3x3x3Loading…

3x3x3 simulator and solver

Play a virtual 3x3x3 in your browser, or enter the colors of your own 3x3x3 and get a solution. Also known as Rubik's Cube.

Info

Pieces
TypeCountStickersPositionsOrientation (physical)Orientation (visual)
161641
21221222
383833
One row per orbit. Orientation counts are per position; multiple values mean positions differ.
Stickers
54
Axes
36 cut planes across them
Solver
Available
Distinct-piece states
≈ 4.33 × 10¹⁹1,038,048,078,587,756,544,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 24 turns of the whole puzzle= 43,252,003,274,489,856,000Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.
Visually distinct states
Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1 × reachable fraction.No visually interchangeable sticker-bearing pieces were found.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.
Put together at random
1 in 360 reaches the original sticker identities8!·3⁸ · 12!·2¹² · 6!·1⁶ = 373,697,308,291,592,355,840,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 1,038,048,078,587,756,544,000 arrangements the moves reach = 360This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Face turns

x
y
z

3×3 beginner method

Solve one layer, the middle edges, then the last layer. Open any phase to read it; its status follows the current cube.

The detected first-layer color defines the reference hold, with that layer below and the opposite color above. Prepare hold establishes the actual working hold for each algorithm.

First-layer cross

Build a cross around the bottom center, matching each edge's side sticker to its side center.

  1. Find an edge containing the first-layer color.
  2. Bring it above its matching side center, then turn it down into D.
  3. Keep the edges already placed. The suggested short sequence places one edge and restores the others.

U face turn

U

Turn this face clockwise.

F half turn

F2

Turn this face halfway around.

First-layer corners

Fill the four corners around the cross. All three stickers of each corner must match their centers.

  1. Find a first-layer corner and its matching bottom slot.
  2. If it is trapped in a wrong bottom slot, lift it into U first.
  3. Align it above the slot and insert it. Repeat for the remaining corners.

Before this phase: First-layer cross.

Insert or lift a corner

R U R'

Use the front-right slot. A corner already in a wrong bottom slot can first be lifted into U; then align and insert it. The other bottom corners and the cross stay solved.

Middle edges

Finish the first two layers by inserting the four edges that do not contain the last-layer color.

  1. Choose an upper-layer edge with neither the first-layer nor last-layer color.
  2. Match its front sticker to a center; insert it left or right according to its other sticker.
  3. If the needed edge is misplaced in the middle, use an insertion to bring it out first.

Before this phase: First-layer cross, First-layer corners.

Insert a middle edge to the right

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

Match the edge's front sticker to the front center. Its upper sticker belongs on the right. To extract a wrong middle edge, insert a top edge into that slot first.

Insert a middle edge to the left

U' L' U L U F U' F'

Match the edge's front sticker to the front center. Its upper sticker belongs on the left.

Last-layer cross

Turn the last-layer edge stickers upward. Their side colors do not need to match yet. This is the edge stage of two-look OLL: make the cross before orienting corners.

  1. Look only at the four last-layer edges: dot, L, line, or cross.
  2. Use the suggested setup and cross algorithm; check the new pattern.
  3. Repeat until all four edge stickers face U. If the cross is already present, skip edge orientation.

Before this phase: First-layer cross, First-layer corners, Middle edges.

Make the last-layer cross

[F: [R, U]]

Ignore the last-layer corners here. For a line, hold it left to right; for an L, use the back and left arms. A dot takes more than one application.

Last-layer face

Orient the four remaining corners so the entire last-layer color faces upward.

  1. The first two layers and last-layer cross stay completed.
  2. Use the suggested Sune, Anti-Sune, or Headlights case with its setup.
  3. Check the face again; a case may need more than one algorithm.
  4. Two-look OLL has seven corner-orientation patterns. The collection uses full OLL numbering: case 27 is Sune and case 26 is Anti-Sune. This beginner method can repeat short algorithms instead of using every direct case.

Before this phase: First-layer cross, First-layer corners, Middle edges, Last-layer cross.

Sune

R U R' U R U2 R'

Orient last-layer corners while keeping the first two layers and the cross. Some cases need another setup and application.

Anti-Sune

R U2 R' U' R U' R'

The inverse corner-orientation case. Use the suggested setup for the current arrangement.

