3×3 and 2×2 cube · CFOP, Roux, ZZ

Cube Handbook

From your first solve to speedsolving: a beginner guide, all 119 CFOP algorithms, Roux, ZZ and 2×2. Each algorithm is the fewest-move solution found by computer, with the speedcubers’ common alg alongside. Press Play on any card to watch a 3D cube play it move by move.

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Watch CFOP in action

One solve from start to finish

Scroll down to watch the cube get scrambled and then solved through the 4 steps. The solution comes from the solver on this page and uses the algorithms in this handbook.

    Start here

    What order to learn in

    1. Notation and grip. Hold the cube with white on the bottom, yellow on top, green in front, orange on the right, red on the left. Every figure on this page uses this orientation. Colors do not match your cube? Change them in .
    2. Intuitive cross. No algorithms needed. Practice solving the cross in under 8 moves and planning it during the 15-second inspection.
    3. Intuitive F2L first, then the tables. Understand how pairing works first. The 41-case table then helps you find shorter solutions.
    4. 2-look OLL (10 algorithms). 3 edge-orientation cases plus the 7 cases OLL 21–27, marked 2-look.
    5. 2-look PLL (6 algorithms). T and Y for corners; Ua, Ub, H and Z for edges.
    6. Full 21 PLL, then full 57 OLL. 1–2 algorithms a day. Tick Learned to track your progress (saved in this browser).
    New to the cube · start here

    Solving the cube for beginners

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    The layer-by-layer method needs only 6 short algorithms. Work through the 7 steps below; each has figures and a 3D cube you can play. When you can do a step, tick Got it. Once you can solve it, move on to CFOP to get faster.

    Hold the cube with white on the bottom, yellow on top (step 1 builds the cross on top, then flips it down). See Notation if the letters R, U, F are new to you.

    Solved it?Steps 1–3 are a slow Cross and F2L, steps 4–7 are 2-look OLL and PLL. Continue with Cross, F2L then OLL and PLL to get under 30 seconds.
    WCA notation · fingertricks

    Notation and turning

    Each letter is a face, turned 90° clockwise as seen when looking straight at that face. A ' means counterclockwise, and a 2 means 180°.

    How to hold the cube (home grip)

    • C Both thumbs rest on the front face, around the middle and bottom rows.
    • T Both index fingers rest lightly on the top face near the two front corners. They flick U and U'.
    • Middle and ring fingers support the back face. The ring fingers also flick D, B and M.
    • Hold lightly with relaxed wrists. Turn R and L with the wrist, not with the fingers.
    • Return to this grip after every move. The fewer regrips you need, the faster you solve.

    Which finger turns each move

    Arrows show the turn direction seen from the front. Press Play to watch the 3D cube do that move.

    Fingertrick drills

    Repeat each sequence until your hands flow without looking. Doing R U R' U' exactly 6 times returns the cube to where it started.

    Notation table

    R L U D F BRight, Left, Up, Down, Front, Back
    r l u d f bTurn 2 layers at once (also written Rw, Lw…)
    M E SMiddle slices. M turns like L, E like D, S like F
    x y zRotate the whole cube like R, U, F
    Move countEach face, double-layer (r, u…) or slice (M, E, S) turn is 1 move, including 180° turns. Whole-cube rotations (x, y, z) are free. U turns that align the layer at the start (and at the end for PLL) are not counted
    Fewest movesThe shortest algorithm available: the optimal solver result (face turns only), or the common speedcubing algorithm when it is as short or shorter (usually thanks to M moves). When the shortest solution uses awkward L, B or D turns, the common algorithm is listed too: longer, but faster to execute
    Step 1 · 23 cases for each edge

    Cross

    Bring the 4 white edges to the bottom face so that the side color of each one matches its center. Nothing to memorize here, but you need to plan: good solvers plan the whole cross during the 15-second inspection, then execute it in 1–2 seconds.

    Full table: a white edge can only be in 12 positions with 2 orientations each; leaving out the solved one gives 23 cases. Pick an edge below. Each algorithm is the fewest-move solution found by computer, holding the cube like every other figure on this page (green in front).

    Each card has two 3D views, from the front-top and from the back-bottom, so the edge is visible wherever it is. Only white edges are colored.

    Edge white paired with:

    Solve the cross on the bottomDo not build it on top and flip the cube, or you cannot see ahead into F2L.
    At most 8 movesEvery cross can be solved in 8 moves, about 6 on average.
    Practice blind crossInspect, close your eyes, solve the cross, then look and check. It is the best inspection drill.
    Step 2 · 41 cases

    F2L

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    Join a white corner with its matching edge into a pair, then insert the pair into its slot. Do it 4 times and the first two layers are done. All figures use the front-rightslot; for other slots, mirror the algorithm or rotate the cube.

    Only the pair being solved and the finished parts are colored; other top-layer pieces are grey. Every algorithm is checked to keep the cross and the other 3 slots intact.

