Sudoku Strategies — From Beginner to Advanced

A practical toolkit of solving techniques, ordered from the moves you will use in every puzzle to the patterns that crack the hardest grids.

1. Scanning and Cross-Hatching

Pick a digit and scan every row and column that contains it. Any 3×3 box crossed out by those lines cannot hold the digit, which often leaves exactly one legal cell. Repeat for all nine digits and many easy placements fall out before you write a single note.

2. Last Digit in a Unit

Whenever a row, column, or box has eight digits placed, the ninth is forced. Always sweep for nearly-finished units first — they are free progress.

3. Naked Pairs

If two cells in a unit both have exactly the same two candidates (say 4 and 7), then 4 and 7 must occupy those two cells in some order. Erase 4 and 7 from the candidates of every other cell in that unit.

4. Pointing Pairs

If all candidates for a digit inside a 3×3 box lie in a single row or column, the digit must go in that line within this box — so it can be eliminated from the rest of that row or column outside the box.

5. Box-Line Reduction

The reverse of pointing pairs: if a digit's candidates within a row (or column) all fall inside one 3×3 box, that digit cannot appear anywhere else in the box. Clear it from the box's other cells.

6. Hidden Pairs and Triples

Sometimes two digits appear as candidates in only two cells of a unit, even though those cells show other candidates too. Those two digits must own those two cells, so every other candidate in them can be removed. The same idea extends to three digits in three cells.

7. Naked Triples

If three cells in a unit collectively use only three digits (for example: {2,5}, {5,8}, {2,8}), those three digits fill those three cells in some order. Remove them from the unit's remaining cells.

8. X-Wing

Find a digit whose candidates form a rectangle: exactly two cells in row A, exactly two in row B, sharing the same two columns. The digit must sit on opposite corners, so every other candidate along both columns can be eliminated. The same pattern works column-first.

9. Swordfish

X-Wing's bigger sibling: a digit confined to the same three columns across three rows (three candidates per row, matching columns). Eliminations apply along the three involved columns. Rare but devastating when found.

10. Chains and Contradictions

When the standard arsenal stalls, follow implications: "if this cell is 3, then that cell is 6, then that unit forces..." until you either place a digit or reach a contradiction that rules out your assumption. Used carefully, this logic (never blind trial and error) solves any valid puzzle.

Practice Plan

1. Master scanning on easy sudoku until you finish grids without notes.
2. Learn pairs and pointing techniques on medium sudoku with full pencil marks.
3. Take on hard sudoku and practice spotting X-Wings and hidden sets.

Need the basics first? Start with the rules of sudoku.