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Rubik's Cube 4×4

Solve the Rubik's Cube 4×4

The 4×4 has no fixed centres and two extra layers. The reduction method turns it back into a 3×3: build the centres, pair the edges, then solve it the way you already know — with two parity cases to watch for.

Start with the notation →
4
layers
24
centre pieces
24
edge pieces
6
algorithms to memorise

The reduction method

Four stages. Each one hands a simpler cube to the next, until the last stage is an ordinary 3×3 solve.

Stage 1

Solve the centre pieces

Gather the four centre pieces of each colour into one solid block in the middle of all six faces.

Stage 2

Pair the edge pieces

Join the 24 edge pieces into 12 matching pairs, so each edge behaves like a single 3×3 edge.

Stage 3

Solve it like a 3×3

Use any 3×3 method. Two states can appear that a 3×3 never produces; those are the parities.

Stage 4

Done

Every face is a single colour.

Notation

This guide keeps the notation of the printed GAN sheet. The prefix comes first and the face second: TR, not Rw.

A single letter turns only that outer face.

R
L
U
D
F
B
TR
A T before the letter turns two layers of that side at once. TR turns the right face together with the layer behind it.
TL
TU
MR
An M before the letter turns only the inner layer of that side, leaving the outer face still.
MU
TR
A plain letter turns 90° clockwise, seen from directly in front of that side.
TR'
An apostrophe means the inverse: turn 90° counterclockwise.
TR2
A 2 means turn the face twice, a half turn. Direction does not matter.
TR'2
'2 is a half turn made counterclockwise. It leaves the cube in the same place as 2; the direction is written down only so your hands follow the printed sheet.

x, y and z rotate the whole cube; nothing is held still.

Stage 1

Solve the centre pieces

Each face needs its four centre pieces gathered into one block. A dashed outline marks the slot the piece you are moving has to reach.

  1. 01Start with the yellow face. Bring all four yellow centre pieces together.
  2. 02Turn the cube over and do the same for the white face.
  3. 03Finish the four remaining faces one at a time.

Centres are not fixed

On a cube with an even number of layers the centres can move, so no colour has a permanent home. Memorise the layout you are building instead.

On the GAN460 it is yellow up, white down, orange left, red right, blue front and green back.

Piece being tracked — solid outlineTarget or working slot — dashed outlineSticker that does not matter yet

The dashed outline on the top face is the target slot. The solid pink outline follows the yellow centre piece you are moving.

Turn the face holding the piece until it sits in the lower left of that face's four centre tiles, then turn the top until the target slot is in the back left of its block.

The centre piece is on a side face

Algorithm 1
Start
Finished state

Algorithm 1

TR U TR'

Use this when the centre piece you need is sitting on one of the side faces.

TR
U
TR'
Open this caseAlgorithm 1

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 1UFR
Before
After · Algorithm 1UFR
After

The yellow centre is complete. Repeat for the remaining faces, keeping the correct colour layout.

Move by move · 3 moves

  1. TRTR — turn the two right layers 90° clockwise.
  2. UU — turn the upper face 90° clockwise.
  3. TR'TR' — turn the two right layers 90° counterclockwise.

The centre piece is on the bottom face

Algorithm 2
Holding view
Bottom viewStart
Finished state

Algorithm 2

TR2 U TR'2

Use this when the centre piece you need is on the bottom face.

TR2
U
TR'2
Open this caseAlgorithm 2

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 2DFR
Before
After · Algorithm 2UFR
After

The yellow centre is complete. Repeat for the remaining faces, keeping the correct colour layout.

Move by move · 3 moves

  1. TR2TR2 — turn the two right layers 180°.
  2. UU — turn the upper face 90° clockwise.
  3. TR'2TR'2 — turn the two right layers 180°.

Do the yellow face first, then white opposite it, then the four remaining faces. From the third face on, the colours must run in the order you are building — a centre in the right place but on the wrong face is still wrong.

Stage 2

Pair the edge pieces

Two edge pieces showing the same two colours belong together. Work in the two edge slots on the right side, marked with dashed outlines.

  1. 01Pick any pair of edge pieces — red and blue in the pictures — and use Algorithm 3 to line them up in the working slots.
  2. 02When the four edges on the top are all paired, flip the cube and repeat until the remaining four are paired too.
Piece being tracked — solid outlineTarget or working slot — dashed outlineSticker that does not matter yet
Front + right view
Front + left viewTwo edge pieces of the same two colours, apartStep 1
The same two pieces, joined into one edgeStep 2
Flip the cube and pair the rest

Algorithm 3

TU' R U R' TU

Lines up two matching edge pieces into a finished pair.

