How to Solve a 4x4 Cube - Step-by-Step Course

Before You Start

This course assumes you can already solve a 3x3 cube - even with the course in front of you. If not yet, start with the 3x3 cube course, because its algorithms come back here in stage 6. You can turn the animations in this course: drag the cube with your finger or mouse.

What a 4x4 cube is made of

The 4x4 cube has 8 corners - the same as on a 3x3. The rest looks different:

• Centres - a 2x2 square on every face, 24 pieces in total. They are not attached to the core, they move around like the other pieces.
• Edges - in every edge position there are two halves with the same colours, 24 in total. The halves are separate pieces and get split up when you scramble.

The reduction method

Since the cube has no fixed centres, nothing decides in advance which face gets which colour. That is why you first build the centres yourself and then join the edge halves into pairs. After that every 2x2 square works like a centre of a 3x3 cube and every pair like one of its edges - the cube behaves like a 3x3 and you solve the rest with a method you know. This is called reduction (reducing a 4x4 to a 3x3):

1. centres - stages 2-4,
2. edge pairing - stage 5,
3. continue like a 3x3 - stage 6, with two situations that do not exist on a 3x3 (stages 7 and 8).

The colours lie opposite each other just like on a 3x3: white opposite yellow, green opposite blue, red opposite orange. On a 4x4 it is up to you to place them that way - in stage 4 we explain exactly how.

1Move Notation

The letters R, L, U, D, F, B mean the same as on a 3x3 cube: a quarter turn of the right, left, up, down, front and back face clockwise, when you look straight at that face. An apostrophe means a turn the other way, and a two - a half turn. On a 4x4 each such letter turns only one, outer layer. Two new kinds of moves are added:

• Rw - the two right layers at once (w for “wide”). The same goes for Lw, Uw and the others.
• 2R - only the second layer from the right, without the outer one. The same goes for 2L - the second layer from the left.

The direction is the same as the ordinary move of that face: 2R and Rw turn the same way as R. Click a move below to see it on the cube:

In other tutorials you may come across lowercase letters (r, u) - sometimes they mean two layers, sometimes only the inner one. In this course the notation is unambiguous: Rw or 2R.

x, y and z are rotations of the whole cube in your hands, as on a 3x3: x like the R move (the front goes to the top), y like the U move (the right face goes to the front), z like the F move (the top goes to the right). On a 4x4 you need them more often, because while doing centres and edges you keep turning a different face towards you.

The most important sequence in this part of the course is 2R U 2R': second layer up, top to the left, second layer down. It takes one centre piece from the front to the top, and the second layer goes back to its place.

2White Centre

Goal: four white centre pieces on one face. Edges and corners do not matter yet.

Turn the cube so that the face with the most white centre pieces is on top - you will build the white square on it. In the animations only the white centre pieces are coloured, the rest is greyed out.

Inserting one centre piece

You insert every white centre piece from the front to the top with the same move:

1. Turn the top (U) so that the back-left corner of the top centre (furthest from you, on the left) is an empty spot - not white.
2. Turn the front (F) so that the white piece is in the bottom-right corner of the front centre.
3. Do 2R U 2R'.

The white piece jumps to the top, and the white pieces that were already there stay on it - after each time there is one more.

When there is no white on the front

• The white piece is on another side - rotate the whole cube (y) so that this side is at the front. The top stays on top.
• The white piece is on the bottom - turn the bottom (D) so that the white piece is in the left half of the bottom centre (closer to the left face), and do 2R' D2 2R. The left half of the bottom swaps with the right half of the front, and the top stays untouched. Then you insert it as usual.

The same rule works from the first to the last white piece - also when there are already three on top. Only one thing matters: there must not be a white piece in the back-left corner of the top, because 2R U 2R' would take it to the front.

3Yellow Centre

Goal: four yellow centre pieces on the face opposite the white ones.

