How to Solve Sudoku Puzzles: A Method That Works
You can solve any Sudoku puzzle by using a repeatable, escalating method: fill in all candidates, then systematically apply the simplest techniques like singles and pairs, only moving to more complex methods like pointing patterns or fish when the current layer yields no more moves. This cycle of scanning for [Naked Singles](/techniques/naked-singles), then [Hidden Singles](/techniques/hidden-singles), followed by pairs and beyond creates a logical workflow that prevents you from jumping to advanced tactics prematurely. By exhausting each logical layer before moving to the next, you build on a solid foundation, making even the hardest puzzles manageable through clear, incremental progress.
Step 1: Fill in All Pencil Marks
Your first move is always to fill in the candidate numbers, or 'pencil marks,' for every empty cell. Look at each row, column, and 3x3 block to determine which digits from 1 to 9 are still missing. Write all possible candidates for a cell in its corner. This complete candidate grid is your roadmap; every solving technique from this point forward relies on analyzing these possibilities. Without accurate pencil marks, you risk missing key patterns and making incorrect eliminations.
- Use a consistent notation style, like small numbers in the corner of each cell.
- Double-check each block after filling marks to ensure no candidate is missed or incorrectly added.
Step 2: The Core Solving Loop - Start with Singles
Begin the core loop by searching for the simplest solves. First, scan for Naked Singles. These are cells where only one candidate number remains because all others have been eliminated by solved digits in its row, column, and block. Place that digit. After placing any Naked Singles, immediately search for Hidden Singles. A Hidden Single is a candidate number that appears only once in a row, column, or block. This digit is the only possible solution for that cell. Placing these singles is the fastest way to fill the grid and trigger new eliminations.
Step 3: Escalate to Pairs and Triples
When your scan for singles comes up empty, escalate to looking for pairs. Search for Naked Pairs first: two cells in the same unit (row, column, or block) that share the exact same two candidates. You can eliminate those two digits from all other cells in that unit. Next, look for Hidden Pairs. This is when two candidates appear only in the same two cells within a unit, hidden among other notes. Finding a Hidden Pair lets you remove all other candidates from those two cells, simplifying them into a Naked Pair. These patterns create powerful eliminations that often reveal new singles.
Step 4: Apply Locked Candidate (Pointing) Patterns
If the grid stalls after pairs, move to locked candidate patterns, also known as Pointing Pairs or Pointing Triples. Examine each 3x3 block. If all instances of a candidate digit are confined to a single row or column within that block, you can 'point' that digit out of the block and eliminate it from the rest of that row or column outside the block. The reverse is also true: if in a row or column, a candidate is locked into one specific block, you can eliminate it from the rest of that block. This technique often clears the way for new singles or pairs to appear.
Step 5: Repeat the Loop and Escalate to Advanced Techniques
This is the key to the method: repetition. Each time you place a digit—whether from a single, a pair deduction, or a pointing pattern—return to the beginning of the loop. Scan for Naked Singles again, then Hidden Singles, then pairs, then pointing patterns. The new elimination from your last solve will have changed the candidate grid, almost certainly creating new opportunities for simpler techniques. Only when you complete a full cycle through singles, pairs, and pointing patterns without finding a single new digit should you consider more advanced strategies like X-Wing, Swordfish, or XY-Wing. This disciplined approach ensures you never miss an easier, available solve.
Key Facts
- ▪A systematic Sudoku solving method begins by filling in all possible candidate numbers for every empty cell, creating a complete pencil mark grid.
- ▪The first and most common solves are Naked Singles, where a cell has only one possible number left.
- ▪Hidden Singles occur when a number can only go in one cell within a row, column, or 3x3 block, even if that cell has other candidates.
- ▪Naked Pairs are two cells in the same unit that share the same two candidates, allowing you to eliminate those digits from other cells in the unit.
- ▪Hidden Pairs are two numbers that only appear in the same two cells of a unit, letting you remove all other candidates from those two cells.
- ▪Locked Candidate or 'Pointing' patterns occur when a candidate is confined to one row/column within a block, allowing elimination from the rest of that row/column.
- ▪The core of the method is a loop: after any digit is placed, restart the search from the simplest technique (singles) and escalate only when needed.
- ▪This escalating cycle ensures you never skip over an easier, available solve by jumping prematurely to complex strategies.
Frequently Asked Questions
What is the most important first step in this method?
Filling in all pencil marks (candidates) completely and accurately. Every subsequent technique relies on analyzing this candidate grid.
How do I know when to move from singles to pairs?
Only move to searching for pairs after you have thoroughly scanned the entire grid for both Naked and Hidden Singles and found none.
What happens after I place a digit from a pair or pointing pattern?
You must restart the solving loop from the beginning. Go back to scanning for Naked Singles, as the new elimination often creates them.
Do I need to learn advanced techniques with this method?
For many puzzles, no. The cycle of singles, pairs, and pointing patterns can solve a large number of puzzles without needing X-Wing or Swordfish.