Sudoku Techniques by Difficulty

This is the map to the whole Sudoku School: every solving technique we cover, ordered from the first thing a beginner learns to the patterns only the hardest grids demand. Work down the list in order and you'll build a complete toolkit — each technique picks up where the last leaves off.

Basic — start here

The techniques that solve Easy and most of Medium. No pattern-spotting, just careful looking.

Crosshatching — Scan a digit's existing rows and columns through a box to find the single cell in the box where it can still go.
Naked Single — A cell where only one candidate remains — the digit must go there.
Hidden Single in Sudoku — A digit that can legally go in only one cell of a unit, even if that cell shows other candidates.
Naked Pair — Two cells in a unit holding the same two candidates claim those digits, removing them elsewhere in the unit.
Hidden Pair in Sudoku — Two digits confined to the same two cells of a unit — every other candidate can be cleared from those two cells.
Naked Triple — Three cells in a unit sharing only three candidates between them claim those digits, removing them elsewhere in the unit.
Pointing Pairs in Sudoku — A candidate confined to one row or column within a box is removed from the rest of that line outside the box.
Box/Line Reduction in Sudoku — A candidate confined to one box within a row or column is removed from the rest of that box.
Snyder Notation — Mark a candidate only in the boxes where it can go in exactly two cells — a compact notation that makes hidden singles and pairs jump out.
The Rule of 45 in Killer Sudoku — Every unit totals 45, so comparing a unit's cage sums against 45 reveals the value of a cell that pokes in or out.
Killer Combinations — The set of digit combinations that can fill a cage of a given size and sum — the lookup every Killer solver leans on.
Full House — A unit with only one empty cell — the single missing digit must go there.

Intermediate

Where scanning runs out and you start eliminating candidates methodically.

Innies and Outies — Sum whole cages against the 45-per-unit total; the single cell that pokes in (innie) or out (outie) is fixed by the difference.
Hidden Triple in Sudoku — Three digits that can go in only the same three cells of a unit — every other candidate can be cleared from those cells.
Naked Quad — Four cells in a unit using only four candidates between them claim those digits, removing them elsewhere in the unit.
Hidden Quad in Sudoku — Four digits that can go in only the same four cells of a unit — clear every other candidate from those four cells.
Skyscraper Sudoku Technique Explained — Two rows where a digit sits in only two cells, sharing one column; the digit is cleared from cells that see both far ends.
Two-String Kite — A strong link in a row and one in a column, sharing a box, eliminate the digit from the cell that sees both free ends.
Cage Splitting — Split a boundary-crossing cage into partial sums via the 45-per-unit rule, pinning down the cells on each side.
Cage/Unit Overlap — Where a cage overlaps a unit, a candidate confined to the overlap is removed from the rest of the cage or the rest of the unit — a candidate, not a sum, technique.
Law of Leftovers — In Jigsaw Sudoku, cells of a region sticking out of a set of rows/columns hold the same digits as the cells of other regions sticking in.
Avoidable Rectangle — Three corners of a rectangle are already solved; the fourth must avoid completing a deadly pattern, eliminating one candidate.

Advanced

The first real patterns — single-digit fish and wings for Hard and Expert grids.

