How to Solve the Rubik's Cube Last Layer: 4 Algorithms

Before you start the last layer

Check these things first:

• Layers 1 and 2 are completely done. White face on the bottom, all four middle layer edges in place. If even one middle layer edge is wrong, the steps below won't give the results described. Go back to how to pair up the middle layer edges if you need to.
• Hold the cube the right way: yellow centre on top, white centre on the bottom. In the pictures, the face with the words FACING YOU is the front. Before you compare with a picture and all the way through an algorithm, keep the front pointing at you; only turn the whole cube when the post tells you to change how you hold it. When the post says "front left", it means the last layer corner on the front face, on your left-hand side.
• Reading the pictures: each case has two pictures. The cube in the pictures is always held the same way: yellow on top, green at the front, orange on the right; red on the left and blue at the back are hidden. The left picture is the cube before the algorithm, the right picture is after. Only the pieces you need to look at are coloured, the rest are grey. The after picture always shows a solved cube; on your cube, the top row of the side faces may still be off, and the later steps take care of that.
• Naming pieces by colour: each last layer corner has three colours. For example, the yellow - green - red corner has one yellow sticker, one green sticker and one red sticker. Its home is the corner between the yellow, green and red faces, which is front left on the last layer. In steps 6 and 7, the captions name each piece by its colours like this so you can find it in the picture.
• Know the notation R, U, F, R', U2. If it is new to you, read Rubik's Cube notation for beginners first.

The last layer splits into four jobs, in this order: yellow cross, yellow face, yellow corners in place, then yellow edges in place. Ruwix puts the final steps in a different order (edges first, then corners) with different algorithms (Ruwix). Either way solves the cube; this post follows the order of the EasyRubic guide so you can switch between the post and the guide without getting mixed up.

Step 4: Yellow cross

Goal: flip the 4 last layer edges so their yellow sticker is on top, making a plus sign around the yellow centre. The side stickers of the edges don't need to match yet, and you can ignore the corners for now. The one algorithm for this step:

F R U R' U' F'

Only look at the yellow stickers of the 4 edges on the top face, and ignore the corners. If you already have the yellow cross, go to step 5. Which case do you have?

• Yellow line across: two edges with yellow on top sit opposite each other and make a straight line with the yellow centre. Turn U so the line runs from left to right, then do the algorithm once.

• Yellow L in the back left: two edges with yellow on top sit next to each other and make a right angle with the yellow centre. Turn U so the L sits in the back left corner (one yellow edge at the back, one yellow edge on the left), then do the algorithm twice.

• Just the yellow centre: no edge has yellow on top. Do the algorithm once, turn U2, then do it twice more.

With just the yellow centre, you are really passing through the two pictures above: after the first go you have an L, after the next you have a line. If that is hard to remember, just do it once and look again to see which picture you have now.

Why doesn't this algorithm break layers 1 and 2?

Look closely and the algorithm has three parts: F, then the four middle moves R U R' U', then F' to put the front back. Those four middle moves are a sequence cubers use everywhere, and J Perm calls it the basic four-move sequence in his guide (J Perm). While you do it, you will see some pieces from layers 1 and 2 get pulled up, but once all six moves are done, layers 1 and 2 are back exactly as they were. We checked this for all four last layer algorithms on the simulator.

In the picture below, layers 1 and 2 are coloured in too. Compare the two pictures: the bottom two rows of the front and right faces are exactly the same before and after the algorithm, and only the last layer changes.

So if layer 1 or layer 2 is off after you finish an algorithm, you definitely turned one move wrong somewhere in the middle. The algorithm is not the problem.

If only one or three edges have yellow on top

You will never see this on a cube that was put together properly. J Perm warns that having one or three yellow edges facing up means the cube can't be solved and needs to be taken apart and put back together (J Perm). Wikipedia explains why: no sequence of turns can flip exactly one edge without touching another edge (Wikipedia). See more in the "When your cube seems broken" section below.

