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Sudoku Techniques: The Complete Guide

Every canonical solving technique, from the patterns you use on every easy puzzle to the chain logic required for expert grids. Each section explains the pattern, how to spot it, and shows a mini-grid example.

How to read the grids

  • Given - clues from the starting puzzle
  • Subject - cells the technique focuses on
  • Eliminated - candidates this technique removes
  • Candidate - pencil marks shown for reference
Basic

Naked Single

A naked single is a cell that has only one possible value left after eliminating digits already present in its row, column, and 3x3 box. It is the most fundamental technique in Sudoku - every puzzle solution is built on chains of naked singles.

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Basic

Hidden Single

A hidden single is a digit that can only legally go in one cell within a row, column, or 3x3 box - even though that cell has other candidates. It is the second most common technique and the foundation of cross-hatching.

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Basic

Naked Pair (and Triple)

When two cells in the same row, column, or box have identical candidate pairs (say, only {3, 8}), those two digits are locked into those two cells. They can be eliminated from every other cell in the same unit.

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Basic

Hidden Pair (and Triple)

When two digits can only appear in the same two cells within a unit - even though those cells have other candidates - the two digits form a hidden pair. All other candidates can be eliminated from those two cells.

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Intermediate

Pointing Pair (Box-Line Reduction)

When a digit can only appear in cells of one row or column within a box, that digit must be placed in that row or column - which means it cannot appear elsewhere in the row or column outside the box.

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Intermediate

Box-Line Reduction (Claiming)

The inverse of a pointing pair. When a digit can only appear in the part of a row or column that intersects a single 3x3 box, the digit is locked inside that box - eliminate it from the rest of the box.

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Intermediate

X-Wing

An X-Wing is the simplest fish technique. When a digit appears in exactly two cells of two different rows, and those four cells form a perfect rectangle in two columns, the digit can be eliminated from every other cell of those two columns (and vice versa).

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Advanced

Swordfish

A Swordfish is the 3-row/3-column generalization of the X-Wing. If a digit has candidates in at most three cells across three different rows, and those candidates all fall within the same three columns, the digit can be eliminated from those columns outside the three rows.

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Advanced

XY-Wing

An XY-Wing uses three bi-value cells - the "pivot" and two "wings" - to eliminate a single digit. If the pivot pencils {X, Y}, one wing pencils {X, Z}, the other wing pencils {Y, Z}, and both wings see the pivot, then any cell seen by BOTH wings cannot contain Z.

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Advanced

XYZ-Wing

A natural extension of the XY-Wing. The pivot pencils three candidates {X, Y, Z}, the two wings pencil {X, Z} and {Y, Z}, and both wings see the pivot. Any cell that sees the pivot AND both wings cannot contain Z.

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Advanced

Unique Rectangle

A well-formed Sudoku has exactly one solution. The Unique Rectangle technique exploits this: if four cells in two rows, two columns, and two boxes are all about to pencil the same two digits, the puzzle would have two solutions - so one of those candidates must be eliminated.

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Advanced

Simple Coloring

When a digit appears in exactly two cells of a unit, those two cells form a "conjugate pair" - one is true, the other is false. Chain conjugate pairs together with two colors and you can deduce contradictions that eliminate the digit from cells that see both colors.

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Which technique do I need for which difficulty?

Different difficulty levels demand different techniques. Use this as a rough guide for what to study next.

Difficulty Techniques you need Notes
Very Easy / Easy Naked Single, Hidden Single Pure scanning. Pencil marks are optional.
Medium Naked Pair, Hidden Pair, Pointing Pair, Box-Line Reduction Pencil marks become essential. Most "stuck" moments are an unspotted pair.
Hard X-Wing, Naked Triple, Hidden Triple, Coloring Fish techniques and chain logic come into play.
Expert Swordfish, XY-Wing, XYZ-Wing, Unique Rectangle, deeper coloring Multiple advanced techniques chained together on a single grid.

Time to practice

Reading is half the work. Try a puzzle now and look for the techniques you just learned.