Turn the cube with the white centre on the bottom (x2). You build the yellow centre on top exactly like the white one: empty spot in the back-left corner of the top, yellow piece in the bottom-right corner of the front, 2R U 2R'.

The white centre on the bottom is safe: 2R briefly moves its right half to the front, but 2R' immediately puts it back. Yellow centre pieces can now only be on the top and on the sides (the bottom is already full of white), so you only need to rotate the cube (y) to bring the side with yellow to the front.

Always check that the yellow is opposite the white - if you build it on a side, the cube cannot be finished.

4The Last Four Centres

Goal: all six centres done, each colour on the correct face.

How to hold the cube

Rotate the cube (z) so that white is on the left and yellow on the right. The remaining four centres now lie on a “ring” around the cube: top, front, bottom and back. You use the same moves as before - 2R U 2R' and 2R' D2 2R do not touch the left and right centres. Instead of a y rotation (which would bring white to the front) you rotate the cube with x, and to swap the front with the back - with y2 (white and yellow then swap sides, but stay on the sides).

Green

Rotate the cube (x) so that the ring face with the most green pieces is on top, and build the green centre on it. Green centre pieces can be on the front (you insert them straight away), on the bottom (2R' D2 2R) or on the back (y2 - the back goes to the front).

Orange - easy to get wrong here

The next colours cannot go just anywhere: they must lie around each other the way they do on a solved cube. First check that white is on the left - if the y2 rotations moved it to the right, rotate the cube y2 (green stays on top). Then rotate the cube (x) so that green is at the back. On a standard cube orange now goes on top, and red will be on the bottom.

You take the orange centre pieces from the front or from the bottom (2R' D2 2R). Do not bring the back to the front any more - the finished green is there.

Blue and red

Rotate the cube once more (x): orange goes to the back, and the two unsolved centres are on the top and at the front. Build blue on top - all the blue pieces are at the front, so 2R U 2R' with front turns is enough. When the top is done, only red pieces are left at the front - the last centre solves itself.

Check the colour order

Before you move on, check two things - now a fix is the easiest, because the edges are not paired yet:

1. Opposite each other are: white and yellow, green and blue, red and orange.
2. Hold the cube with white on the bottom and green at the front - red must be on the left and orange on the right.

If something does not match, do not rebuild the centres - swap them:

• Two adjacent centres are swapped (the first point does not match) - put them on the top and at the front and do (2R U2 2R') F2 U2 (2R U2 2R').
• Red and orange are swapped (only the first point matches) - hold the cube with white on the bottom and green at the front, rotate it (z) so that these two centres are on the top and bottom, and do (2R U2 2R') F2 U2 (2R U2 2R'), then x2, once more (2R U2 2R') F2 U2 (2R U2 2R') and finally x.

5Edge Pairing

Goal: in each of the 12 edge positions two halves with the same colours - on every face the edge looks like a single colour. The centres stay solved.

An edge is “unpaired” when its two halves have different colours. You join them one pair at a time with the same pattern. All the moves in this stage (apart from the algorithm) turn only the outer layers or the whole cube, so they do not break the centres or finished pairs.

1. Rotate the whole cube so that an unpaired edge is at the front left (vertical, between the front and the left face). Look at its upper half - e.g. green-orange.
2. Find the other half with the same colours and bring it to the front-right edge with moves that do not touch the left edge:
   • from the top: turn the top (U) until it is on the right side of the top, and do R',
   • from the bottom: turn the bottom (D) until it is on the right side of the bottom, and do R,
   • from the back right: R2, from the back left: B2 and R2.
3. If the half ended up at the bottom of the right edge, do R U R' F R' F' R - the edge flips and the half will be at the top.
4. Now both upper halves - left and right - have the same colour at the front and the same on the side. Do Uw' R U R' F R' F' R Uw. The halves join in the right edge.

