Rubik's Solver

Beginner method · published 1 November 2026

Solve a 2×2 cube yourself, in three stages.

This lesson teaches a complete method for the 2×2 cube that you can use without a computer. You build one layer by repeating a single four-move trigger, then finish the other layer with three memorised sequences. It is not the fastest method. It is short to learn and every rule below has been checked against every position it claims to handle.

Before you start: grip and notation

A 2×2 has eight corner pieces and nothing else. There are no centre stickers to tell you which colour belongs on which face, so you decide that yourself by picking a reference corner. Every move in this lesson turns one of three layers: the top (U), the right (R) or the front (F). You never need to turn the left, back or bottom layer.

A letter alone means a quarter turn clockwise, as seen when you look straight at that face. An apostrophe (′) means counter-clockwise. A 2 means a half turn, and its direction does not matter.

The moves used in this lesson
MoveWhat your hands do
UTurn the TOP layer a quarter turn CLOCKWISE, looking down at the top face.
U'Turn the TOP layer a quarter turn COUNTER-CLOCKWISE, looking down at the top face.
U2Turn the TOP layer a half turn (180°, either direction).
RTurn the RIGHT layer a quarter turn CLOCKWISE, looking at the cube from the right.
R'Turn the RIGHT layer a quarter turn COUNTER-CLOCKWISE, looking at the cube from the right.
R2Turn the RIGHT layer a half turn (180°, either direction).
FTurn the FRONT layer a quarter turn CLOCKWISE, looking at the cube from the front.
F'Turn the FRONT layer a quarter turn COUNTER-CLOCKWISE, looking at the cube from the front.

The diagrams show each face from outside. Their colours follow one common scheme (Up: white; Down: yellow; Front: green; Back: blue; Right: red; Left: orange), with the yellow layer built first. If your cube uses different colours, the method is the same: substitute your own first-layer colour wherever this page says yellow.

1. Build the first layer with one trigger

Choose any corner that has a yellow sticker. Hold the cube so that corner sits at the bottom-back-left with yellow facing down. It is now your reference: the rest of the bottom layer is built around it. You are only changing your grip here; no layer turns.

Each bottom corner shares one side colour with each of its neighbours. With the reference corner showing blue at the back and orange on the left, the bottom-back-right corner must carry yellow and blue, the bottom-front-left must carry yellow and orange, and the corner diagonally opposite carries yellow with the two remaining colours (green and red here). Work out which piece belongs in each slot before you move it.

Insert one corner

  1. Bring an empty slot to the front-right. Turn the whole cube around its vertical axis, keeping yellow on the bottom, until a bottom slot that still needs its corner is at the front-right.
  2. Put the right corner above it. Find the corner that belongs in that slot. If it is in the top layer, turn U until it sits directly above the slot, at the top-front-right.
  3. Repeat the trigger. Perform R U R' U', then look at the slot. Repeat the four moves until the corner sits in the slot with yellow facing down. It never takes more than five repetitions.

The trigger is safe to repeat because, of the four bottom corners, it only ever moves the one at the front-right. Corners you have already placed stay where they are, however many times you repeat it. Six repetitions bring the whole cube back to where you started, so if you count past five, stop: either the wrong corner is above the slot or the slot is not at the front-right.

If the corner you need is stuck in the bottom layer, in the wrong slot or twisted in the right one, turn the whole cube to bring that slot to the front-right and perform the trigger once. The corner rises into the top layer, and you can then insert it normally.

Corner waiting above its slot Up: yellow Y Up: white W Up: blue B Up: blue B Down: white W Down: yellow Y Down: yellow Y Down: yellow Y Right: green G Right: orange O Right: green G Right: red R Left: orange O Left: red R Left: orange O Left: orange O Front: red R Front: green G Front: red R Front: green G Back: white W Back: white W Back: blue B Back: blue B UpDownRightLeftFrontBack
0. Corner waiting above its slot
After R U R′ U′ × 1 Up: red R Up: white W Up: blue B Up: red R Down: green G Down: yellow Y Down: yellow Y Down: yellow Y Right: green G Right: blue B Right: yellow Y Right: red R Left: orange O Left: white W Left: orange O Left: orange O Front: white W Front: green G Front: red R Front: green G Back: orange O Back: white W Back: blue B Back: blue B UpDownRightLeftFrontBack
1. After R U R′ U′ × 1
After R U R′ U′ × 2 Up: red R Up: white W Up: red R Up: white W Down: green G Down: yellow Y Down: yellow Y Down: yellow Y Right: yellow Y Right: blue B Right: red R Right: red R Left: orange O Left: white W Left: orange O Left: orange O Front: green G Front: green G Front: white W Front: green G Back: blue B Back: orange O Back: blue B Back: blue B UpDownRightLeftFrontBack
2. After R U R′ U′ × 2
After R U R′ U′ × 3 Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
3. After R U R′ U′ × 3

In this example the yellow-green-red corner starts above its slot with yellow facing up. After three triggers it drops into place, and the top layer happens to finish solved too. Usually the top will still be mixed; that is expected, and the next two stages deal with it.

