21 cases
All 21 cases, each finishing the cube in one algorithm.
The last algorithm of every solve. Twenty-one cases, all of them worth knowing well — this is the set where fluency pays off most, because it is the one you use every single solve. Learn the recognition as carefully as the fingers: knowing a T-perm is useless if it takes you two seconds to see that it is a T-perm.
All four corners are home, so one side is a solid bar of its own colour and the other three show headlights. The three wrong edges cycle anticlockwise: with the solved edge at the back, the front edge belongs on the right.
The same picture as Ua — a solid bar on one side, headlights on the other three — with the cycle running the other way. Hold the solved edge at the back and the right-hand edge belongs at the front.
Four sets of headlights, and every edge belongs on the face opposite the one it is sitting on. The case looks identical from all four sides, so there is no angle to hunt for.
Four sets of headlights again, but the edges have swapped with their neighbours rather than their opposites: the front edge shows a side colour, not the back colour.
Every edge is already home, so each side shows its own colour through the middle. One corner is home too; two matching corner stickers mark the face to hold at the back, and from there the back-left corner travels to the back-right.
Indistinguishable from Aa at a glance: edges all solved, one corner home, one set of headlights — on the right in the diagram. Turn them to the back as you would for Aa and the cycle runs the other way: the back-right corner travels to the back-left.
All four edges solved and not one set of headlights anywhere — no two corner stickers on any face match. That combination happens for E and nothing else. All four corners are wrong, swapping in pairs.
Headlights on one face with a stranger of an edge between them. That edge swaps with the one directly across the layer, and the two corners on the far face swap with each other.
One face is solved outright — a solid bar of three. Hold it on the left and the front reads own colour, own colour, stranger. The two corners on the right swap, and so do the right and back edges.
A solid bar of three on one side again. Hold it on the left and the front reads own colour, then two stickers of the right face’s colour. The right-hand corners swap along with the right and front edges.
Headlights on one face with a wrong edge between them, and a two-block — a corner sitting with its own edge — on a neighbouring face. Hold the headlights on your left and Ra’s two-block is at the front.
The mirror of Ra: headlights with a stranger between them and a two-block on a neighbouring face. The diagram has the headlights facing you; turn them to your left and Rb’s two-block sits at the back, where Ra’s is at the front.
A solid bar of three on one side, like the J perms, but nothing lines up beside it: hold the bar on your left and the front shows three different colours. The two right-hand corners swap and the front and back edges trade places.
One corner sits complete with both of its edges — three solved pieces wrapping a corner of the layer. Diagonally opposite, the other solved corner has both its edges swapped, and the two remaining corners swap diagonally.
Two two-blocks on adjacent faces, sitting at opposite ends of the layer, and no run of three anywhere. The corners swap diagonally, and so do two of the edges.
Two two-blocks on opposite faces, offset against each other so the layer leans like the strokes of an N. In Na the front block sits on the right of the front face.
The mirror image of Na: the same pair of opposed two-blocks, but the front one sits on the left of the front face.
Exactly one two-block and exactly one set of headlights — the signature of every G perm. Hold the two-block on the front face: for Ga it sits at the right-hand end, with the headlights on the left.
One two-block and one set of headlights. With the two-block held at the right-hand end of the front face, Gb puts the headlights at the back.
One two-block, one set of headlights. The diagram shows the block lying along the back; bring it round to the front and it sits at the left-hand end, with the headlights on the right.
One two-block, one set of headlights, with the block along the back in the diagram again. Bring it to the front — left-hand end, as for Gc — and Gd puts the headlights at the back.