3x3 — Blindfolded

M2 for edges, Old Pochmann for corners, Speffz letters.

Choosing which corners to cycle, one pair of letters at a time. Each pair is one 3-cycle with the buffer, built from a commutator in the table below.

1. From a scramble to cycles

1. Find the buffer's letters. UFR is the buffer. Its stickers are C (U face), J (F face) and M (R face). The Speffz letters below show where each sticker is.
2. Follow the buffer. The sticker in the buffer's C spot belongs to some corner. That corner's letter is the first target. Look at the corner that sits on that letter's spot: its piece's letter is the next target. Keep going until the chain reaches a letter on the buffer's corner again.
3. Pair the letters in order: (1st, 2nd), (3rd, 4th), and so on. Each pair is one 3-cycle: the piece in the buffer goes to the first letter, the piece there goes to the second, and the piece there comes back to the buffer. Solving the pair is the commutator for its two letters in the table (section 6).
4. An odd number of letters leaves one letter over: section 4.

Worked example

Scramble (corners only, face turns):

Each frame shows the position still to solve after the pairs before it. The coloured outlines follow the corners of each pair.

2. When the cycle closes early

The chain above can come back to the buffer before every corner is solved. Then start a new chain at an unsolved corner. The first letter of that corner (the break letter, underlined) starts it, and the chain runs on until it reaches a letter on the same corner again. A break adds letters to the list, and the pairs are taken in list order as before.

Which sticker starts the break is a free choice, one of the three stickers of the unsolved corner. The table gives the total moves for each choice in the worked example below. The rule this site uses: pick the break letter that makes the total cheapest. If you do not remember the table, take the first letter of the corner in letter order (the Practice tab's rule).

3. Twisted corners

A corner that is in its own place but twisted is left out of the letters. It is fixed at the end with a twist row. Directions are seen from outside the corner: clockwise means its U or D sticker moves on to the next face clockwise.

• Each twist row changes exactly two corners: the buffer and one other corner K. The buffer changes the other way, so the total twist stays zero.
• To fix K twisted clockwise, use the row whose K turns anticlockwise (and so the buffer turns clockwise).
• Two twisted corners: use one row for each. The buffer's twists cancel out.

4. An odd number of letters

The parity algorithm R U R' F' R U R' U' R' F R2 U' R' U' swaps the buffer's corner UFR with UBR, and swaps the edges UF and UR. With an odd number of corner letters, the last letter Z is done like this:

1. Turn the cube with a D, L or B setup that brings Z's sticker to B (the U sticker of UBR). The setup leaves UFR, UF and UR where they are.
2. Do the parity algorithm.
3. Undo the setup. Z's sticker and the buffer sticker C have swapped places, so the cube has the last corner home.

The edges end with UF and UR swapped by this algorithm. The Edge cycles tab covers the edge side.

5. Choosing a setup move

Some pairs have no direct commutator. The Commutators tab's five steps build a commutator from one layer that holds two of the three stickers. When no such layer exists, use a setup move: turn one target sticker into a position where the five steps work, then undo the setup.

1. Try to build the commutator directly (the Commutators tab, "Building one yourself").
2. If that fails, do one move that brings one target sticker into a spot where step 1 works. Prefer a move that does not touch the buffer. Do the commutator, then undo the move.
3. If no single move works, try two moves (or three for the hardest pairs).

No simple rule decides which pairs need a setup. These numbers are the whole table, from the generator.

6. Look up a pair

Pick the first and second letter. C, J and M (the buffer) are not offered, and the second letter is never on the same corner as the first.

7. Exercises: set up, then solve

Start from a solved cube. Apply the setup scramble, look at the corners, and try the solve yourself before opening the solution. Pictures show the corners only; edges are greyed.