X-Wing Sudoku Technique Explained — One digit confined to the same two columns across two rows (or vice versa) — eliminate it from the rest of those lines.
XY-Wing Sudoku Technique — A pivot cell with two candidates links two pincer cells; the digit they share is removed from any cell both pincers see.
Swordfish Sudoku Technique Explained — One digit confined to the same three columns across three rows (or vice versa) — eliminate it from the rest of those columns.
Empty Rectangle — A box whose candidates for a digit lie in a single row and column, plus a conjugate pair, force an elimination at their intersection.
Finned X-Wing — An almost-X-Wing with one extra candidate (a fin); the digit is eliminated only from cover cells that also see the fin.
XYZ-Wing Sudoku Technique Explained — A pivot with three candidates and two bi-value pincers remove the shared digit from any cell that sees all three wing cells.
W-Wing Sudoku Technique Explained — Two cells with the same two candidates, joined by a strong link on one of them, eliminate the other digit from cells that see both.
Remote Pairs — A chain of cells all holding the same two candidates; cells seeing both ends of the chain lose both digits.
Simple Colouring — Colour a digit's conjugate-pair chain in two alternating colours; a colour that appears twice in a unit is false, and cells seeing both colours lose the digit.
Turbot Fish — A four-cell chain on a single digit — two strong links joined by a weak one — that eliminates the digit where both ends can see.
X-Cycles — A loop of alternating strong and weak links on one digit; continuous loops eliminate around the ring, a broken loop forces the digit at the discontinuity.
3D Medusa — Two-colour clustering across bi-value cells and bi-location units for all digits together; any colour clash forces the opposite colour true.
Hidden Unique Rectangle — A unique-rectangle variant that uses a strong link on the extra digit to force an elimination and dodge the deadly pattern.
Grouped X-Cycles — A single-digit loop in which a node can be a group of candidates sharing a box-line, extending the reach of an ordinary X-Cycle.
Multi-Colouring — When two colour clusters on one digit interact, a colour in one cluster can be proven false, eliminating candidates simple colouring cannot reach.
Unique Loop — Two digits circling an even loop of cells across two boxes per step would give two solutions; one cell must break the pattern.
Gurth's Theorem — If a uniquely-solvable puzzle's givens are symmetric under a rotation with a digit relabeling, the solution inherits that symmetry — often fixing the centre cell to 5.
Sashimi Fish — A finned fish whose fin is essential because a base unit would otherwise be empty; eliminations still land only on cover cells that see the fin.
BUG-Lite — A subset of cells forms a bivalue pattern whose digits could swap into a second solution; one cell must break it, forcing an elimination.

Expert

Last-resort logic for the toughest puzzles, where every simpler idea is exhausted.

Jellyfish — One digit confined to the same four columns across four rows (or vice versa) — eliminate it from the rest of those columns.
Finned Swordfish — An almost-Swordfish with one extra candidate; the digit is eliminated only from cover cells that also see the fin.
BUG+1 — When all cells but one are bi-value, the extra candidate in that one cell must be the solution, or the puzzle would have two answers.
Sue de Coq — Cells at a box-and-line intersection, plus almost-locked sets in the box and line, force eliminations in both.
The Phistomefel Ring — In any solved Sudoku, the 16 cells around the centre box contain exactly the same multiset of digits as the four 2×2 corners of the grid.
Unique Rectangle — Because a valid puzzle has only one solution, a four-cell rectangle sharing two candidates is forbidden — which forces an elimination.
WXYZ-Wing Sudoku Technique — Four cells using four candidates, bent across a box and line, remove a digit seen by every cell that could hold it.
X-Chain — A chain of alternating strong and weak links for one digit; cells seeing both ends of an even chain can't hold it.
XY-Chain — A chain of bi-value cells whose ends both force the same digit; cells seeing both ends can't hold it.
Forcing Chains — Follow both values of a bi-value cell; if both branches force the same digit somewhere, that conclusion is certain.
Aligned Pair Exclusion — Two cells that see each other cannot take any digit pair that a commonly-seen almost-locked set forbids, shrinking their candidates.
Finned Jellyfish — An almost-Jellyfish with one extra candidate; the digit is eliminated only from cover cells that also see the fin.
Franken Fish — A fish in which at least one base or cover unit is a box, mixing a box with rows or columns to reach new eliminations.
Mutant Fish — The most general fish: base and cover sets each mix rows, columns and boxes in any combination.
Squirmbag — A five-by-five fish; valid but almost always replaceable by a smaller dual fish, so it is a curiosity more than a workhorse.
ALS-XZ — Two almost locked sets sharing a restricted common digit X force a second common digit Z out of any cell that sees all its copies in both sets.
Death Blossom — A stem cell whose every candidate links to an almost locked set; a digit common to all the petals can be eliminated from cells seeing it in each.
Alternating Inference Chains — A chain of candidates joined by alternating strong and weak inferences; its two endpoints yield an elimination or a placement.
ALS-XY-Wing — Three almost locked sets — a pivot joined to two others by restricted commons — force a digit shared by the outer two out of cells seeing it in both.
Kraken Fish — A fish with an uncovered candidate is completed by chaining from that candidate; if every branch and the fish reach the same elimination, it holds.
Unavoidable Sets — A minimal set of cells whose digits admit two valid arrangements; a unique puzzle must give a clue in every unavoidable set, which underpins deadly-pattern logic.
Grouped Chains — An Alternating Inference Chain in which a node can be a group of candidates sharing a box-line, extending the reach of an ordinary chain.

Where to go next

Not sure which level you're at? Pick a difficulty and see what it asks of you: Easy, Medium, Hard, Expert or Evil. New to candidates? Start with pencil marks — every technique below the basic level depends on them.