Headlights

R2 D R' U2 R D' R' U2 R'

Orient a pair of last-layer corners. This restores the first two layers at the end of the algorithm.

Last-layer corners

Put each oriented last-layer corner between the correct three centers.

  1. Look for corners whose side colors match, and align the upper layer.
  2. Use an adjacent or diagonal corner swap as suggested.
  3. Edges may change position here. Keep the corners oriented and solve the edges next.
  4. In two-look PLL, T handles an adjacent corner swap and Y a diagonal swap. Skip corner permutation when the corners are already correct.

Before this phase: First-layer cross, First-layer corners, Middle edges, Last-layer cross, Last-layer face.

Adjacent corner swap

[R, U] R' F R2 U' R' U' R U R' F'

Swap the two upper-right corners. Last-layer edges also move; they are solved in the next phase.

Diagonal corner swap

F R U' R' U' R U R' F' [R, U] R' F R F'

Swap diagonally opposite last-layer corners. Last-layer edges also move; their orientation stays intact.

Last-layer edges

Cycle the final edges into their matching slots. All corners and earlier layers stay solved.

  1. If an edge matches its side center, keep it at the back of the working hold.
  2. Use the three-edge cycle in the required direction.
  3. With no matching edge, use one cycle to create a simpler case, then finish.
  4. The two-look PLL collection also offers H for opposite edge swaps and Z for adjacent edge swaps. They are direct alternatives to repeated three-edge cycles. Upper-layer alignment may be needed before and after a case.

Before this phase: First-layer cross, First-layer corners, Middle edges, Last-layer cross, Last-layer face, Last-layer corners.

Cycle three edges

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

Keep a correctly placed last-layer edge at the back. Cycle the other three without moving any corners.

Cycle three edges in reverse

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

The opposite three-edge cycle. With no matching edge, one cycle creates a case with a matching edge.

3×3 CFOP

Cross, corner–edge pairs, orientation, then permutation. The suggestions use intuitive F2L insertions and the full OLL/PLL collections.

The detected first-layer color defines the reference hold, with that layer below and the opposite color above. Prepare hold establishes the actual working hold for each algorithm.

First-layer cross

Build a cross around the bottom center, matching each edge's side sticker to its side center.

  1. Find an edge containing the first-layer color.
  2. Bring it above its matching side center, then turn it down into D.
  3. Keep the edges already placed. The suggested short sequence places one edge and restores the others.

U face turn

U

Turn this face clockwise.

F half turn

F2

Turn this face halfway around.

F2L pairs

F2L means First Two Layers. After the cross, solve each first-layer corner together with its matching middle-layer edge. Four pairs complete the first two layers.

  1. Find a matching corner and edge, and the slot between their side centers.
  2. Extract pieces if needed, connect them in U, then insert the pair.
  3. Repeat for four slots while preserving the cross and completed pairs.
  4. These basic insertions open a slot, connect or align the pair and close the slot. They are building blocks for intuitive solving, rather than a list of every F2L case. Suggestions may combine them for the current position.

Before this phase: First-layer cross.

Pair insertion through R

R U R'

Open the slot, align or connect the corner and edge in U, then close the slot. These short insertions also extract pieces from a wrong slot. Preserve the cross and completed pairs.

Pair insertion through R

R U' R'

Open the slot, align or connect the corner and edge in U, then close the slot. These short insertions also extract pieces from a wrong slot. Preserve the cross and completed pairs.

OLL

OLL means Orientation of the Last Layer. Keep F2L solved and make the whole top face one color; side-color positions are handled by PLL afterwards.

  1. Read the upper-color pattern on U and the side faces.
  2. Use the suggested hold and the matching OLL case.
  3. Align U to the case before applying. A complete top face is an OLL skip.
  4. If learning fewer algorithms first, two-look OLL makes the cross and then orients the corners; those algorithms are in the collection.

Before this phase: First-layer cross, F2L pairs.

