2x2 Rubik's Cube Solver

How to enter your 2x2 into the solver

Pick a colour, then tap the squares that show it. Hold the cube with one face toward you: that is Front, and whatever points at the ceiling is Up. To see the Right, Left or Back, turn the whole cube on the table so that face comes round to you, keeping Up on top. For Up, tip the cube toward you; for Down, tip it away. Paint each face exactly as it looks from there.

Every colour appears on exactly four squares, and the counter above the net turns red until it does. A 2x2 has no centres to say which colour belongs on which face, so the solver works it out from the corners: two colours that never share a corner are opposite each other. Any colour scheme works, and so does holding the cube any way up.

Following the solution step by step

Turn the cube back to the way you held it for Front and Up, and keep it that way. The solution only ever turns three faces, U Up, R Right and F Front, so the corner at the bottom, back and left never moves and you never lose your place. A plain letter is a quarter turn clockwise as you look straight at that face, a letter with a dash, R', is a quarter turn anticlockwise, and R2 is a half turn. The face to turn next is outlined on the net, and Step walks the solution one move at a time with the net updating as it goes.

Why it is always the shortest solution

Hold one corner still and a 2x2 has 3,674,160 positions. That is few enough to work out, once, how far every single one of them is from solved, which the page does in a fraction of a second the first time you press Solve. After that, solving is walking downhill: from your position, take any turn that leads one step closer, and repeat. Nothing is estimated, so no shorter solution exists than the one it gives. The Rubik's Cube has too many positions for that, which is why a 3x3 solver settles for a good answer rather than the best one.

Counting a half turn as one move, no position is more than 11 turns from solved, so 11 is the 2x2's God's number. Only 2,644 positions need all eleven:

Those are the page's own counts, and they match the published ones exactly, which is how it was checked before it went up. It was also tested on a thousand random cubes in random colour schemes, and a brute-force search confirmed that nothing shorter existed for each answer it checked.

When it says your cube cannot be right

A painted net that no real 2x2 could show is nearly always one of two slips, and the solver says which. A twisted corner is a corner with its three colours in the wrong order, as if it had been turned in place; a real cube cannot do that unless it has been taken apart or had a corner popped and put back. The other is a corner with a colour combination no 2x2 has, such as two opposite colours side by side, which means a square has been painted wrong.

More cubes

The full-size cube has its own Rubik's Cube solver, and its two odd cousins do too: the Void Cube, which has no centres, and the Gear Cube, which only turns in half turns. Why the 3x3 has 43 quintillion positions and how its God's number was found are in the mathematics of the Rubik's Cube.

We do not make twisty puzzles, but we do make a 2x2x2 of a very different kind: the Key and Keyway Cube, eight small cubes that lock together with keys sliding into keyways, in one order only. If the sequence was the part you liked, the Snake Cube is 27 blocks on a cord that can only be wrong in their order. There are more solvers on the puzzle tools page.