What black stickers mean
F2L is not an upper-face solving step. The center, edges, and corners that started in the U layer stay black wherever they move. Every other piece keeps its color, so target pieces remain visible when they enter the upper layer.
How random cases are generated
- Mix the full cube with a long sequence that avoids consecutive turns of the same face.
- Solve only the D-Cross projection of that mixed state.
- Accept the case only when D-Cross is solved and all four F2L pairs are broken.
- Show both the mix and the cross repair so playback matches the real state.
Solution methods in the trainer
Applying a scramble shows the pair-by-pair CFOP technique solution by default. Like a human solver, it keeps the cross and finished pairs intact at every step.
The fast near-optimal method uses a weighted heuristic search to find a solution usually within a few moves of optimal almost instantly, and from there you can run the optimality proof to check it against the HTM optimum. Search solutions may temporarily break the cross mid-sequence; only the final first-two-layers state is guaranteed.
When the search exhausts its budget it honestly reports a best-found solution instead of claiming optimality.
The three basic inserts and their triggers
Most F2L cases end in one of three short inserts: R U' R' from the right, its mirror L' U L, or F' U' F through the front. The pair edge's orientation decides which face can insert it.
Longer solutions are built from the same triggers. U R U' R' adds one setup move before the insert, and the sequences for a twisted or an already-solved corner repeat a trigger to take a piece out before returning the pair.
The F2L example solutions in the learning library are standard CFOP algorithms, so the moves you watch are the moves worth memorizing.
A useful repetition order
- Describe the locations of the four corners and edges before turning.
- Choose a pair order and keep checking D-Cross.
- Replay the scramble one move at a time when a piece path is unclear.
- Open the same link and try starting with a different pair.