the easiest pair. Before you start, look at all four pairs and pick the one that already looks like case 1 or 2.
• Don't let the white sticker face up. If you can choose an insert that doesn't flip the corner's white sticker to the top, the solution will be shorter.
• Look ahead. J Perm calls tracking the pieces while you turn, so you can guess the next step, the most important skill in speedsolving. But J Perm also recommends only practising it once the F2L cases have become automatic (J Perm).

For a reference number: the SpeedSolving Wiki says one F2L slot takes about 6.7 moves on average, which is about 26.8 moves for all four slots (SpeedSolving Wiki). The three basic cases in this post are 3, 4 and 7 moves long (see the summary table above).

Practice for intuitive F2L

1. Practise one case at a time. From a solved cube, do a case's solution backwards (for example R U' R' for case 1) to set it up, then solve it again. Do this for all three basic cases.
2. Solve slowly with no time limit. Scramble the cube, do the cross, then solve the four pairs really slowly. For each pair, say it out loud: which case is this, and which case do I need to turn it into?
3. Count your moves. Write down how many moves each pair took. If a pair takes more than 10 moves, try to find a shorter way.
4. Time yourself. Once you can solve smoothly, use the 3x3 timer and keep an eye on your average time.

The J Perm video below goes through all of intuitive F2L in a few minutes (in English):

https://www.youtube.com/watch?v=Ar_Zit1VLG0 Video: "Learn F2L in 6 minutes (Full Intuitive F2L Tutorial)" – J Perm channel on YouTube.

Common mistakes

• Forgetting to close the slot. If you open the slot with R and finish with any move other than R', the cross is broken.
• Inserting a wrongly joined pair. Before you insert, check again: the two stickers of the same colour must sit next to each other on the same face.
• Pushing a piece out through a finished slot. When a piece is stuck, push it out through the slot it is in, not by opening a slot you have already finished.
• Memorising before understanding. If you remember a sequence without knowing why it works, you will get stuck as soon as a case looks a bit different.

Next step

Once you can solve all four pairs without looking back at this post, you can slowly pick up the full F2L algorithms for the hard cases. The post What is CFOP has a road map for the whole of CFOP.

With the EasyRubic app, you can scan your real cube with the camera and see the solution step by step on a 3D cube. Download EasyRubic to practise your own F2L pairs.

Sources

• F2L (SpeedSolving.com Wiki)
• F2L – J Perm
• First Two Layers (F2L) – Ruwix