Reduction · parity detected automatically
4x4 Rubiks Solver
Enter your reduced 4×4 — centres built, edges paired — and this solver finishes it in twenty moves. It also does the thing every other 4×4 tool leaves you to work out yourself: it detects both parity cases, tells you which one you have, gives you the algorithm, and then solves what is left. Roughly half of all 4×4 solves hit one.
Solution
20 moves. From here the 4×4 turns exactly like a 3×3 — treat each pair of wings as one edge and turn whole outer faces only.
Pick a colour, then click the squares
One square here stands for a whole 2×2 centre block or a whole paired dedge on your 4×4.
The reduction method, start to finish
Build the six centres
A 4x4 has no fixed centres. Each face's centre is four separate pieces, and they can go anywhere, so you have to build all six and get them in the right relationship to each other. Do white first, then yellow opposite it, then the four sides as a ring. The one rule that matters: with white up and green in front, red must be on the right. Get that wrong and the cube cannot be finished.Rw U Rw' U Rw U2 Rw'Pair the twelve dedges
Every 3x3 edge is two wing pieces here — a dedge. Find two wings that belong together, bring them to the front-left and front-right slots, and join them with a wide turn, a U turn to store the pair, and a wide turn back. Eight pairs go quickly; the last four need care, and the last two need an algorithm because there is nowhere left to store them.Uw' R U R' F R' F' R UwSolve it as a 3x3
With centres built and edges paired the cube behaves exactly like a 3x3 whose pieces are double width. Turn only whole outer faces from here — a wide turn or an inner slice would break the reduction. This is where the solver above takes over: enter the reduced cube on the 3x3 net and it returns 20 moves.Fix parity if it appears
About half of all 4x4 solves hit one of two situations no 3x3 can produce: a single dedge flipped in place, or two dedges that need swapping. These are OLL parity and PLL parity. They are not mistakes — they are the hidden inner slice telling you it has an odd permutation. The tool above detects both automatically and names which one you have.
The two parities, side by side
Both are detected by the tool above from the state you enter, because both make the reduced cube an impossible 3×3 in a specific, recognisable way.
| OLL parity | PLL parity | |
|---|---|---|
| What you see | One dedge flipped in place | Two dedges need swapping |
| When it appears | During the last-layer orientation | During the last-layer permutation |
| Frequency | 50% of solves | 50% of solves |
| Why a 3x3 solver refuses | Edge flips must come in pairs | Corner and edge parity must match |
| Real cause | One dedge was paired the wrong way round | The inner slice has an odd permutation |
| Cost | About 15 extra turns | About 6 extra turns |
The 4x4 algorithms
Written in WCA wide notation, where Rw means the two right layers turned together. Many sites write that as a lower-case r, which elsewhere means the inner slice alone — the two give different cubes, so the ambiguity is worth avoiding.
| Name | Algorithm | What it does | When |
|---|---|---|---|
| OLL parity | 2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2 | Flips the front dedge of the top layer in place, leaving everything else alone. | Exactly one last-layer edge is flipped and no 3×3 algorithm will fix it. |
| PLL parity | U2 2R2 U2 2R2 Uw2 2R2 Uw2 | Swaps the front and back dedges of the top layer, changing the permutation parity. | Two edges need swapping and the corners are already correct. |
| Edge pairing (3-2-3) | Uw' R U R' F R' F' R Uw | Pairs the last two dedges without breaking the finished centres. | The final two edge pairs, once every other pair is built. |
| Last two centres | Rw U Rw' U Rw U2 Rw' | Cycles three centre pieces on the last two faces. | Finishing centres when only a few pieces remain misplaced. |
How big a 4x4 actually is
Positions
7.4 × 10⁴⁵
170 septillion 3×3s
Pieces
56
8 corners, 24 wings, 24 centres
Stickers
96
16 per face
God's number
unknown
Proven to be under 60
The jump from 3×3 to 4×4 is not incremental. Every centre piece becomes four interchangeable pieces that can nonetheless end up on the wrong face; every edge becomes two wings that have to be matched; and the whole thing loses the fixed reference frame that centres provide. Reduction exists because it turns all of that back into a puzzle you already know how to solve.
Parity is not a defect in your cube
It is very common to assume a 4×4 showing parity has been assembled wrong. It has not. The two cases are legitimate positions that a correctly built 4×4 reaches all the time, and every serious 4×4 method includes an algorithm for each. If you want to check whether a cube really is misassembled, put it on the 3×3 solver after reducing — anything beyond the two parity cases is a genuine fault.
Common questions
- What is 4x4 parity and why does it happen?
- A 4x4 has an inner slice a 3x3 does not. Turning it permutes wings without touching anything the reduced cube can see, so a 4x4 can end up in a state that, read as a 3x3, is impossible: one edge flipped alone, or two edges swapped. Neither can be produced by 3x3 face turns, which is exactly why a 3x3 solver rejects it and a parity algorithm is needed.
- How often does 4x4 parity occur?
- OLL parity appears in half of all solves and PLL parity in half, independently — so roughly a quarter of solves have neither, a quarter have both, and half have exactly one. If you have never seen it, you have been unusually lucky or you have not solved many 4x4s.
- Why does this page take a 3x3 net instead of all 96 stickers?
- Because the honest answer to 'solve my 4x4' is 'reduce it first'. No browser can hold a distance table for a 4x4's 7.4 × 10^45 positions, and the searches that do solve one directly run on servers for minutes. What a browser can do perfectly is the last stage — and the parity detection that makes the last stage possible at all.
- How many positions does a 4x4 have?
- 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 — about 7.4 × 10^45. That is 170 septillion times as many as a 3x3. God's number for a 4x4 is not known; the best proven bound is somewhere under 60 moves.
- Can I use the 3x3 solver for my 4x4?
- Once it is reduced, yes, and that is what this page does. Before it is reduced, no — the wings and centre pieces are invisible to a 3x3 model, so a 3x3 solver would happily return a sequence that leaves your 4x4 scrambled.