OLL 1

R U2 R2 F R F' U2 R' F R F'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 2

[F: [R, U]] [Fw: [R, U]]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 3

[Fw: [R, U]] U' [F: [R, U]]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 4

[Fw: [R, U]] U [F: [R, U]]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 5

Rw' U2 R U R' U Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 6

Rw U2 R' U' R U' Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 7

Rw U R' U R U2 Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 8

Rw' U' R U' R' U2 Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 9

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 10

R U R' U R' F R F' R U2 R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 11

Rw' R2 U R' U R U2 R' U M'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 12

M' R' U' R U' R' U2 R U' M

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 13

(Rw U' Rw' U' Rw U Rw' y' R' U R) y

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 14

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 15

Rw' U' Rw R' U' R U Rw' U Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 16

Rw U Rw' R U R' U' Rw U' Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 17

R U R' U R' F R F' U2 R' F R F'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 18

(y R U2 R2 F R F' U2 M' U R U' Rw') y'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 19

[M: U [R, U]] [R', F]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 20

M U R U R' U' M2 U R U' Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 21

(R U2 R') (U' R U R') (U' R U' R')

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 22

R U2 R2 U' R2 U' R2 U2 R

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 23

R2 D R' U2 R D' R' U2 R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 24

(Rw U R' U') (Rw' F R F')

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 25

(y F' (Rw U R' U') Rw' F R) y'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 26

R U2 R' U' R U' R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 27

(R U R' U) (R U2 R')

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 28

Rw U R' U' M U R U' R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 29

(y R U R' U' R U' R' F' U' F R U R') y'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 30

(y' F U R U2 R' U' R U2 R' U' F') y

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 31

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 32

R U B' U' R' U R B R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 33

[R, U] [R', F]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 34

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 35

R U2 R2 F R F' R U2 R'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 36

R' U' R U' R' U R U Lw U' R' U x

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 37

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 38

(R U R' U) (R U' R' U') [R', F]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 39

L F' L' U' L U F U' L'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 40

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 41

R U R' U R U2 R' F R U R' U' F'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 42

R' U' R U' R' U2 R F R U R' U' F'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 43

(y R' U' F' U F R) y'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 44

[Fw: [R, U]]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 45

[F: [R, U]]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 46

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

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 47

[F': [L', U']2]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 48

[F: [R, U]2]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 49

Rw U' Rw2 U Rw2 U Rw2 U' Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 50

Rw' U Rw2 U' Rw2 U' Rw2 U Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 51

[Fw: [R, U]2]

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 52

(R' U' R U' R' U y' R' U R B) y

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 53

Rw' U' R U' R' U R U' R' U2 Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 54

Rw U R' U R U' R' U R U2 Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 55

(y R' F R U R U' R2 F' R2 U' R' U R U R') y'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 56

Rw' U' Rw U' R' U R U' R' U R Rw' U Rw

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

OLL 57

R U R' U' M' U R U' Rw'

Match the upper-color pattern, including its side stickers. Orient the complete last layer while preserving F2L.

PLL

PLL means Permutation of the Last Layer. Arrange the already-oriented last-layer corners and edges while preserving F2L.

  1. Match the side-color blocks and exchanged pieces.
  2. Align the upper layer to the case, apply its algorithm, then use the final U alignment (AUF, Adjust Upper Face) if needed.
  3. Two-look PLL separates corner permutation from edge permutation and is a smaller set to learn first.

Before this phase: First-layer cross, F2L pairs, OLL.

Aa

[x: (R' U R') D2 (R U' R') D2 R2]

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ab

[x: R2 D2 (R U R') D2 (R U' R)]

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

E

[x': (R U' R' D) (R U R' D') (R U R' D) (R U' R' D')]

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

F

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ga

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Gb

F' U' F R2 Uw R' U R U' R Uw' R2

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Gc

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Gd

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

H

[M2: U] U2 [M2: U]

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ja

R' U L' U2 R U' R' U2 R L U'

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Jb

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Na

R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Nb

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ra

R U' R' U' R U R D R' U' R D' R' U2 R' U'

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Rb

R' U2 R U2 R' F R U R' U' R' F' R2 U'

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

T

[R, U] (R' F R2 U') R' U' (R U R' F')

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ua

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Ub

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

V

(R' U R' U' y R' F' R2 U' R' U R' F R F) y'

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Y

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

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Z

M2 U M2 U M' U2 M2 U2 M' U2

Match the side-color permutation. This permutes the oriented last layer; an upper-layer alignment may be needed before or afterwards.

Kociemba two-phase

Visualize the computer solver's two phases. The suggested sequence is calculated for the current cube; it is not a fixed human solving recipe.

