Learn · the 2×2 · the Ortega method
Get fast on the 2×2
The standard competition method: any face first, never mind the sides, then one look to orient and one look to finish both layers at once. Twelve algorithms in all, every one verified.
Ortega changes the beginner method in two places. First, the opening: build a white face rather than a layer, ignoring whether the side colours match, which takes a beginner's minute down to a few seconds of looking. Second, the ending: instead of finishing the top and hoping, one algorithm permutes both layers together.
In between sits the familiar middle step. All seven ways the top can need orienting are below; you know two already if you came from the 3×3 journey.
Orient: the seven cases
the double Sune · 2 in 27
the Pi · 4 in 27
the headlights · 4 in 27
the chameleon · 4 in 27
the bowtie · 4 in 27
the Antisune · 4 in 27
the Sune · 4 in 27
Finish: permute both layers
Count the solved pairs of corners on each layer and pick the row that matches. Holding the cube upside down turns a bottom case into a top case, so five algorithms cover all nine combinations.
top adjacent
top diagonal
both adjacent
adjacent and diagonal
both diagonal
That is the whole method. Practise it against genuine random-state scrambles on the timer, which bakes them in from the same verified solver that checked the algorithms above.
Checked by simulation before publishing: each position shown plus the moves shown must finish the job, every orientation claim is proved by enumeration of all 27 reachable tops, and the worst-case counts are computed, not promised.