Check before moving on: the whole bottom face is yellow, and on each side the two bottom stickers match each other. Yellow alone is not enough; a bottom corner with the right colour underneath but the wrong side colours is in the wrong slot.

2. Twist the top corners to face up

Keep the finished layer on the bottom from now on. The aim of this stage is a fully white top face. The side colours of the top layer can stay mixed until stage 3.

Count the top corners that already show white on the top face. Then turn U until the top-front-left corner matches the description for your count, and perform the twisting sequence R U R' U R U2 R'.

Where to put the top-front-left corner before the twisting sequence
White stickers on topTurn U until the top-front-left corner…
4Nothing to do. Go to stage 3.
1is the one showing white on top.
0shows white on its left side.
2shows white on its front side.

Then count again and repeat. You will need the sequence at most three times. A suitable top-front-left corner always exists for the 0 and 2 cases, so if you cannot find one, recheck that the finished layer is on the bottom.

Before the twisting sequence Up: orange O Up: white W Up: red R Up: green G Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: blue B Right: white W Right: red R Right: red R Left: red R Left: green G Left: orange O Left: orange O Front: white W Front: blue B Front: green G Front: green G Back: white W Back: orange O Back: blue B Back: blue B UpDownRightLeftFrontBack
Before the twisting sequence
After the twisting sequence Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
After the twisting sequence

Here only the top-front-left corner shows white on top, so one application finishes the top face. Notice that the sequence also carries the top corners to different places. It returns only the bottom layer to where it was. Do not judge the result by the side colours yet.

3. Swap the top corners into place

The top is now white, but the side stickers of the top layer may not line up. Look around the four sides of the top layer for a matching pair: two top stickers on the same side that have the same colour. Turn U to check every side.

Choosing the final sequence
Matching pairsWhat to do
All four sidesTurn U until the top layer matches the bottom. You are finished.
Exactly one sideTurn U until that pair is on the left side, then perform the adjacent swap R U R' U' R' F R2 U' R' U' R U R' F'.
NonePerform the diagonal swap F R U' R' U' R U R' F' R U R' U' R' F R F' from any position of the top layer.

After either swap, turn U until the top layer's side colours match the layer below. Exactly one swap is enough in every case.

The adjacent swap

This exchanges the two top corners on the right side and leaves the left pair alone, which is why the matching pair must face left.

Before the adjacent swap Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: blue B Right: green G Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Front: red R Front: green G Front: green G Front: green G Back: blue B Back: red R Back: blue B Back: blue B UpDownRightLeftFrontBack
Before the adjacent swap
After the adjacent swap Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
After the adjacent swap

The diagonal swap

This exchanges the top-front-right and top-back-left corners. It is the longest sequence in the method, so practise it in two halves: the first nine moves end with F′, and the second half starts with R.

Before the diagonal swap Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: orange O Right: red R Right: red R Right: red R Left: orange O Left: red R Left: orange O Left: orange O Front: blue B Front: green G Front: green G Front: green G Back: green G Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
Before the diagonal swap
After the diagonal swap Up: white W Up: white W Up: white W Up: white W Down: yellow Y Down: yellow Y Down: yellow Y Down: yellow Y Right: red R Right: red R Right: red R Right: red R Left: orange O Left: orange O Left: orange O Left: orange O Front: green G Front: green G Front: green G Front: green G Back: blue B Back: blue B Back: blue B Back: blue B UpDownRightLeftFrontBack
After the diagonal swap

When it goes wrong

The corner will not drop in. Six triggers return everything to where it started, so endless repetition will never help. Check that the slot you are filling is at the front-right, that the correct corner is directly above it, and that each R lifts the front of the right layer upward.

The bottom layer broke during stage 2 or 3. That almost always means a move was skipped or turned the wrong way, or the cube was rotated mid-sequence. These sequences rebuild the bottom only when every move is made exactly. On a 2×2 the quickest repair is usually to rebuild the first layer with the trigger, which takes a minute, rather than trying to undo an unknown error.

Three twisting sequences and the top is still not white. Recheck the table: the 0 and 2 cases look at a sticker on the side of the top-front-left corner, not on top. Make sure you count only stickers facing up.

I used the diagonal swap, but now one side matches. You had a matching pair you did not see, so the diagonal swap turned one case into another. Nothing is lost: the top is still white, so use the adjacent swap now.

I want to check my own position. Enter it into the 2×2 solver to see a shortest solution. Use that to get unstuck, then return to the method on your next solve.

How this lesson was checked

The twisting sequence and the two swaps are widely shared in the cubing community, where they are known as the Sune, the T-permutation and the Y-permutation. We did not invent them. What this page adds is a check of every rule it states, using the same piece model that runs the 2×2 solver:

These checks run as automated tests whenever the site changes. They prove the rules are correct for the model. They cannot prove that the wording is clear to you; if a step confused you, tell us which one and we will improve it.

Curious how many moves a 2×2 really needs? See God's number for the puzzles on this site. For more practice reading moves on a 3×3, try the move lab.