Random state where it counts
Scramble Generator
Scrambles for six puzzles, generated the way the WCA generates them. For 3×3, 2×2 and Pyraminx that means random state: a position is drawn uniformly from every legal one, solved, and the inverse of that solution is what you see. For 4×4, 5×5 and megaminx it means the WCA’s random-move formats, and each panel tells you which it is using.
3×3 scramble
random-stateL2 D2 B2 R' F2 R B2 R' U2 L2 F2 D' B L F' D R B' U F2
A uniformly random position, printed as the inverse of its two-phase solution. Typically 18–20 turns.
What each generator does
| Puzzle | Method | Typical length | How the position is chosen |
|---|---|---|---|
| 3×3 | Random state | 18–20 turns | Uniform over 4.3 × 10¹⁹ positions, solved by two-phase search |
| 2×2 | Random state | 8–11 turns | Uniform over 3,674,160 positions, solved optimally |
| Pyraminx | Random state | 8–11 turns plus tips | Uniform over 933,120 positions, solved optimally |
| 4×4 | Random move | 44 turns | Random face and depth, no immediate repeats |
| 5×5 | Random move | 60 turns | The WCA uses random moves here too |
| Megaminx | WCA format | 77 turns | Seven lines of alternating R and D, each closed with U |
Why the inverse of a solution makes a good scramble
It is the only way to guarantee the position without also biasing it. If you want a specific random position P, you cannot get there by turning at random — you have to compute a sequence that reaches it. Solving P gives a sequence from P to solved; reversing that sequence and inverting each move gives one from solved to P.
The scramble is short as a side effect. A two-phase solution for a random cube is 18–20 moves, so the scramble is 18–20 moves, and every one of them is doing work. A random-move scramble of the same length would leave the cube noticeably less mixed, because some of its turns cancel.
The megaminx format
Megaminx scrambles look nothing like cube scrambles, and that is deliberate. The format is seven lines, each of five R/D pairs followed by a single U or U'. Every R and D is a double turn — ++ is two fifths clockwise, -- is two fifths anticlockwise.
The rigid structure exists because judges read megaminx scrambles aloud and apply them by hand, and a fixed pattern of only two faces is far less error-prone than free-form notation across twelve. The line breaks are part of the format, not presentation.
Scrambling with the timer
The speedcubing timer generates a fresh random-state 3×3 scramble after every solve automatically, so you do not have to come back here between attempts. This page is for when you want a specific puzzle, or a scramble to copy somewhere else.
Common questions
- What is a random-state scramble?
- One where every solvable position is equally likely. The generator picks a position uniformly at random, solves it, and prints the inverse of that solution. A random-move scramble does the opposite — it picks moves and hopes the position is well mixed — which biases towards states that happen to be reachable in that many turns.
- Why does a random-move scramble matter in competition?
- Because it can hand someone a five-move case. A 25-move random sequence occasionally cancels down to something trivially easy, and with hundreds of competitors that happens. Random state cannot: the position is drawn first and the moves are derived from it, so an easy case is exactly as likely as it should be, which is almost never.
- How long is a WCA 3x3 scramble?
- Usually 18 to 20 moves. That is not a fixed length — it is however long the inverse of the solution turns out to be, which for a random position lands between 18 and 20 almost every time. Anything much shorter would mean the generator drew an unusually easy position.
- Why is 4x4 random-move here?
- Honesty: no practical random-state 4x4 scrambler fits in a browser tab. The WCA's official tool uses a multi-stage reduction solver that needs hundreds of megabytes of tables. What you get here is 44 random turns with no immediate repeats, which mixes a 4x4 thoroughly but is not formally uniform, and the panel says so.
- Can I use these scrambles for practice?
- Yes, and the random-state ones are indistinguishable from competition scrambles. If you are practising for a competition, the 3x3, 2x2 and Pyraminx generators here produce exactly the same distribution the WCA's tool does.
Keep going
- Speedcubing timerScrambles generated automatically between solves, with Ao5 and Ao12.
- Rubik's cube solverPaste a scramble into the solver to see how it comes apart.
- 2×2 Rubik's cube solverThe optimal solver that powers the 2×2 scrambles here.
- Pyraminx solverThe optimal solver behind the Pyraminx scrambles.