These are the 24 techniques the grader works with, in the order a solver usually meets them. The tier a technique sits in decides the lowest band a puzzle needing it can be: a puzzle that cannot be finished without an X-Wing is never a Gentle, however few cells are blank.
The worked examples are real positions, found by the solver in generated puzzles rather than drawn by hand — so what you see is what it actually does.
Tier 1 — first asked for by Gentle
Tier 2 — first asked for by Moderate
- Pointing Pair/TripleIf every home for a digit inside a box lies on one line, the digit leaves the rest of that line.
- Box/Line ReductionIf every home for a digit on a line lies inside one box, the digit leaves the rest of that box.
- Naked PairTwo cells in a unit sharing the same two candidates lock those digits away.
- Hidden PairTwo digits confined to the same two cells push every other candidate out of them.
Tier 3 — first asked for by Tough
- Naked TripleThree cells in a unit sharing three candidates between them lock those digits away.
- Hidden TripleThree digits confined to the same three cells clear everything else out of them.
- Naked QuadFour cells in a unit sharing four candidates between them lock those digits away.
- Hidden QuadFour digits confined to the same four cells clear everything else out of them.
- X-WingA digit confined to the same two columns in two different rows leaves those columns elsewhere.
- Simple ColouringFollow one digit through its two-cell units, colour the chain alternately, and one colour must be true.
- Y-WingA pivot cell and two pincers force a digit into one of the pincers, clearing it from what both see.
- SwordfishThe X-Wing pattern with three rows and three columns instead of two.
Tier 4 — first asked for by Diabolical
- BUG+1When every unsolved cell but one holds two candidates, the odd cell takes the digit that breaks the symmetry.
- XYZ-WingA Y-Wing whose pivot also carries the eliminating digit.
- W-WingTwo matching pairs joined by a strong link force one of them to take the other digit.
- Unique RectangleFour corners holding the same two candidates would give the puzzle two solutions, so the shape must be broken.
- Remote PairsA chain of identical two-candidate cells alternates, so its ends between them cover both digits.
- JellyfishThe same fish pattern again, at size four.