Hard Sudoku Techniques
These nine techniques are what you reach for when the medium methods stop paying out. The first two extend the subset idea you already know; the rest are different in kind — they follow one shape across the whole grid, or chain cells together until the grid contradicts itself. None of them needs a guess.
- Naked QuadsFour cells in a unit holding only four candidates between them, so those four shapes leave every other cell.
- Hidden QuadsFour shapes confined to the same four cells, so every other candidate in those cells can go.
- X-WingOne shape restricted to the same two columns in two different rows — a rectangle that clears both columns.
- SkyscraperA near-miss X-Wing: two pairs share one column, and the two loose ends clear anything that sees both.
- Two-String KiteA row and a column that both hold one shape twice and meet in the same box, pinning down a single cell.
- XY-WingThree two-candidate cells forming a pivot and two wings, which together rule one shape out of anything both wings see.
- XYZ-WingAn XY-Wing whose pivot holds a third candidate, tightening the elimination to cells that see all three.
- Remote PairsA chain of cells that all share the same two candidates, alternating along its length so the ends are opposites.
- Simple ColouringMarking one shape’s forced pairs in two alternating labels until a cell that sees both labels gives itself away.
Not there yet? The medium techniques cover pairs, triples and locked candidates — learn those first, because most of the methods here assume you already keep pencil marks.