LSE Roux: Solve the Last Six Edges with Only M and U

What is LSE?

LSE stands for Last Six Edges. According to the SpeedSolving Wiki, the Roux method was put forward by Gilles Roux in 2003 and has four steps: a first 1x2x3 block, a second block on the opposite side, the 4 top corners (CMLL), and then LSE (SpeedSolving Wiki).

When you start LSE, your cube has exactly 6 edges left to solve:

• 4 in the middle slice: front top, back top, front bottom, back bottom.
• 2 on the left and right of the top layer.

Along with them are the top and bottom centres, which also sit in the middle slice. The best thing about LSE: the whole step uses only M and U, so your hands hardly ever need to change grip. The SpeedSolving Wiki says that if you solve LSE the shortest way, it takes only about 11 moves on average (SpeedSolving Wiki). The beginner way in this post is longer, but easier to get the hang of.

LSE has three parts, named after the Roux step numbers:

1. 4a, edge orientation (EO): all 6 edges have their yellow or white sticker on the top or bottom face.
2. 4b, left and right edges: bring the yellow-red and yellow-orange edges to the top of the two blocks.
3. 4c, middle slice: put the last 4 edges in the middle slice in place. Once that is done, the cube is solved.

Ruwix shows a different beginner way that puts the two bottom edges in first, but it admits that way takes more moves (Ruwix). This post follows the original Roux order: flip the edges, then the left and right edges, then the middle slice.

How to hold the cube and read the pictures

• Yellow on top, the two blocks at the bottom: red block on the left, orange block on the right. When the cube is solved, the front face has the green centre.
• Each picture shows two cubes. The left one is the case you have, the right one is the cube after the algorithm.
• Only the 6 LSE edges, the 4 top corners and the centres are coloured. The two blocks are grey because LSE never touches them.
• The pictures show only the top, front and right faces. The back bottom edge is hidden, so the text under each picture tells you whether it is right or wrong. On a real cube, tilt it forward a little to look.
• The right-hand picture is always a solved cube. On a real cube, after 4a and 4b, the pieces for the next part may still be out of place: that is the job of the next part.

The M move

M turns the middle slice, between the left and right faces, in the same direction as L: the front top edge moves down to front bottom. M' turns the other way, and M2 is a half turn. If the notation is new to you, see Rubik's Cube notation for beginners.

A common finger trick: push M' up from the bottom of the back face with your right ring finger, or pull M down from the top with your ring finger. Pick whichever feels comfortable, as long as it goes the right way.

Step 4a: flip the edges (EO)

Good edges and bad edges

All 6 LSE edges have one yellow or white sticker. First, look at the top centre. If it is green or blue, do M (or M') once so the top is yellow or white.

Then count:

• A good edge: its yellow or white sticker is on the top or bottom face.
• A bad edge: its yellow or white sticker is on a side face (front, back, left, right).

The number of bad edges is always even: 0, 2, 4 or 6. If you count an odd number, count again. The one people forget most is the back bottom edge.

The cases below are grouped by the number of bad edges. Before you compare with a picture, turn U so the bad edges on top sit where the text says. Don't worry about the two bottom edges: U never touches them.

4 bad: 3 on top, 1 on the bottom (arrow)

Three bad edges on top and one on the bottom look like an arrow, so many Roux solvers call this the "arrow" case. It is also the shortest case.

Bad bottom edge at the front: turn U so the only good edge on top is at the back, then do M' U M.

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

Bad bottom edge at the back: turn U so the only good edge on top is at the front, then do M U M'. The back bottom edge is hidden in the picture, but it is a bad one.

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

4 bad: all 4 on top

Both bottom edges are good, and all 4 top edges are bad. You can hold the cube any way:

M U2 M U2 M U M

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

4 bad: 2 on top, 2 on the bottom

Both bottom edges are bad, and 2 top edges are bad.

The two top ones are next to each other: turn U so they are at the front and left, then do M2 U M U M.

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

The two top ones are opposite each other: turn U so they are at the left and right, then do M U2 M U2 M' U M'.

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

2 bad, both on top

Both bottom edges are good.

Next to each other: turn U so they are at the front and right, then do M U M U2 M U M.

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

Opposite each other: turn U so they are at the front and back, then do M U M' U' M U M'.

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

2 bad, with at least one on the bottom

Both on the bottom (all 4 top edges are good): do M U M U' M' U M'. The picture only shows the front bottom edge; the hidden back bottom edge is bad too.

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

One on top, one on the bottom: turn U so the bad top edge is opposite the bad bottom edge.

• Bad bottom edge at the front: put the bad top edge at the back, do M U M U M' U M'.

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

• Bad bottom edge at the back: put the bad top edge at the front, do M U M' U M U M'.

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

6 bad

All 6 edges are bad. Do M' U M once: then only 2 bad edges are left. Count again and compare with the pictures above. The picture below is that same algorithm, used for the arrow case.

