Method, algorithms and WCA scrambles
Megaminx Solver
There is no megaminx solver on this page, and there is not one anywhere else either — a megaminx has 1.01 × 1068 positions, and nothing that fits in a browser can search them. What does work is the method below: five stages, algorithms you already know from a 3×3, and about 175 turns. Plus a scramble generator in the WCA’s own format.
WCA megaminx scramble
7 lines · 77 turns
- R-- D++ R-- D++ R++ D++ R++ D++ R++ U'
- R++ D++ R-- D-- R++ D++ R-- D++ R++ U
- R-- D-- R++ D++ R-- D-- R-- D-- R++ U'
- R++ D-- R-- D++ R++ D-- R++ D-- R-- U
- R-- D++ R++ D-- R-- D++ R-- D++ R-- U'
- R++ D++ R++ D++ R-- D-- R++ D-- R++ U
- R-- D-- R-- D++ R++ D++ R-- D-- R-- U'
Why no solver exists
Positions
1.01 × 10⁶⁸
A 3×3 has 4.3 × 10¹⁹
Pieces
62
20 corners, 30 edges, 12 centres
Faces
12
Regular dodecahedron
God's number
unknown
Only bounds have been published
The reason is not that nobody has tried. Kociemba’s two-phase algorithm works on a 3×3 because the cube has a useful subgroup — the positions reachable without quarter-turning R, L, F or B — and the space of cosets around it is small enough to tabulate exactly. That is what turns an impossible search into two tractable ones.
A megaminx has no comparable decomposition with coset spaces a computer can hold. The published work on megaminx solving produces upper bounds — sequences guaranteed to work — rather than optimal solutions, and the search that finds them runs for a long time on real hardware.
The honest consequence is that a megaminx has to be solved by method, not by search. The good news is that the method is not hard if you can already solve a cube.
The megaminx method
Grey star and first layer
Pick a face — grey on most megaminxes, white on some — and build a five-pointed star of edges around it, matching each edge's second colour to the neighbouring centre. Then fill the five corners. It is exactly the white cross and white corners of a 3x3, just with five of everything instead of four, and it needs no algorithms.Second layer
Ten edges go in around the first layer, using the same right-hand and left-hand inserts you already know from a 3x3. There is one extra decision each time — a megaminx face has five neighbours, not four — but the algorithm is unchanged.U R U' R' U' F' U F (mirror for the left)Grey star on the far side
Turn the megaminx over and make a star on the opposite face, ignoring the corners. This is the yellow cross step, and Sune does the job. Expect to run it two or three times.R U R' U R U2 R'Third and fourth layers (S2L)
This is where a megaminx stops feeling like a cube. Rather than solving layer by layer, most methods now build corner-edge pairs around the star and insert them, working around the puzzle in a ring. It is F2L, five times over, and it is the bulk of the solve — roughly half of all the turns.Last layer
Orient the edges, orient the corners, then permute both. The algorithms are the ones you know from a 3x3, applied repeatedly around a five-sided face instead of a four-sided one. A competent solve is about 150 to 200 turns in total.R U R' U R U2 R' then R U' R' D R U R' D'
The algorithms
Every one of these is a 3×3 algorithm applied unchanged. That is not a simplification — any three adjacent faces of a megaminx behave like three adjacent faces of a cube, so algorithms that never touch a fourth face transfer exactly.
| Name | Algorithm | What it does | When |
|---|---|---|---|
| Grey star (edge orientation) | R U R' U R U2 R' | Orients the last-layer edges. Same Sune as on a cube. | Making the star on the top face. |
| Edge permutation | R U R' U R U2 R' U (repeat until solved) | Cycles the last-layer edges around. | Star made, edges still in the wrong places. |
| Corner orientation | R' D' R D R' D' R D (x2 per corner) | Twists one corner in place; repeat around the layer. | The classic corner-twist commutator, unchanged from the cube. |
| Corner permutation | R U' R' D R U R' D' (repeat) | Cycles three corners. | The last stage of a layer-by-layer megaminx solve. |
Reading a WCA megaminx scramble
Seven lines, each of five R/D pairs and then a single U or U'. Only two faces are ever named apart from the closing U, which is what makes it possible for a judge to apply by hand without mistakes.
R++— the right face, two fifths clockwise (144°)R--— the right face, two fifths anticlockwiseD++andD--— the same on the down-right faceU— one fifth of a turn (72°) of the top face
Every R and D is a double turn. That is deliberate: it keeps every scramble exactly 77 turns long and mixes the puzzle faster than single turns would.
If you want a puzzle a browser can solve perfectly
The Pyraminx and the 2×2 both fit entirely in memory, so both solvers on this site return provably shortest answers. The 3×3 is too big for that but small enough for two-phase search, which gets within a move or two of optimal in about a fifth of a second. The megaminx is the point where that whole approach runs out.
Common questions
- Is there a megaminx solver that works like the Rubik's cube one?
- No, and not on this site either. A megaminx has about 1.01 × 10^68 positions against a 3x3's 4.3 × 10^19. Kociemba's method works because a 3x3 has a subgroup whose coset space is small enough to tabulate; no comparable decomposition of the megaminx has coset spaces that fit in a computer, let alone a browser tab. Every published result on megaminx solving is a bound, never an optimal solver.
- How many positions does a megaminx have?
- 100,669,616,553,523,347,122,516,032,313,645,505,168,688,116,411,019,768,627,200,000,000,000. Written out that is roughly 1.01 × 10^68. For scale, there are about 10^80 atoms in the observable universe.
- How long does a megaminx solve take?
- About 150 to 200 turns with a layer-by-layer method, and one to two minutes for someone comfortable with it. The world record is under 27 seconds. Most of the time goes on the third and fourth layers, which is why almost every improvement in megaminx times comes from the S2L stage.
- Do Rubik's cube algorithms work on a megaminx?
- Most of the useful ones do, unchanged. Sune, the right-hand insert, the corner-twist commutator R U' R' D R U R' D' — all of them work on a megaminx because they only ever touch three faces at a time, and any three adjacent faces of a megaminx behave like three adjacent faces of a cube. That is why a cuber can pick one up and solve it in an afternoon.
- What does R++ mean in a megaminx scramble?
- Two fifths of a turn clockwise — 144 degrees. R-- is the same amount anticlockwise. Every R and D in a WCA megaminx scramble is a double turn, which keeps the scramble a fixed length and makes it quicker for a judge to apply by hand.