Use the cube's original U/D axis. Prepare hold restores that frame after whole-cube rotations or slice moves. Face half-turns are animated as two quarter-turns.

Phase 1: Reduce to G1

Orient all eight corners and all twelve edges, and put the four middle-slice edges into the middle slice. The pieces can still be permuted.

  1. The search may use any face turn to reach this goal.
  2. Corner orientation is measured against the U/D faces. Edge orientation follows the solver's facelet frame, including the F/B stickers on middle-slice edges.
  3. The goal is the subgroup G1, whose positions can be solved using U and D turns plus R2, L2, F2 and B2.

Phase 2: Solve within G1

Permute the oriented corners and edges into their solved positions while keeping the cube inside G1 after each face turn.

  1. First complete phase 1: orient every piece and place the middle-slice edges in their slice.
  2. Use only U, U′, U2, D, D′, D2, R2, L2, F2 and B2.
  3. The search computes the complete remaining sequence for this position. Run suggested step and Skip phase both play the whole phase.

Before this phase: Phase 1: Reduce to G1.

Well known algorithms and patterns

Beginner

Right trigger

[R, U]

Left trigger

[L', U']

Middle edge — right

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

Middle edge — left

U' L' U L U F U' F'

Last-layer cross

[F: [R, U]]

Sune

(R U R' U) (R U2 R')

Anti-Sune

R U2 R' U' R U' R'

Corner twist (repeat with setup)

[R', D']

Keep a twisted corner at UFR. Repeat twice or four times, then use U to bring the next corner to UFR. Finish the whole corner procedure to restore the temporarily disturbed lower layers.

Corner permutation — T

[R, U] (R' F R2 U') R' U' (R U R' F')

Edge cycle — Ua

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

Edge cycle — Ub

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

OLL

OLL 1

R U2 R2 F R F' U2 R' F R F'

OLL 2

[F: [R, U]] [Fw: [R, U]]

OLL 3

[Fw: [R, U]] U' [F: [R, U]]

OLL 4

[Fw: [R, U]] U [F: [R, U]]

OLL 5

Rw' U2 R U R' U Rw

OLL 6

Rw U2 R' U' R U' Rw'

OLL 7

Rw U R' U R U2 Rw'

OLL 8

Rw' U' R U' R' U2 Rw

OLL 9

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

OLL 10

R U R' U R' F R F' R U2 R'

OLL 11

Rw' R2 U R' U R U2 R' U M'

OLL 12

M' R' U' R U' R' U2 R U' M

OLL 13

Rw U' Rw' U' Rw U Rw' y' R' U R

OLL 14

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

OLL 15

Rw' U' Rw R' U' R U Rw' U Rw

OLL 16

Rw U Rw' R U R' U' Rw U' Rw'

OLL 17

R U R' U R' F R F' U2 R' F R F'

OLL 18

y R U2 R2 F R F' U2 M' U R U' Rw'

OLL 19

[M: U [R, U]] [R', F]

OLL 20

M U R U R' U' M2 U R U' Rw'

OLL 21

(R U2 R') (U' R U R') (U' R U' R')

OLL 22

R U2 R2 U' R2 U' R2 U2 R

OLL 23

R2 D R' U2 R D' R' U2 R'

OLL 24

(Rw U R' U') (Rw' F R F')

OLL 25

y F' (Rw U R' U') Rw' F R

OLL 26

R U2 R' U' R U' R'

OLL 27

(R U R' U) (R U2 R')

OLL 28

Rw U R' U' M U R U' R'

OLL 29

y R U R' U' R U' R' F' U' F R U R'

OLL 30

y' F U R U2 R' U' R U2 R' U' F'

OLL 31

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

OLL 32

R U B' U' R' U R B R'

OLL 33

[R, U] [R', F]

OLL 34

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

OLL 35

R U2 R2 F R F' R U2 R'

OLL 36

R' U' R U' R' U R U Lw U' R' U x

OLL 37

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

OLL 38

(R U R' U) (R U' R' U') [R', F]

OLL 39

L F' L' U' L U F U' L'

OLL 40

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

OLL 41

R U R' U R U2 R' F R U R' U' F'

OLL 42

R' U' R U' R' U2 R F R U R' U' F'

OLL 43

y R' U' F' U F R

OLL 44

[Fw: [R, U]]

