Sudoku Techniques — A Solver's Glossary

Twenty techniques every sudoku solver should know, organized from the singles you'll find on easy puzzles up to the chain reasoning that cracks the toughest ones. Each page is plain-language with a worked example — and a daily puzzle to practice on.

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Beginner

Foundational placements you'll use on every puzzle.

Naked single

★☆☆☆☆

A cell where only one digit fits.

Hidden single

★☆☆☆☆

A digit that fits in only one cell of a unit.

Intermediate

Elimination patterns that unstick most medium and hard puzzles.

Pointing line

★★☆☆☆

A digit confined to one row or column inside a box.

Box-line reduction

★★☆☆☆

A digit in a row or column trapped inside one box.

Naked pair

★★☆☆☆

Two cells in a unit sharing exactly the same two candidates.

Hidden pair

★★★☆☆

Two digits that fit in only the same two cells.

Naked triple

★★★☆☆

Three cells sharing only three candidate digits between them.

Hidden triple

★★★☆☆

Three digits that fit in only the same three cells.

Naked quad

★★★☆☆

Four cells sharing only four candidate digits between them.

Hidden quad

★★★☆☆

Four digits that fit in only the same four cells.

Advanced

Fish and wing patterns — the bridge into expert solving.

X-Wing

★★★☆☆

A digit locked into the same two columns across two rows.

Swordfish

★★★★☆

X-Wing's bigger sibling: three rows, three columns.

Skyscraper

★★★☆☆

Two rows where a digit has two candidates each, sharing one column.

Two-string kite

★★★☆☆

A row and column where a digit has two cells, anchored in a shared box.

Empty rectangle

★★★★☆

A box where a digit forms an L, paired with a strong link outside.

Y-Wing

★★★★☆

A bivalue pivot with two bivalue wings sharing a common digit.

XYZ-Wing

★★★★☆

A trivalue pivot pinching a digit across three cells.

W-Wing

★★★★☆

Two matching bivalue cells connected by a strong link.

Expert

Chain and uniqueness reasoning — the techniques that crack the hardest puzzles.

Simple coloring

★★★★★

A two-color chain on a single digit reveals contradictions.

Unique rectangle

★★★★☆

Assume the puzzle has one solution — and avoid creating a deadly pattern.