How it works: Uw' moves the upper rows of the sides one face to the right, so the upper-left half goes into the right edge (and the one that was there moves to the back). R U R' F R' F' R flips the right edge - the half you brought goes down. Uw puts the centres back and brings the other half back to the top of the right edge - the pair is done. Finished pairs in the top layer change places along the way, but they do not break up.

Repeat these steps until all the edges are paired - usually about 10 times is enough. The other half is never in the same left edge: if it were there, the edge would already be paired.

The last two edges are paired the same way: put one at the front left and the other at the front right, so that the upper halves match each other. The algorithm then pairs both at once - the first animation shows exactly this case.

6Continue Like a 3x3

Goal: a solved cube - just like a 3x3, with two special situations (stages 7 and 8).

The centres and edges are done, so the cube behaves like a 3x3: a 2x2 square is a centre, a pair of halves is an edge. The colour of a face is now set by its centre - exactly as on a 3x3. Solve it with the method from the 3x3 cube course (yellow on top): daisy, white cross, white corners, second layer, yellow cross, yellow edges, corners into place and corner twisting.

Use only outer-layer moves (R, U, F, L, D, B) and whole-cube rotations. Moves like Rw, Uw or 2R would break the centres and pairs - they only appear in the algorithms from stages 7 and 8, which restore order by themselves.

In two places a 4x4 cube can show you something you will never see on a 3x3:

• in the yellow cross stage - one or three yellow edges on top (stage 7),
• in the “corners into place” stage - exactly two corners in place (stage 8).

Speedcubers call this parity. It is not a mistake in your solving - it comes from how the edges and centres were joined. Each of these situations happens in roughly every other solve, independently of the other, so you will usually get at least one. There is one algorithm for each.

7Flipped Edge

Goal: 0, 2 or 4 yellow edges on top - as on a 3x3 - and then the usual yellow cross.

When in the yellow cross stage you see one or three edges with yellow facing up, one edge is flipped - impossible on a 3x3. Turn the top (U) so that an edge without yellow on top is at the front, and do:

Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'

The algorithm is long, but it has a simple rhythm: there is a U2 between every wide move. After the first Rw U2 you rotate the whole cube (x) and from then on you hold it in the new position. Along the way the cube looks badly scrambled - do not stop. At the end yellow is on top again, and the first two layers return to their place.

After the algorithm the top layer is a little mixed up (other edges may change places), but the number of yellow edges on top is now even. Finish the yellow cross with F R U R' U' F', as on a 3x3.

8Two Corners in Place

Goal: 0, 1 or 4 corners in place - as on a 3x3 - and then the usual corner placement.

In the “corners into place” stage on a 3x3 there are zero, one or all four yellow corners in place. On a 4x4 there can be exactly two - then the algorithm from the 3x3 course will not help. The same applies when no corner was in place and after the algorithm from the 3x3 course exactly two are. Do this from any side:

2R2 U2 2R2 Uw2 2R2 Uw2

The algorithm swaps the front and back edges of the top layer (and turns the top itself by a half turn - the lower layers stay untouched). After it, go back to the “yellow edges” stage (R U R' U R U2 R' U) and continue solving like a 3x3 - this time the corners can be placed.

Mind the notation: 2R2 is a half turn of only the second layer from the right, and Uw2 - a half turn of the two top layers at once.

Done - the 4x4 cube is solved. The first solves will take a dozen or so minutes, but after a few times the centres and edges will start to flow.

Cheat Sheet: All Algorithms

Everything you need to remember in one place. The stage 6 algorithms are in the 3x3 course cheat sheet.

