Every technique the solver knows, in order — weakest first. Drill each one on real puzzles that actually contain it, then name it in a puzzle's trophy room to unlock the next.
How a stage unlocks
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Beat a puzzle. Any puzzle counts — one of a stage's own drills below, or one you've already solved, even from before you ever opened this page.
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Open its trophy room. A trophy icon appears at the top of that play's own page only once you've beaten it — it isn't there while you're still solving. Tap it to open the trophy room.
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Name what you found. Pick the cell where you spotted it, choose the technique and digit, and submit. Get it right and that stage passes immediately, unlocking the next one; get it wrong and it costs one of three strikes on that puzzle, but never blocks you from trying again on another.