Step 5: Yellow face

Now that you have the yellow cross, the next job is to twist the 4 last layer corners so all nine stickers on top are yellow. The algorithm for this step is called Sune:

R U R' U R U2 R'

This post only uses Sune to make the yellow face. To spot it quickly and see its reverse algorithm, see more about Sune and Antisune.

Count how many corners have yellow on top (0, 1 or 2), then check which face the yellow sticker of each other corner is on (front, right, left or back). Pick the matching case, then turn U until it lines up exactly. There are 7 cases. You don't need to memorise all seven right away: remember the two one-corner cases, and for the rest compare with the pictures below or with Step 5 of the guide. The pictures only show the top, front and right faces; for yellow on the left or back, go by the words. Which case do you have?

1 corner with yellow on top

Turn U so that corner sits at front left. Then look at the front right corner of the last layer:

• Its yellow sticker is on the front: do Sune once and you are done.

• Its yellow sticker is on the right: do Sune, turn U2, then do Sune again.

The first case is the exact pattern Sune solves in one go, which is why many people get the hang of it first. The other five cases are all Sune repeated a few times, with a U move in between.

No corners with yellow on top

All 4 last layer corners have their yellow sticker on a side face. Turn U until you see one of these two patterns:

• Yellow on the left and the right: two yellow stickers on the left face, two on the right face. Do Sune twice in a row.

• Two yellow on the left: two yellow stickers on the left face, one on the front, one on the back. Do Sune, turn U', then do Sune again.

2 corners with yellow on top

• The two corners are diagonal: keep those two corners at back left and front right. The front left corner has its yellow sticker on the front, and the back right corner has its yellow sticker on the right. Do Sune twice, turn U2, then do Sune a third time.

• Two corners at the back, the two front corners have yellow on the left and right: the front left corner has yellow on the left face, the front right corner has yellow on the right face. Do Sune, U2, Sune, U', Sune.

• Two corners at the back, both front corners have yellow on the front: do Sune, U', Sune, U2, Sune.

When you do Sune, the side stickers of the last layer get scrambled. That is fine: the last two steps sort them out. As long as the top is all yellow and layers 1 and 2 are still intact, you did it right.

Step 6: Put the yellow corners in place

The top is yellow, so now look at the sides. Each last layer corner has 2 stickers on the sides (ignore the yellow one). A corner is in place when those 2 stickers match the colours of the 2 centres on the faces next to it. For example, the front left corner: its front sticker matches the front centre (green), and its left sticker matches the left centre (red). In the pictures in the guide, a corner that is in place has a yellow ring.

Held the way the pictures show (yellow on top, green at the front, orange on the right), each last layer corner has its own home:

• The yellow - green - red corner: front left.
• The yellow - green - orange corner: front right.
• The yellow - blue - orange corner: back right.
• The yellow - blue - red corner: back left.

On your cube, if the front isn't green, just go by the centres: a corner belongs in the spot between the three centres that share its colours.

The algorithm for this step (speedcubers call it the A-perm):

R' F R' B2 R F' R' B2 R2

This algorithm keeps the front left corner where it is and swaps the other 3 last layer corners around. How to do it:

1. Look at each of the 4 last layer corners. If all 4 are already in place, go to step 7.
2. Can't see any corner in place? Turn U and look again, trying all 4 positions.
3. Compare with the cases below.

Which case do you have?

• 1 corner in place, the other 3 go clockwise: turn the whole cube so the corner in place sits at front left. Looking down from above, the other 3 corners need to move clockwise to get home. Do the algorithm once.

In the picture: the corner in place is the yellow - green - red last layer corner at front left (green sticker on the front, red sticker on the hidden left face). The other three are all in the wrong spots. At front right is the yellow - blue - red corner (blue sticker on the front, red sticker on the right), which needs to go to back left. At back right is the yellow - green - orange corner (green sticker on the right), which needs to go to front right. At back left is the yellow - blue - orange corner (hidden), which needs to go to back right.