OLL 45

[F: [R, U]]

OLL 46

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

OLL 47

[F': [L', U']2]

OLL 48

[F: [R, U]2]

OLL 49

Rw U' Rw2 U Rw2 U Rw2 U' Rw

OLL 50

Rw' U Rw2 U' Rw2 U' Rw2 U Rw'

OLL 51

[Fw: [R, U]2]

OLL 52

R' U' R U' R' U y' R' U R B

OLL 53

Rw' U' R U' R' U R U' R' U2 Rw

OLL 54

Rw U R' U R U' R' U R U2 Rw'

OLL 55

y R' F R U R U' R2 F' R2 U' R' U R U R'

OLL 56

Rw' U' Rw U' R' U R U' R' U R Rw' U Rw

OLL 57

R U R' U' M' U R U' Rw'

PLL

Aa

[x: (R' U R') D2 (R U' R') D2 R2]

Ab

[x: R2 D2 (R U R') D2 (R U' R)]

E

[x': (R U' R' D) (R U R' D') (R U R' D) (R U' R' D')]

F

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

Ga

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

Gb

F' U' F R2 Uw R' U R U' R Uw' R2

Gc

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

Gd

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

H

[M2: U] U2 [M2: U]

Ja

R' U L' U2 R U' R' U2 R L U'

Jb

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

Na

R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'

Nb

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

Ra

R U' R' U' R U R D R' U' R D' R' U2 R' U'

Rb

R' U2 R U2 R' F R U R' U' R' F' R2 U'

T

[R, U] (R' F R2 U') R' U' (R U R' F')

Ua

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

Ub

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

V

R' U R' U' y R' F' R2 U' R' U R' F R F

Y

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

Z

M2 U M2 U M' U2 M2 U2 M' U2

F2L

F2L — right insertion

R U R'

Basic intuitive F2L insertion. Match the corner–edge pair and its destination slot before applying. Use the inverse insertion to extract a piece from an incorrect slot; preserve the cross and completed pairs.

F2L — right reverse insertion

R U' R'

Basic intuitive F2L insertion. Match the corner–edge pair and its destination slot before applying. Use the inverse insertion to extract a piece from an incorrect slot; preserve the cross and completed pairs.

F2L — front insertion

F' U F

Basic intuitive F2L insertion. Match the corner–edge pair and its destination slot before applying. Use the inverse insertion to extract a piece from an incorrect slot; preserve the cross and completed pairs.

F2L — front reverse insertion

F' U' F

Basic intuitive F2L insertion. Match the corner–edge pair and its destination slot before applying. Use the inverse insertion to extract a piece from an incorrect slot; preserve the cross and completed pairs.

2-look OLL

2-look OLL — edge line

[F: [R, U]]

2-look OLL — edge L

[F: U R U' R']

2-look OLL — edge dot

[F: [R, U]] U2 [F: U R U' R']

2-look OLL — corner case 21

(R U2 R') (U' R U R') (U' R U' R')

2-look OLL — corner case 22

R U2 R2 U' R2 U' R2 U2 R

2-look OLL — corner case 23

R2 D R' U2 R D' R' U2 R'

2-look OLL — corner case 24

(Rw U R' U') (Rw' F R F')

2-look OLL — corner case 25

y F' (Rw U R' U') Rw' F R

2-look OLL — corner case 26

R U2 R' U' R U' R'

2-look OLL — corner case 27

(R U R' U) (R U2 R')

2-look PLL

2-look PLL — T

[R, U] (R' F R2 U') R' U' (R U R' F')

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

2-look PLL — Y

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

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

2-look PLL — Ua

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

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

2-look PLL — Ub

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

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

2-look PLL — H

[M2: U] U2 [M2: U]

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

2-look PLL — Z

M2 U M2 U M' U2 M2 U2 M' U2

Permute corners first (T for adjacent or Y for diagonal), then permute edges (Ua, Ub, H or Z). Match the side-color pattern and align U before and after applying.

Patterns

Checkerboard

M2 E2 S2

Superflip

U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2

Six spots

U D' R L' F B' U D'

Four spots

[M2: E] E'

Derived commutator variant: swaps four centers, preserving all corners and edges.

Cube in a cube

F L F U' R U F2 L2 U' L' B D' B' L2 U