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Seven stages · eight algorithms

Rubik's Cube 3x3 Solution

The complete 3×3 solution is seven stages and eight algorithms: white cross, white corners, middle layer, yellow cross, yellow face, corner positions, last edges. Learn those and you can solve any cube from any state in about a hundred moves. Every algorithm below has been run against a cube model and checked, and the solver at the bottom will answer your exact cube in twenty.

The seven stages

  1. White cross

    Put the four white edges around the white centre, each one matching the side colour it touches. No algorithm — do it by looking. If a white edge is in the bottom layer, turn that face twice to bring it up. Aim for a cross whose side stickers line up with the four centres, not just a white plus sign.

  2. White corners

    Find a white corner in the top layer, put it directly above the slot it belongs in, then repeat the right-hand insert until it drops in white-side-down. It takes one, three or five repetitions depending on how the corner is twisted. When all four are in, the first layer is done and the side colours form solid bands.
    U R U' R'

  3. Middle layer edges

    Turn the cube so the finished white layer is on the bottom. Find a top-layer edge with no yellow on it, turn U until its front colour matches the front centre, then send it left or right depending on where it belongs. If an edge is stuck in the wrong slot, insert any other edge to kick it out.
    U R U' R' U' F' U F (right) U' L' U L U F U' F' (left)

  4. Yellow cross

    Ignore the corners entirely; you are only shaping the yellow edges. You will see a dot, an L, a line or the finished cross. Run the algorithm once from a dot to get a line or an L, again to get the cross. Hold an L so its two arms point up and left; hold a line so it runs left to right.
    F U R U' R' F'

  5. Yellow face

    Now orient the corners so the whole top is yellow. Hold the cube so at least one yellow corner sits at the front-left, run Sune, and reassess. Between one and three repetitions always finishes it. Do not panic when the rest of the cube looks destroyed mid-algorithm — it comes back.
    R U R' U R U2 R'

  6. Corner positions

    The top is yellow but the corners may be in the wrong places. Find a corner that is already home — its three colours match the three faces it touches — hold it at the back right, and run the cycle until the other three land. If none is home, run it once anywhere and one will appear.
    U R U' L' U R' U' L

  7. Last four edges

    Everything is placed except up to three top edges. Hold the one edge that is already correct at the back and run the U-perm. If nothing is correct, run it once and one will be. This is the last step; the cube is solved when it ends.
    R U' R U R U R U' R' U' R2

The eight algorithms, in one table

Print this. It is the whole solution sheet — everything above condensed into the sequences you will be looking at while your hands learn them.

NameAlgorithmWhat it doesWhen
Right-hand insertU R U' R'Takes a corner from the top layer and puts it into the front-right slot.Building the first layer's corners, and the workhorse of the second layer.
Left-hand insertU' L' U LThe mirror image: takes a corner into the front-left slot.Same job on the other side. Learn it as a mirror, not as a new sequence.
Right edge insertU R U' R' U' F' U FSends the front-top edge into the front-right slot of the middle layer.Second layer, when the edge needs to go right.
Left edge insertU' L' U L U F U' F'Sends the front-top edge into the front-left slot.Second layer, when the edge needs to go left.
Cross (FUR)F U R U' R' F'Turns a dot into a line, a line into an L, and an L into the cross.Making the yellow cross on the last layer. Run it up to three times.
SuneR U R' U R U2 R'Rotates three of the last-layer corners, leaving one where it is.Orienting the last-layer corners so the whole top face is yellow.
Corner cycleU R U' L' U R' U' LCycles three last-layer corners without changing their orientation.Putting the last-layer corners into their correct positions.
Edge cycle (U-perm)R U' R U R U R U' R' U' R2Cycles three last-layer edges anticlockwise, leaving the fourth alone.The final step, once the corners are home.

How long each stage should take

Move counts are typical ranges for a random scramble, in half-turn metric.
StageTypical movesAlgorithms neededWhat usually goes wrong
White cross8–12noneForgetting to match the side colours to the centres
White corners20–301Turning the whole cube instead of repeating the insert
Middle layer24–322 (mirrors)Not kicking a wrongly-placed edge out first
Yellow cross6–181Holding the L or the line the wrong way round
Yellow face7–211Not checking after each repetition
Corner positions8–241Failing to spot the corner that is already home
Last edges11–221Holding the solved edge at the front instead of the back

Stuck on one specific cube?

Enter it below. If a stage will not finish, the state itself may be impossible — a corner twisted in its socket or two pieces swapped during reassembly — and the solver names which fault it is instead of spinning forever.

Move 1 of 20 — Front face clockwise

Solution

20 moves

The first 9 moves put every corner and edge the right way up and the middle-slice edges back in the middle slice. The last 11 finish the cube using only U, D and half turns.

Pick a colour, then click the squares

Up
U
Right
R
Front
F
Down
D
Left
L
Back
B

Tab to any square and press 1–6 to paint it. Hold the mouse down to drag across several at once.

Applies the moves to a solved cube. Useful if you already have a competition scramble and want to see how it is meant to come apart.

Common questions

How many moves is the beginner's 3x3 solution?
Roughly 100 turns from a random scramble, sometimes 120. That is five times the theoretical minimum of 20 and about twice what a CFOP speedcuber uses, and the trade is deliberate: eight algorithms instead of the 78 that CFOP needs.
Which algorithms do I actually have to memorise?
Four, if you count mirrors as one. The right-hand insert U R U' R' and its left mirror do the first two layers between them. F U R U' R' F' makes the yellow cross. R U R' U R U2 R' — Sune — finishes the yellow face. The two last-layer cycles complete the solve. Everything else is recognition, not memory.
Why does the cube look destroyed halfway through an algorithm?
Because it is, temporarily. Every last-layer algorithm has to break the first two layers to move pieces around and then rebuild them. That is why the move counts are what they are. Trust the sequence, finish it, and the damage undoes itself.
Can I mix this solution with the solver?
That is the fastest way to learn it. Solve as far as you can by hand, then enter the half-finished cube on any solver page and step through the answer on the 3D cube to see what you were missing. The solver never assumes your cube is scrambled from solved.

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