• 1 corner in place, the other 3 go anticlockwise: still put the corner in place at front left, but the other 3 need to go the opposite way. Do the algorithm twice, holding the cube the same way.

In the picture: the corner in place is still the yellow - green - red corner at front left (green sticker on the front). The other three: at front right is the yellow - blue - orange corner (orange sticker on the front, blue sticker on the right), which needs to go to back right. At back right is the yellow - blue - red corner (blue sticker on the right), which needs to go to back left. At back left is the yellow - green - orange corner (hidden), which needs to go to front right.

• 2 diagonal corners in place, the other 2 swap diagonally: turn the whole cube so the 2 corners in place sit at front right and back left. Do the algorithm, turn U, then do the algorithm again.

In the picture: the two corners in place are the yellow - green - orange corner at front right (green sticker on the front, orange sticker on the right) and the yellow - blue - red corner at back left (hidden). The other two swap diagonally: at front left is the yellow - blue - orange corner (blue sticker on the front), which needs to go to back right; at back right is the yellow - green - red corner (red sticker on the right), which needs to go to front left.

• 2 left corners (front and back) in place, the 2 right corners swap: if the two corners in place are next to each other, turn the whole cube so they are on the left. Turn U once, do the algorithm, then turn U2.

In the picture: the two corners in place are the yellow - green - red corner at front left (green sticker on the front) and the yellow - blue - red corner at back left (hidden). The two right corners swap with each other: at front right is the yellow - blue - orange corner (orange sticker on the front, blue sticker on the right), which needs to go to the back; at back right is the yellow - green - orange corner (green sticker on the right), which needs to come to the front.

The algorithm has a B2 move (turning the back face). Lots of beginners turn the back face the wrong way; with B2 the direction doesn't matter, so just make sure you turn the back face and not the front.

Step 7: Put the yellow edges in place

The very last step. After step 6, all 4 corners are in place, so there is usually at least one side face with its whole top row in one colour. The algorithm (U-perm):

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

This algorithm only swaps 3 last layer edges around, and doesn't touch the 4 corners you just sorted. How to do it:

1. Find a side face with its whole top row in one colour (2 corners and the edge between them). Turn the whole cube to put that face at the back.
2. Look at the last layer edge on the front face: does it need to go right or left?

Which case do you have?

• The front edge needs to go right: its front sticker matches the right centre. Do the algorithm once.

In the picture: the blue face at the back already has its whole top row in blue (hidden). The top row of the front face is green - orange - green: the front edge is the yellow - orange edge, which needs to go right, where the orange centre is. The top row of the right face is orange - red - orange: the right edge is the yellow - red edge, which needs to go left. The left edge (hidden) is the yellow - green edge, which needs to come to the front.

• The front edge needs to go left: its front sticker matches the left centre. Do the algorithm twice.

In the picture: the back is still done. The top row of the front face is green - red - green: the front edge is the yellow - red edge, which needs to go left, where the red centre is. The top row of the right face is orange - green - orange: the right edge is the yellow - green edge, which needs to come to the front. The left edge (hidden) is the yellow - orange edge, which needs to go right.

If no face has its whole top row in one colour yet, all 4 edges are in the wrong place. There are two cases:

• Each edge swaps with the opposite one: the front sticker of the front edge matches the back centre, and the right sticker of the right edge matches the left centre. Do the algorithm, turn U, do the algorithm again, then turn U'.

In the picture: the top row of the front face is green - blue - green (the yellow - blue edge needs to go to the back), and the top row of the right face is orange - red - orange (the yellow - red edge needs to go left). The two hidden edges are the yellow - green edge at the back and the yellow - orange edge on the left.

• Each edge swaps with the one next to it: turn U until the front edge and the right edge need to swap with each other: the front sticker of the front edge matches the right centre, and the right sticker of the right edge matches the front centre. Do the algorithm, turn U', do the algorithm again, then turn U.

