How to Solve Sudoku

Solving Sudoku is a process of constraint-based elimination. You never guess — every digit is determined by what cannot go anywhere else. This guide walks through the techniques in the order you should learn them, from beginner scanning through expert chain-based logic.

Step 1: Naked Singles (basic scanning)

A naked single is a cell where only one digit can possibly fit because the other eight digits already appear in that row, column, or box. To find naked singles, scan each empty cell and check: which digits already appear in its row, column, or 3×3 box? If eight digits are eliminated, the remaining digit must go in that cell. Easy and Kids Sudoku puzzles are often solvable using naked singles alone.

Step 2: Hidden Singles

A hidden single is a cell where only one digit can fit even though multiple digits appear as candidates. To find a hidden single, pick a row, column, or box, then for each digit 1–9 missing from that unit, identify which cells could hold it. If only one cell can hold a particular digit, that is the placement — regardless of how many other candidates that cell has. Hidden singles are the primary technique for Medium Sudoku.

Step 3: Naked Pairs, Triples, and Quads

A naked pair is two cells in the same row, column, or box that share exactly two candidates. Those two candidates can be eliminated from every other cell in that unit — because the two cells must contain those two digits in some order. Naked triples extend the same logic to three cells sharing three candidates, and naked quads to four cells with four candidates.

Step 4: Hidden Pairs, Triples, and Quads

A hidden pair is two digits that appear as candidates in exactly two cells of a unit. Those two cells must contain those two digits, so all other candidates can be eliminated from those cells. Hidden pairs are subtle because they require looking at which digits are constrained, not which cells are constrained.

Step 5: Pointing Pairs and Box-Line Reduction

If a candidate digit appears in only one row or column within a 3×3 box, that digit can be eliminated from the rest of that row or column outside the box. This technique works both ways: a candidate restricted to one box within a row or column can be eliminated from the rest of the box. Together, pointing pairs and box-line reduction unlock most Hard Sudoku puzzles.

Step 6: X-Wing

X-Wing applies when a candidate digit appears in exactly two cells of two different rows, AND those cells share the same two columns. Those four cells form a rectangle. The digit can be eliminated from every other cell in those two columns. The same logic works with columns swapped for rows.

Step 7: Swordfish

Swordfish extends X-Wing to three rows and three columns. A candidate appears in two or three cells in each of three rows, with all those cells confined to the same three columns. The candidate can be eliminated from every other cell in those three columns.

Step 8: Y-Wing (XY-Wing)

Y-Wing uses three cells: a pivot cell with two candidates X and Y, and two pincer cells. One pincer shares X with the pivot and has a different second candidate Z. The other pincer shares Y with the pivot and the same candidate Z. Then any cell that sees both pincers cannot contain Z, because whichever pincer ends up being Z would force a contradiction otherwise.

Step 9: Colouring (Simple Colours and Multi-Colours)

Colouring tracks the implications of a single digit through the grid. Find a cell with that candidate, mark it Colour A. Trace through bilocal links (units where the candidate has only two valid cells), alternating Colour A and Colour B. Two cells of the same colour in the same unit force a contradiction — the candidate must be the other colour.

Step 10: AIC and Forcing Chains

Alternating Inference Chains (AIC) generalise X-Wing, Y-Wing, and colouring into a unified technique. AICs follow chains of strong and weak inferences across multiple digits, eliminating candidates that any branch of the chain would force into contradiction. Forcing chains take this further by testing all possibilities from a starting cell.

Practice path

Master the techniques in order. Most solvers spend a week on naked singles and hidden singles before moving to pairs and triples. Pointing pairs and X-Wing each take a week or two. Y-Wing typically takes a month of regular practice. Colouring and AIC are advanced techniques used by world-class solvers and take 2–3 months of dedicated study.

Each technique below has its own page with a worked explanation of how to spot it and when it applies.

• Naked Single — beginner. A naked single is a cell where only one digit remains possible, because the other eight already appear in that cell's row, column, or 3×3 box.
• Hidden Single — beginner. A hidden single is a digit that can legally go in only one cell within a row, column, or 3×3 box — even though that cell may have several other candidates of its own.
• Naked Pair — intermediate. A naked pair is two cells in the same row, column, or box that both have exactly the same two candidates and nothing else.
• Pointing Pair — intermediate. A pointing pair occurs when all remaining candidates for a digit inside one 3×3 box fall in the same row or the same column.
• X-Wing — advanced. An X-Wing appears when a digit is a candidate in exactly two cells in each of two different rows, and those cells sit in the same two columns — forming a rectangle.
• Swordfish — advanced. A swordfish is the three-row version of an X-Wing.

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