    Easy · 6 casesYou only need the 6 basic cases below, including the 4 inserts R U R’, U R U’ R’, F’ U’ F, U’ F’ U F. For anything else, split the corner and edge apart and bring them to one of these 6.

    Understand, do not memorizeMost cases go: separate the corner and edge, join them into a pair, then insert with R U R' or F' U' F.
    Look-aheadWhile inserting the current pair, look for the next one. Practice by solving slowly without pausing.
    Avoid cube rotationsUse U to bring the pair into position instead of rotating with y.
    Step 3 · 57 cases

    OLL

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    Make the top face all yellow. The 3D figure looks down at an angle. The small inset is the top face seen straight on, with the front at the bottom; bars on its border are yellow stickers facing sideways. Numbering follows the standard.

    Just starting? Use 2-look OLL. First make the yellow cross with one of the 3 algorithms below, then orient the corners with OLL 21–27.

    2-look OLL: yellow cross 3

    Easy · 2-look OLL, 10 algorithmsStep 1: make the yellow cross with one of 3 algorithms. Step 2: orient the 4 corners with one of the 7 algorithms OLL 21–27.

    Step 4 · 21 cases

    PLL

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    The top is yellow; now move the last-layer pieces into place. Arrows show where the pieces go. To recognize a case, look for headlights (two matching corners on one side) and bars of 3 matching stickers.

    Just starting? 2-look PLL. Swap corners with T (2 adjacent corners) or Y (2 diagonal corners), then cycle edges with Ua, Ub, H or Z.

    Easy · 2-look PLL, 6 algorithmsStep 1: swap corners with T (adjacent) or Y (diagonal). Step 2: cycle edges with Ua, Ub, H or Z.

    CFOP · after OLL and PLL

    Advanced CFOP

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    Two sets that shorten the last layer. Each algorithm is the fewest-move solution using only R, U, F, found by computer and checked to keep F2L intact.

    Advanced materialCOLL and Winter Variation are for solvers who know full OLL and PLL. Choose Full at the top to see all 67 algorithms.

    COLL · 40 algorithmsUse it when the yellow cross is done but the corners are not. One algorithm orients and permutes all 4 corners, leaving only an edge PLL (Ua, Ub, H, Z) or a solved cube.
    Winter Variation · 27 algorithmsUse it when the last pair goes in with R U R’ and the yellow edges are oriented. It inserts the pair and orients all 4 corners, skipping OLL.

    COLL

    Winter Variation

    Figures: the last pair waits above the front-right slot, ready for R U R’. The inset is the top face seen straight on.

    Roux method · blocks and M moves

    Roux

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    Roux solves in blocks instead of layers: two 1×2×3 blocks on the left and right, then the 4 top corners, then the last 6 edges with only M and U. About 45–50 moves on average, with just 42 CMLL algorithms to learn.

    2-look CMLL · 9 algorithms

    CMLL · 42 cases

    Solve the 4 top corners while keeping both blocks (the M slice and top edges may get scrambled). Figures color only the blocks and corners. Algorithms use only R, U, F.

    Try a Roux solveTab Solve a cube has a Roux mode: scan or enter a cube, choose Roux and see the full 4-step solution.
    ZZ method · orient the edges first

    ZZ

    ZZ orients all 12 edges right at the start. After that you only need R, U, L, never rotate the cube, and the last layer always starts with a yellow cross.

    Two F2L blocks · step by step

    After EOLine, hold white on the bottom, green in front. The DF and DB edges are already in place and every edge is oriented, so L, R and U are all you need. Build the left block first, then the right one.

    Last pair · R and U only · 20 cases

    Pair and insert the front-right corner and edge once the rest of the first two layers is done. Every algorithm uses only R and U and is the fewest moves possible. The front-left slot works the same way, mirrored: R becomes L′, R′ becomes L, and U turns the other way.

    What is a “bad” edge?Hold green in front. An edge is “good” if it can go home with only R, L, U, D, and “bad” if it needs a quarter turn of F or B. Quick check: on the front, back, top and bottom faces, an edge showing green/blue on U/D, or showing yellow/white on F/B, is bad. There is always an even number of bad edges.
    2×2 cube · Ortega method

    2×2

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    A 2×2 has only 8 corners. Ortega solves it in 3 steps: make one face a single color (positions do not matter yet), orient the opposite face with one of 7 algorithms, then permute both layers with one of 5. To go faster: finish the whole first layer, then solve the rest with one CLL algorithm.

    Algorithms use only R, U, F, so you never have to regrip. A 2×2 timer is in the Practice.

    Ortega · step 2: OLL (7)

    Ortega · step 3: PBL (5)

    Two views so the bottom layer is visible too. If only the bottom layer is swapped, flip the cube (z2) and treat it as the top.

    CLL · 42 cases

    With the first layer fully solved, solve the 4 top corners in one algorithm.