In the picture: the top row of the front face is green - orange - green (the yellow - orange edge needs to go right), and the top row of the right face is orange - green - orange (the yellow - green edge needs to come to the front). On the hidden side, the back edge is the yellow - red edge and the left edge is the yellow - blue edge: these two swap with each other too.

Can't remember these two cases? No problem: do the algorithm once from any side, and one face will end up with its whole top row in one colour. Then carry on as in the first two cases.

Finish this step and your cube is solved.

When your cube seems broken

The last layer is where small mistakes show up the most. Here are the usual situations and what to do:

• Layer 1 or layer 2 is off after an algorithm. You turned one move wrong, most often mixing up R and R' or missing a U. There is no easy way to "undo", so solve again from where it went wrong: usually just a few middle layer edges have popped out, so pair them up again with step 3 and carry on.
• Exactly one or three edges have yellow on top in step 4. An edge got flipped the wrong way round when the cube was taken apart (or popped out from turning too hard). According to J Perm, you need to take the cube apart and put it back together (J Perm); Ruwix also suggests taking an edge out and flipping it back (Ruwix).
• Only one corner is twisted wrong, everything else is done. No algorithm can fix this, because no sequence of turns twists just one corner. Someone, maybe you, twisted that corner by hand. Twist it back by hand or take it out and put it back the right way.
• Only two pieces are swapped. This is also a sign the cube was put back together wrong, because normal turning never swaps exactly one pair of pieces.

According to Wikipedia, no sequence of turns can twist just one corner or swap just one pair of pieces, and a cube taken apart and put back together at random has only about a 1 in 12 chance of being solvable (Wikipedia). So if your cube was just taken apart, don't waste time hunting for a "special algorithm": the surest fix is to put it back together from a solved state. The post Which Rubik's Cube to buy as a beginner has a few tips on picking a cube that doesn't pop when you turn it.

The four last layer algorithms to remember

All together, the whole last layer needs just these four algorithms, each shown with the case it solves in one go:

• Yellow cross: F R U R' U' F'

• Yellow face (Sune): R U R' U R U2 R'

• Yellow corners in place (A-perm): R' F R' B2 R F' R' B2 R2

• Yellow edges in place (U-perm): R U' R U R U R U' R' U' R2

A practice tip: take one algorithm at a time, one a day. Go slowly and say each move quietly as you turn, until your hands remember it on their own. Once you know all four by heart, the last layer will take just a few dozen seconds. J Perm says that with the beginner method and some practice, you can solve the whole cube in about 2 to 4 minutes (J Perm).

Video to watch

If you want to see someone's hands doing it, this video from J Perm (in English) is a very popular beginner guide. It uses a few different algorithms for the last layer, so when you practise, stick to one way so you don't get mixed up.

Timing and practice

Once you can solve the last layer every time, you can start timing yourself with the 3x3 timer to track your progress.

Stuck halfway? With the EasyRubic app, you can scan your real cube with the camera and see the solution step by step on a 3D cube.

Get EasyRubic and solve the last layer for the first time.

What's next: 2-look OLL and 2-look PLL

The four last layer steps in this post are easy to remember, but you have to repeat algorithms a lot. Once you can solve the whole cube without looking at a guide, you can merge them into two jobs, each with at most two algorithms. This is how cubers move into the CFOP method.

• Steps 4 and 5 become 2-look OLL: you still make the yellow cross first, then solve the yellow face with exactly one algorithm for each case, instead of repeating Sune two or three times. The Sune you just used is one of them. Read 2-look OLL.
• Steps 6 and 7 become 2-look PLL: you still put the corners in place first and the edges after, but each case has its own algorithm, so you only do it once. The step 7 algorithm in this post is part of that set too. Read 2-look PLL.

Start with 2-look OLL, since you already know two of its algorithms. To see where OLL and PLL fit in the whole method, read What is CFOP.

Sources

• How To Solve The Rubik's Cube – Beginners Method (Ruwix)
• How To Solve The 3x3 Rubik's Cube – J Perm
• Rubik's Cube – Wikipedia