I took my Rubik's Cube apart and now it won't solve. What happened?

A Rubik's Cube (or any 3x3 twisty puzzle) reassembled from loose pieces has a 1 in 12 chance of being solvable. The other 11 times it is in a state that no sequence of face turns can reach from solved, so no solver, app or person, can fix it by turning. A piece has to physically come back out.

How do I tell whether my cube is actually unsolvable?

Solve it as far as you can. A rebuilt cube leaves you at the last layer with one, two or three anomalies at once: a corner twisted in place, an edge flipped in place, or two pieces swapped. More than one can be true together, and usually is. Two flipped edges are ordinary and solvable. Two twisted corners are solvable only if they twist in opposite directions; twisted the same way, the cube is not.

How do I fix a cube that was rebuilt wrong?

Take the cube fully apart and rebuild it in the solved state, placing every piece deliberately. That works for every case and cannot leave you worse off. Removing single pieces also works, but only if you correct every anomaly you found rather than one of them: a rebuild commonly breaks more than one rule at once, and fixing a single piece then leaves the cube just as unsolvable as before.

Why is a rebuilt cube only solvable 1 time in 12?

Turning the faces of a cube can never change three quantities: the total twist of the corners (fixed modulo 3), whether the number of flipped edges is odd or even, and whether the overall permutation of the pieces is odd or even. That is 3 x 2 x 2 = 12 separate families of arrangements, and face turns can only move you around inside the one you are already in. Exactly one of the twelve contains the solved cube, so a random rebuild is solvable one time in twelve. Of the eleven that are not, seven break more than one of the three rules at once.

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My Rubik’s Cube was taken apart, and now it won’t solve

Why it happens, how to tell which case you have, and how to fix each one

A Rubik’s Cube — or any 3×3 twisty puzzle — rebuilt from loose pieces has a 1 in 12 chance of being solvable. The other eleven times it is sitting in a state that no sequence of face turns can ever reach from a solved cube — so no solver, no app and no person can fix it by turning the faces. That is not a difficulty problem. It is an impossibility, and the only fix is to take a piece back out.

This catches people out because everything about the cube looks normal. It turns smoothly, the colours are all present, and it scrambles and unscrambles the way it always did. You can solve two layers without a hint of trouble. The problem only shows itself at the very end, and by then it looks like you made a mistake.

You didn’t. The cube did, when it went back together.

Which rules are broken?

Solve the cube as far as you can — by hand, or let something solve it for you. A cube that was rebuilt wrong takes you all the way to the last layer and then leaves you with one, two or three of these at the same time. They are independent, and a random rebuild usually breaks more than one:

1. One corner twisted in place

Every piece is home. One corner is in its correct slot but rotated, so two of its three colours face the wrong way. Turn it 120° in your head and the cube is finished.

2. One edge flipped in place

Every piece is home. One edge sits in its correct slot the wrong way round, its two colours swapped with each other.

3. Two pieces swapped

Two corners, or two edges, are sitting in each other’s places. Everything else is correct. No algorithm will exchange just those two and leave the rest alone.

Count them. Whatever you do to the cube, the same set of anomalies keeps reappearing, because turning the faces cannot fix any of them. That count is what tells you how much work the repair is.

Some pairs are perfectly normal, and one pair is not. It is worth being careful here, because the difference decides whether you keep solving or go and get a screwdriver.

Two flipped edges — ordinary. Solvable. Flips only ever happen in pairs, so this is what a normal scramble looks like. Keep going.
Three pieces cycling round — ordinary. Solvable. A three-cycle is an even rearrangement.
Two twisted corners, twisting in opposite directions — one clockwise, one anticlockwise. Solvable. The twists cancel.
Two twisted corners, twisting the same way — both clockwise, or both anticlockwise. Not solvable. Their twists add up instead of cancelling, and no sequence of turns will separate them.

Why a cube can be put together wrong at all

Turning the faces of a cube is surprisingly restricted. There are three things the turns can never change, no matter how many you make:

Total corner twist. Give each corner a score of 0, 1 or 2 for how far it is rotated. The sum of those scores, divided by 3, always leaves the same remainder. One corner twisted on its own changes that remainder, so it can never happen by turning.
Edge flips come in pairs. The number of flipped edges is always even. Flipping one on its own is unreachable.
Permutation parity. Every face turn moves four corners and four edges in cycles, which is an even rearrangement. Swapping exactly two pieces is an odd one, and odd never comes out of a pile of evens.

Three choices, two choices, two choices — 3 × 2 × 2 = 12 separate families of arrangements. Face turns shuffle you around inside whichever family you are in and can never move you between them. Exactly one of the twelve contains the solved cube. Drop the pieces in without thinking and you land in a family at random, which is where the one-in-twelve comes from.

It also explains why the anomalies arrive in bunches. The rules are independent, so a rebuild can break any combination of them — and of the eleven families that are not the solved one, seven break more than one rule at once. A cube showing only a single anomaly is the minority case, not the normal one. That is the whole reason the repair below insists on fixing everything you found rather than the first thing you noticed.

Fixing it

The reliable way, and the one to use if you are at all unsure

Take the cube apart and put it back together already solved — every piece placed deliberately, each colour where you can see it belongs. This is what CubeLens tells you to do when it finds one of these cubes, and it is the advice that cannot go wrong: if you build it solved, it is by definition in the solvable family, whatever was wrong before and however many rules it broke.

It is also the only fix that does not depend on your having diagnosed the cube correctly, which is why it is first.

On most cubes, turn one layer about 45° and lever an edge piece out from the middle of that layer — it is the piece with the most room to move. Once the first edge is out the rest come away easily.

The quick way — fixing pieces individually

If you would rather not rebuild the whole thing, take out the pieces that are wrong and put them back corrected. Correct every anomaly you counted, not the first one you noticed — seven of the eleven broken families break more than one rule, and fixing one piece there leaves the cube exactly as unsolvable as it was, with an hour of solving ahead of you before you find out.

Twisted corner: pop that corner out and reseat it rotated one third of a turn, so its colours line up with the faces around it. If two corners are twisted the same way, both need it.
Flipped edge: pop that edge out and put it back the other way round.
Two swapped pieces: pop both out and put each into the other’s slot.

Then solve as normal. If it still will not finish, one of the anomalies was missed — go back to the reliable way above rather than hunting for another piece to lever out.

Before you lever anything

Magnetic cubes hold their pieces harder than they look and the magnets can come loose. Work slowly.
Some modern cubes — several GAN mechanisms among them — do not come apart the classic way and can be damaged by forcing an edge out. Check how yours is meant to disassemble first.
Lever against a plastic edge, not a sticker. A fingernail or a guitar pick is kinder than a screwdriver.

Finding out before you waste an hour

The frustrating part of all this is that you normally discover it at the end, after solving two and a half layers of a cube that was never going to finish.

CubeLens checks for it at the start instead. Every scanned cube is validated against what a real cube can physically be, before anything is solved, and if the cube cannot exist it says so and names a rule that was broken — a corner twisted in place, an edge flipped in place, or two pieces swapped — rather than handing you a confident solution that cannot work. It reports a broken rule rather than all of them, which is the other reason its advice, and the advice above, is to rebuild the cube solved. Scanning, checking and every solving method are included.

Written by the author of CubeLens, an iPhone app that scans a real cube with the camera and teaches you to solve it. Rubik’s Cube is a trademark of Spin Master, used here only to refer to the puzzle this page is about. CubeLens is an independent app and is not affiliated with, endorsed by, or connected to Spin Master or any other puzzle manufacturer.