Open this caseAlgorithm 3

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 3UFR
Before
After · Algorithm 3UFR
After

The shown wings are paired. Continue pairing the remaining edges.

Move by move · 5 moves

  1. TU'TU' — turn the two upper layers 90° counterclockwise.
  2. RR — turn the right face 90° clockwise.
  3. UU — turn the upper face 90° clockwise.
  4. R'R' — turn the right face 90° counterclockwise.
  5. TUTU — turn the two upper layers 90° clockwise.

If the last two pairs will not come together, Algorithm 4 breaks the deadlock.

Algorithm 4

TU' R U R' F R' F' R TU

Use this when the last two edge pairs refuse to resolve.

Front + right view
Front + left viewBefore
Front + right view
Front + left viewAfter
Open this caseAlgorithm 4

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 4UFR
Before
After · Algorithm 4UFR
After

The shown wings are paired. Continue pairing the remaining edges.

Move by move · 9 moves

  1. TU'TU' — turn the two upper layers 90° counterclockwise.
  2. RR — turn the right face 90° clockwise.
  3. UU — turn the upper face 90° clockwise.
  4. R'R' — turn the right face 90° counterclockwise.
  5. FF — turn the front face 90° clockwise.
  6. R'R' — turn the right face 90° counterclockwise.
  7. F'F' — turn the front face 90° counterclockwise.
  8. RR — turn the right face 90° clockwise.
  9. TUTU — turn the two upper layers 90° clockwise.

A finished pair does not have to sit beside matching centres yet. Pairing is all that matters here; the 3×3 solve puts the pairs where they belong.

Stage 3

Solve it like a 3×3 and fix the parities

The cube now behaves like a 3×3, so solve it with the method you already use. Stop when one of the two states below appears — neither of them can happen on a real 3×3.

Parity A — the cross will not close

Two variations show up while making the cross on the top side. The same algorithm fixes both.

Algorithm 5

TR U2 x TR U2 TR U2' TR' U2 TL U2 TR' U2' TR U2 TR' U2' TR'

Fixes Parity A, the cross that will not close.

Open this caseAlgorithm 5

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 5UFR
Before
After · Algorithm 5UFR
After

The flipped edge pair is corrected. Continue solving the last layer as on a 3×3.

Move by move · 18 moves

  1. TRTR — turn the two right layers 90° clockwise.
  2. U2U2 — turn the upper face 180°.
  3. xx — turn the whole cube in the direction of R 90° clockwise.
  4. TRTR — turn the two right layers 90° clockwise.
  5. U2U2 — turn the upper face 180°.
  6. TRTR — turn the two right layers 90° clockwise.
  7. U2'U2' — turn the upper face 180°.
  8. TR'TR' — turn the two right layers 90° counterclockwise.
  9. U2U2 — turn the upper face 180°.
  10. TLTL — turn the two left layers 90° clockwise.
  11. U2U2 — turn the upper face 180°.
  12. TR'TR' — turn the two right layers 90° counterclockwise.
  13. U2'U2' — turn the upper face 180°.
  14. TRTR — turn the two right layers 90° clockwise.
  15. U2U2 — turn the upper face 180°.
  16. TR'TR' — turn the two right layers 90° counterclockwise.
  17. U2'U2' — turn the upper face 180°.
  18. TR'TR' — turn the two right layers 90° counterclockwise.

Parity B — two opposite edges will not swap

The top face is solved except for two edges sitting directly opposite each other.

Algorithm 6

MR2 U2 MR2 TU2 MR2 MU2

Fixes Parity B, the two opposite edges that will not swap.

Open this caseAlgorithm 6

Before and after show the same example as the animation. Grey stickers hide pieces outside this example; the GAN diagrams above simplify the step.

Before · Algorithm 6UFR
Before
After · Algorithm 6UFR
After

The exchanged edge pairs are corrected. Check the last layer and continue the 3×3 solve.

Move by move · 6 moves

  1. MR2MR2 — turn the inner slice next to the right face 180°.
  2. U2U2 — turn the upper face 180°.
  3. MR2MR2 — turn the inner slice next to the right face 180°.
  4. TU2TU2 — turn the two upper layers 180°.
  5. MR2MR2 — turn the inner slice next to the right face 180°.
  6. MU2MU2 — turn the inner slice under the upper face 180°.

If the last layer ends in any of the three states the sheet shows, run Algorithm 6 once in any direction, then carry on with your usual 3×3 method.

Stage 4

Done

All six faces are a single colour. If a face is still mixed, go back to the stage that broke and repeat it.