Sudoku Techniques

Updated 15 October 2026

A Sudoku technique is a named pattern of candidates that justifies placing a digit or erasing a candidate without guessing. This page lists the techniques Suuudokuuu’s solving engine implements, in the order a solver should try them, from the single cheapest deduction in the game, through the subset patterns that unlock most mid-difficulty puzzles, to the forcing chains that carry the hardest ones, followed by the named chain patterns the engine finds as part of its chain techniques.

It is not every technique ever named. The engine also detects Empty Rectangle, Sue de Coq and ALS-XZ, and the difficulty rating prices them, but they have no page here yet. Other named techniques have no detector at all; when the engine cannot finish a puzzle with what it implements, the hint and the solver say so rather than guess.

Every technique page here carries a worked example board that was produced by running the solving engine bundled with the Suuudokuuu app over a real puzzle position. The highlighted pattern cells, the eliminated candidates and the placement under each board are the engine’s own output, so the explanation and the diagram can never drift apart.

Tier 1 — Singles

Singles place a digit directly. They need no elimination pattern, they never remove a candidate without also solving a cell, and a puzzle solvable with singles alone is what most apps call easy.

• Full House — the last empty cell in a row, column or box takes the one digit that unit is still missing.
• Naked Single — a cell whose row, column and box between them rule out eight digits, leaving one candidate.
• Hidden Single — a digit that fits in only one cell of a unit, even though that cell still has other candidates.

Tier 2 — Intersections

Intersection techniques work on the overlap between a box and a line. They never place a digit on their own; they remove candidates, and those removals usually expose a single on the next pass.

• Pointing Pair — a digit confined to two cells of a box that share a line is erased from the rest of that line.
• Pointing Triple — the same deduction with three cells instead of two.
• Box Line Reduction — the mirror image: a digit confined to one box along a line is erased from the rest of that box.

Tier 3 — Subsets

Subsets reserve a group of digits for a group of cells. Naked subsets are found by looking at cells and counting the digits they can hold; hidden subsets are found by looking at digits and counting the cells that can hold them. Both are elimination techniques, and both scale from two cells up to four.

• Naked Pair — two cells in a unit hold the same two candidates and nothing else.
• Naked Triple — three cells whose candidates together use only three digits.
• Naked Quad — four cells whose candidates together use only four digits.
• Hidden Pair — two digits that fit in only two cells of a unit.
• Hidden Triple — three digits confined to the same three cells.
• Hidden Quad — four digits confined to the same four cells.

Tier 4 — Fish, wings and chains

Beyond the subsets, techniques stop reasoning about a single unit and start reasoning across two or more units, or across a path of cells, at once. Fish patterns trap a digit in the same set of rows and columns; wings link a small handful of cells through shared candidates; chains follow strong and weak links as far as the board allows. These are the techniques that carry the hardest puzzles Suuudokuuu generates.

• X-Wing — a digit confined to the same two columns across two rows is erased from the rest of those columns.
• Swordfish — the same fish pattern spread across three lines instead of two.
• Jellyfish — the same fish pattern spread across four lines.
• Finned X-Wing — an X-Wing with one extra candidate that still supports a smaller, safe set of eliminations.
• Finned Swordfish — the same fin logic applied to a Swordfish.
• Sashimi X-Wing — a finned X-Wing where one base line is missing its normal corner candidate entirely.
• Sashimi Swordfish — the same missing-corner pattern applied to a Swordfish.
• XY-Wing — three bivalue cells arranged so a shared candidate can be erased from any cell that sees both pincers.
• XYZ-Wing — an XY-Wing whose pivot also carries the shared candidate, tightening the elimination further.
• W-Wing — two matching bivalue cells tied together by a strong link on one of their shared candidates.
• X-Chain — a chain of strong and weak links on one digit connecting two cells that share a peer.
• XY-Chain — a chain of bivalue cells whose two endpoints force an elimination wherever they overlap.
• Simple Coloring — a two-color network of strong links on one digit, cleared wherever a cell sees both colors.
• AIC — an alternating inference chain that generalises the fish, wing and chain patterns above into one technique.

Tier 5 — Uniqueness and forcing chains

The last tier steps outside fixed patterns. Uniqueness techniques use the fact that a proper puzzle has exactly one solution, and rule out any move that would leave two. Forcing chains assume a candidate, follow the singles it forces, and keep only what survives every case. Every board in the Hell tier needs one of them, and the record puzzles in the Infinity tier lean on them heavily.

• Unique Rectangle — three corners of a two-box rectangle hold the same pair, so the fourth corner cannot take either digit.
• Bivalue Universal Grave — every empty cell is bivalue except one, which must take the digit that appears three times in its units.
• Nishio Forcing Chain — a candidate whose singles lead to a contradiction is erased.
• Cell Forcing Chain — every candidate of one cell leads to the same placement or elimination.
• Region Forcing Chain — every possible cell for a digit in one unit leads to the same placement or elimination.

Named chain patterns

Some well-known patterns are short chains with names of their own. The engine finds each one with its X-Chain or XY-Chain detector and reports it under that name; these pages show the shape on a real example.

• Turbot Fish — the four-cell X-Chain: two strong links on one digit joined by a weak link.
• Skyscraper — a Turbot Fish whose strong links run along two parallel rows or columns.
• 2-String Kite — a Turbot Fish that joins a row link and a column link inside one box.
• Remote Pair — an XY-Chain whose cells all hold the same two digits.

How to use this list

Work down the list, not across it. A solver that reaches for a naked quad while an unspotted hidden single is sitting on the board is doing far more work than the puzzle asks for, and the same is true of a human. Suuudokuuu applies the techniques in exactly the order above and stops at the first one that fires, which is also how the app decides what to show when you ask for a hint.

The fish patterns, the wings and the chains above follow the same principle as the subsets — reserving digits for cells — but they reason across two or more units at once, or across a path of cells, rather than inside a single unit.