Every Sudoku solving technique on one page, organized from beginner to advanced. Bookmark this reference card and consult it whenever you get stuck on a puzzle.
Work through techniques in order of difficulty. Start with Beginner techniques on every puzzle. If those do not make progress, move to Intermediate. Only reach for Advanced techniques when simpler methods are exhausted. Most published puzzles, even hard ones, can be solved with techniques through the Intermediate level.
Each technique below includes a brief description, when to apply it, and a link to a detailed strategy page with visual examples. For a step-by-step approach to solving, see our complete strategies guide.
These foundational techniques are all you need for easy puzzles. They rely on direct observation without complex pattern recognition.
When a cell has only one possible candidate remaining after checking its row, column, and box, that number must go there. Always the first technique to apply. Works on every puzzle.
When a number can only appear in one cell within a row, column, or box, it must go in that cell, regardless of other candidates present. Apply after Naked Singles. Essential for easy and medium puzzles.
Scan rows and columns intersecting a box to eliminate candidates. If a number already exists in a crossing row or column, it cannot appear in those cells within the box. A visual scanning technique that works well for quickly filling boxes.
These techniques require pencil marks (candidate notation). They involve identifying relationships between cells within the same row, column, or box to eliminate candidates.
When two cells in the same house contain exactly the same two candidates, those two numbers can be eliminated from all other cells in that house. Look for two cells with identical two-candidate sets on medium puzzles and harder.
When two candidates appear only in the same two cells within a house, all other candidates in those two cells can be removed. Requires pencil marks to spot effectively on medium to hard puzzles.
When a candidate within a box is confined to a single row or column, that candidate can be eliminated from the rest of that row or column outside the box. Look for candidates restricted to one line within a box on medium puzzles.
When a candidate in a row or column is confined to a single box, that candidate can be eliminated from other cells in that box. The complement of Pointing Pairs. Apply on medium to hard puzzles.
Three cells in the same house that together contain exactly three candidates. Those three numbers can be removed from all other cells in that house. An extension of Naked Pairs to three cells on hard puzzles.
Three candidates that appear only within three cells in a house. All other candidates in those three cells can be eliminated. Harder to spot than Naked Triples, used on hard puzzles.
These powerful techniques span multiple rows, columns, and boxes. They are needed for expert and evil-rated puzzles where simpler methods reach a dead end.
When a candidate appears in exactly two cells in each of two rows, and those cells share the same two columns, the candidate can be eliminated from all other cells in those columns (and vice versa for column-based X-Wings). Used on hard to expert puzzles.
An extension of X-Wing to three rows and three columns. When a candidate appears in two or three cells in each of three rows, and all those cells fall within three columns, the candidate can be eliminated from other cells in those columns. Used on expert puzzles.
Further extension to four rows and four columns. Rare in published puzzles but follows the same pattern logic as X-Wing and Swordfish. Only needed in the most extreme expert puzzles.
Three cells forming a pivot-and-wings pattern. The pivot cell has two candidates (XY), each wing shares one candidate with the pivot and has a common candidate (Z). Z can be eliminated from cells that see both wings. Used on expert puzzles.
Exploits the rule that a valid Sudoku has exactly one solution. If four cells in two rows and two boxes form a rectangle with the same two candidates, additional candidates must be true to prevent multiple solutions. Used on expert puzzles.
Assign two colors to a candidate's conjugate pairs (cells where it appears exactly twice in a house). Follow the chain of alternating colors. If a contradiction arises in one color, the other must be true. A chain-based technique for deep eliminations on expert puzzles.
Assume a candidate is true in a cell and follow the logical consequences. Then assume it is false and follow again. If both assumptions lead to the same conclusion for another cell, that conclusion must be true. A last-resort logical technique for expert and evil puzzles.
Easy Puzzles: Naked Singles and Hidden Singles are sufficient. No pencil marks needed. Typically 36 to 45 given clues.
Medium Puzzles: Add Naked Pairs, Pointing Pairs, and Box/Line Reduction. Pencil marks become helpful. Typically 30 to 35 clues.
Hard Puzzles: Hidden Pairs, Naked Triples, and Hidden Triples come into play. Pencil marks are essential. Typically 26 to 30 clues.
Expert Puzzles: X-Wing, Swordfish, XY-Wing, and chain-based techniques. Full candidate notation required. Typically 22 to 27 clues.
Follow this systematic approach when solving any Sudoku puzzle:
1. Scan for Naked Singles - Check every empty cell. If only one number fits, fill it in immediately.
2. Scan for Hidden Singles - For each number 1 to 9, check each row, column, and box. If a number can only go in one cell, place it.
3. Fill in pencil marks - For remaining empty cells, note all possible candidates.
4. Apply elimination techniques - Use Naked Pairs, Pointing Pairs, and Box/Line Reduction to remove candidates.
5. Repeat steps 1 and 2 - After eliminations, new singles often appear. Cycle through basic techniques again.
6. Escalate to advanced techniques - If stuck, look for X-Wings, Swordfish, XY-Wings, and other advanced patterns.
House: A row, column, or 3x3 box - any unit that must contain digits 1 to 9.
Candidate: A possible number that could go in an empty cell.
Given / Clue: A number pre-filled in the puzzle at the start.
Pencil Mark: Small notation of candidate numbers written in a cell.
Conjugate Pair: Two cells in a house where a candidate appears in exactly those two cells.
Elimination: Removing a candidate from a cell based on logical deduction.
Always start with the simplest techniques and work up. Begin with Naked Singles and Hidden Singles on every puzzle. If those stall, try Naked Pairs and Pointing Pairs. Only move to advanced techniques like X-Wing and Swordfish when intermediate methods are exhausted. This approach is the most efficient because simpler techniques are faster to apply and often unlock new placements that make advanced techniques unnecessary.
Naked Singles is the easiest strategy. You simply check each empty cell and count how many numbers are already present in its row, column, and box. If only one number is missing from those three units combined, that number goes in the cell. No pencil marks or complex reasoning required.
No. Easy puzzles can almost always be solved using only Naked Singles and Hidden Singles. You will not need pairs, triples, X-Wings, or any advanced technique. These harder methods become necessary starting at medium difficulty and are essential for hard and expert puzzles.
Naked techniques focus on cells: you look at what candidates a cell contains. If two cells have exactly two candidates, that is a naked pair. Hidden techniques focus on numbers: you look at where a number can go within a unit. If two numbers can only go in two cells, that is a hidden pair. Both achieve candidate elimination but from different perspectives.
Start using pencil marks when you move to medium difficulty puzzles. For easy puzzles, you can usually solve by scanning alone. But medium and harder puzzles require tracking candidates in each cell to spot pairs, triples, and advanced patterns. Good pencil mark habits built at medium difficulty will serve you well at every harder level.
Ready to put your skills to the test?
Try Final Sudoku - an ad-free Sudoku experience with smart tools