Printable cheat sheet (A4 / PDF)

1. Centre - empty spot in the back-left corner of the top, centre piece in the bottom-right corner of the front: 2R U 2R'. From the bottom to the front: left half of the bottom, 2R' D2 2R.
2. Centre order - white, yellow opposite; then white on the left, yellow on the right: green, orange on top with green at the back, finally blue and red. Check: white on the bottom, green at the front - red on the left. Swapping two adjacent centres (top and front): (2R U2 2R') F2 U2 (2R U2 2R').
3. Edges - unpaired one at the front left, the other half at the front right, both at the top: Uw' R U R' F R' F' R Uw. Half at the bottom of the right edge: first R U R' F R' F' R.
4. Flipped edge (1 or 3 yellow edges) - edge without yellow on top at the front: Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'.
5. Two corners in place - from any side: 2R2 U2 2R2 Uw2 2R2 Uw2, then yellow edges again.

Solve It Yourself

A practice simulator. You can scramble the whole cube or choose a stage - then you get a random cube with the previous stages solved. You turn an inner layer by dragging a sticker in the second row, or with the 2R and 2L buttons.

Common Problems

I did an algorithm and it is worse than before

The most common cause on a 4x4 is mixing up layers: Rw turns two layers, 2R only the inner one, and R only the outer one. The second - direction: 2L, Lw and D, just like L, count as “clockwise” looking at that face (go back to stage 1 and click these moves). Do the algorithm slowly, move by move along with the animation, and do not stop halfway.

When inserting a centre piece, one that was already on top escapes

There was a white piece in the back-left corner of the top - 2R U 2R' sends that corner to the front. Before the move always turn the top so that the back-left corner is an empty spot.

The centres are in the wrong order

It is best to catch this right after the centres - at the end of stage 4 there is a check and a centre swap. If you only notice it while solving like a 3x3, there are two symptoms: an edge does not fit between any two neighbouring centres (two adjacent centres swapped), or a corner does not fit any slot even though the colours around it match (red swapped with orange - the colours are in mirrored order). Then swap the centres as in stage 4. The swap algorithm breaks up a few edge pairs, so afterwards pair them again (stage 5) and solve the 3x3 part from scratch.

After the stage 5 algorithm the centres are scattered

The Uw at the end was missing, or one layer was turned instead of the two top ones. Uw' and Uw must turn both top layers together.

My cube has a different colour scheme

Older and unusual cubes may have a different layout. Then you can read the centre order from any corner, because corners always have their colours in the right order. Example for stage 4: hold the cube with the white centre on the left and green at the back, find the white-green-orange corner (or the one with your third colour) and turn the outer layers until its white sticker faces left and its green one faces back. The third sticker then faces up or down - that is where you build the centre of that colour.

The cube locks up when turning an inner layer

This is a common problem on a 4x4: before a 2R or Uw turn the other layers must be aligned, otherwise the pieces catch on each other, and on cheap cubes they can even pop out. Magnetic cubes align the layers by themselves and make learning much easier. See 4x4 cubes.

How long does it take to learn?

If you can solve a 3x3, there are only a few new things: two moves for the centres, two for the edges and two parities. Most people solve the 4x4 with the course after two or three evenings. This method needs around 300-400 moves, so at first a solve takes 10 minutes or longer, but with practice it drops below 3 minutes.

What Next?

Once you can solve the cube a few times without looking at the course, start timing yourself. You will gain the most on the centres and edges:

• Bars instead of single centre pieces - make a bar of two centre pieces on the front (vertical, in the right column), turn the top so that its left half is empty, and insert the bar at once: 2R U2 2R' swaps the left half of the top with the right half of the front.
• Several edges at once - advanced solvers pair halves “on the fly”, without an algorithm for each pair (the 3-2-3 or 6-6 method).
• The Yau method - the most popular among competitors: first two centres, then three edges of the white cross, then the rest of the centres and edges. The cross is built along the way, so the 3x3 part is shorter.
• Shorter parities - competitors use versions with 2R moves that can be executed faster, and recognise PLL parity as soon as the yellow face is solved.

The next step is the 5x5 cube - you solve it with the same reduction, and its fixed centres and lack of parity in the 3x3 part make it even simpler. You will find the course below.