Learn · Level 3 · permutations
The 21 permutations
The top face is yellow; the pieces still sit in the wrong places. Twenty-one patterns cover everything that can remain, and a computer check proves it: all 288 arrangements an oriented last layer can reach belong to exactly one case here. Each case has one algorithm, and together they end every solve.
Each tile shows the top of the cube from above. Arrows mark which pieces trade places; the coloured ticks around the rim are the side stickers, and they carry the recognition cues, the solid bars and the matched pairs cubers call headlights. Every algorithm is played for you on the case page, move by move.
Sixteen of the twenty-one turn up once in eighteen solves each, and between them they account for nearly nine solves in ten. The rarest, the two N perms and H, appear once in 72. The two you will meet first are the U perms, the three-edge cycles taught back in Level 2.
Edges only
Corners only
Adjacent swap
Diagonal swap
Checked by simulation before publishing: the position shown plus the moves shown must produce a finished cube, and the algorithm must touch nothing outside its own job. The diagram and the player are drawn from the same simulated position, so they cannot disagree. Completeness is checked by enumeration: the 21 definitions cover all 288 reachable permutations, each exactly once.