    4×4 cube · reduce to a 3×3

    4×4

    A 4×4 has no fixed centers and each edge comes in 2 halves. The common approach is to reduce it to a 3×3: build the 6 centers, pair the 12 edges, then solve it like a 3×3. A 4×4 can also show 2 situations called parity that a 3×3 never has; each needs just one algorithm.

    4×4 notation

    International (WCA) convention: looking straight at the named face, a plain letter is a 90° clockwise turn, ′ is counterclockwise and 2 is a half turn. Layers are counted from that face inwards. The coloured part of each picture is what turns; press Play to see the move. U, D, F, B and L are written the same way as R.

    Don’t mix them upWCA 4×4 scrambles only use outer-face moves (R) and two-layer moves (Rw, Uw, Fw). The inner-slice move 2R never appears in scrambles but is common in algorithms. Many sources write lowercase r for Rw; this page always writes Rw and 2R to keep things clear.

    The simple way · 4 steps

    Competition · the Yau method

    Many competitors use Yau: the cross is built while doing centers, so the 3×3 stage starts straight at F2L, and edge pairing is faster with fewer free edges.

    Spot parity earlyOLL parity: an odd number of yellow edges face up at OLL. PLL parity: the last layer shows something outside the 21 PLLs, such as only 2 edges swapped.
    WCA rules for 4×415 seconds of inspection, 5 solves averaged over the middle 3 (best and worst dropped). There is usually a time limit and a cutoff after the first 2 solves. Put the cube down and touch the timer with both hands to start and stop.
    Time goalsFirst solves: 3–5 minutes. Yau + 2-look CFOP: about 1 minute. Sub-40 needs good intuitive F2L, full OLL/PLL and smooth edge pairing.

    4×4 algorithms

    Timer practiceTab Practice has a 4×4 mode with scrambles in WCA notation.
    Choosing a method

    Comparing methods

    Every method solves the same 3×3, but splits the work differently. The table shows typical speedsolving numbers (average moves, each face or slice turn counting as 1); individual results vary a little.

    MethodStepsMove countAlgorithmRotate the whole cubeUsersCompetitionGood for
    Beginner7 layer-by-layer steps~1106A few—Not used in competitionSolving the cube for the first time
    CFOPCross, F2L, OLL, PLL55–6016 (2-look) · 119 (full)Yes, for back slots~84%The top choiceThe most popular, lots of resources, easy look-ahead
    RouxFirst block, second block, CMLL, last six edges45–5042Almost never~6%Good, strongest one-handedIntuitive solving, few algorithms, lots of M moves
    ZZEOLine, 2 blocks, last layer50–5528 · 40 COLL · 493 ZBLLNo~2%Good, especially one-handedTurning only R, U, L with very easy look-ahead
    2×2 OrtegaFirst face, OLL, PBL15–2012 · 42 CLLFlip for PBL—Standard for 2×2Cube 2×2

    Who uses which method?

    Roux in the world top 100 (3×3 average)6/100
    Roux in the world top 100 (3×3 one-handed)32/100
    Roux in the 2025 World Championship 3×3 final2/16

    Sources: the r/Cubers community Cubing Mega-Survey 2022 and WCA top-100 counts, compiled at scheopner.com. The WCA does not record methods, so these are estimates; the rest use other methods or did not answer.

    Fastest and best for competition?

    CFOP · the top choice for 3×3 competitionMost of the world’s best use CFOP. Algorithms are mostly R, U, F so turning is very fast, look-ahead is easy, and there are plenty of resources and coaches.
    Roux · fewest moves, strong one-handedAbout 45–50 moves, fewer than CFOP. Turning is slower because of the M moves, but the lower move count makes up for it. Very strong one-handed: nearly a third of the top 100.
    ZZ · no rotationsNever rotates the cube, good for one-handed. The first step (EOLine) is hard to plan in 15 seconds, and with few users there are fewer resources.
    2×2 and 4×42×2: start with Ortega, then CLL. 4×4: Yau + CFOP is the most common choice in competition.
    Where should I start?If you cannot solve it yet, start with Beginner. Once you can, CFOP is the safest choice. If you like few algorithms and thinking in blocks, try Roux. The Timer and Solve a cube work for every method.
    Camera scan · CFOP solution

    Solve a cube from photos

    Photograph the 6 faces one by one, check the colors, then press Solve all, or Next step only if you are mid-solve and only want the next step. The solution follows the 4 CFOP steps, each with a figure and the case name from the handbook, plus a short computer solution (Kociemba) for comparison. Photos are processed on your device and never uploaded.

    Puzzle

    Turn on the camera or upload a photo of one face. Fit the face inside the grid, in good light, without glare.

    Timer and recognition drills · saved on this device

    Practice

    Daily challenge · the same scramble for everyone

    Challenge

    Your first solve of the day counts. Afterwards, share your result and compare with everyone on the leaderboard.

    Scramble with this sequence (hold green in front, yellow on top)
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    Hold Space (or touch and hold here) until the time turns green, release to start. Press any key or tap to stop.