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

Step 4b: the left and right edges

Now all 6 edges are oriented. Before you start:

1. Turn U so the 4 top corners match the two blocks. Every 4b algorithm keeps them there.
2. The top centre can be yellow or white. Some pictures below have a white centre on top: that's fine, the algorithm still works. Step 4c fixes it.

Do one edge at a time: yellow-red first (to the top of the red block, on the left), then yellow-orange (to the top of the orange block, on the right). Every 4b algorithm keeps the edge orientation you just did in 4a.

The yellow-red edge

Find the yellow-red edge and pick the algorithm for where it is.

In the top layer, at the front: M2 U' M2 U

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

In the top layer, at the back: M2 U M2 U'

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

On the bottom, at the front: U M2 U'

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

On the bottom, at the back (hidden in the picture, tilt the cube to look): U' M2 U

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

In the top layer but on the wrong side, the right: U' M' U2 M U'

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

The first four algorithms share one idea: the yellow-red edge is at the bottom of the middle slice (or M2 brings it down there), U turns its home spot into the middle slice, M2 brings it up into that spot, and then U turns back so the corners match the blocks.

The yellow-orange edge

The yellow-red edge is now on top of the red block. Now find the yellow-orange edge.

In the top layer, at the front: M2 U' M' U2 M' U'

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

In the top layer, at the back: M2 U M U2 M U

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

On the bottom, at the front: U M U2 M U

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

On the bottom, at the back: U' M' U2 M' U'

[cube3 BD BDL BDR BU DF DFL DFR DL DR FU: z2 U' 2L' U2 2L' U'] ## Step 4c: the middle slice

There are 4 edges left in the middle slice: front top, back top, front bottom, back bottom. If the top centre is white, do M2 first so yellow is on top. M2 does not mess up any edge. The SpeedSolving Wiki calls this part L4E or L4EP (SpeedSolving Wiki).

The algorithms use only M and U2, and always put the corners and the left and right edges back where they were. Look at which edges are already in place (same colour as the centre of the face they sit on), and where the others need to go.

Three edges cycle

One edge is already in place, and the other three swap around in a cycle.

Front bottom already in place; front top needs to go to back top, back top to back bottom, back bottom to front top: M U2 M' U2

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

Front bottom already in place; the cycle goes the other way (front top needs to go to back bottom): U2 M U2 M'

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

Back top already in place; front top needs to go down to front bottom, front bottom across to back bottom, back bottom to front top: M2 U2 M U2 M

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

Front top already in place; back top needs to go to front bottom, front bottom across to back bottom, back bottom up to back top: M U2 M U2 M2

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

Two pairs swap

No edge is in place, and the edges swap in pairs.

Top with top, bottom with bottom (front top with back top, front bottom with back bottom): M2 U2 M2 U2

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

Top with bottom on the same side (front top with front bottom, back top with back bottom): M U2 M2 U2 M

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

Diagonal swap (front top with back bottom, back top with front bottom): U2 M U2 M2 U2 M U2

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

Doesn't match any picture?

There are 8 kinds of three-edge cycle, but this post only shows 4. If your cube doesn't look like any picture, turn the whole cube half a turn (y2) so the back is at the front, then compare again: the other 4 kinds are just the 4 pictures above seen from the back. We checked on the simulator that this covers every 4c case.

Faster: joining the parts together

Once you can solve LSE smoothly in three parts, you can start joining them. The SpeedSolving Wiki says the more popular way in the Roux community is EOLR: orient the edges and place the left and right edges at the same time, then do 4c (SpeedSolving Wiki). The same page says Gilles Roux himself recommends solving LSE flexibly, half by intuition, without strictly splitting it into steps.

Tip for beginners: don't rush into EOLR yet. Get 4a, 4b and 4c really solid first, because EOLR is also built on reading edge orientation and where the yellow-red and yellow-orange edges are.

Common mistakes

• Forgetting to fix the centre before counting bad edges. The top must be yellow or white, otherwise the whole count is wrong.
• Forgetting the back bottom edge. It is hidden, but you still have to count it. An odd count is a sign you missed it.
• Mixing up M and M'. M goes the same way as L: the front top edge moves down. If an algorithm doesn't give you the picture, the most common reason is M going the wrong way.
• Not turning U so the corners match the blocks before 4b. Then the yellow-red edge ends up in the "right" spot but out of line with the block.
• An odd U turn in 4c. Every 4c algorithm uses only U2. A single quarter U turn throws off all 4 corners and the left and right edges.

What's next

To see each case on a 3D cube with arrows showing the way, open the last steps of the Roux guide: flip the edges, left and right edges and middle slice. If you are comparing Roux with other ways to solve, the post Rubik's Cube solving methods gives the big picture.

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 to practise LSE on your own cube.

Video

Want to see it in motion? The short video below from the Irving Chung channel on YouTube shows more of what this post covers. The video belongs to that channel and is embedded straight from YouTube.

Sources

• Last Six Edges (SpeedSolving.com Wiki)
• Roux method (SpeedSolving.com Wiki)
• Roux Method Tutorial – Ruwix