How to Solve Sudoku Puzzles: A Complete Walkthrough, Part 1

Step 1: The Systematic Opening Scan (One Digit at a Time)

Do not look at the whole grid at once. Instead, pick a single digit from 1 to 9 and scan the entire puzzle for all its given positions. For each found 'given,' mentally cross out that digit as a possibility from the entire row, column, and 3x3 box it occupies. This process of elimination is the core of Sudoku logic. For example, if you scan for '5' and find one in the top-left box, you know no other cell in that row, that column, or that 3x3 box can be a 5. Repeat this scan for all digits from 1 to 9. This initial pass gives you a mental map of where each number can and cannot go, which is crucial for spotting the first easy placements.

• Start with the digit that appears most often in the givens, as it will have the most eliminations.
• Use your finger or a pencil tip to trace the row, column, and box of each given to avoid missing an elimination.

Step 2: Find and Place All Naked Singles

After your full-digit scan, examine every empty cell. A Naked Single is a cell where, after all your mental eliminations, only one possible digit remains. This is the easiest move in Sudoku. Place that digit firmly in the cell. For instance, if a cell is in a row that already has 1,2,3, in a column with 4,5,6, and in a box with 7,8, then the only missing digit is 9. That cell is a Naked Single for 9. Work through the entire grid cell by cell to find these. Every number you place creates new eliminations, so after placing a few, pause and mentally update the possibilities for affected rows, columns, and boxes. This often creates a cascade, revealing more Naked Singles.

Step 3: Fill in Pencil Marks for Every Empty Cell

Once no more obvious Naked Singles appear, it's time for full pencil marking. This is a critical habit for progressing beyond the simplest puzzles. In each remaining empty cell, write small, neat numbers (called candidates or pencil marks) for every digit that is not eliminated by the row, column, or box. If a cell could be a 3, 7, or 9, pencil in '379'. This visual record replaces your mental tracking and is essential for spotting the next level of patterns. Accuracy here is vital; one wrong pencil mark can lead you down a wrong path. Take your time to ensure each cell's candidates are correct based on all currently placed numbers.

Step 4: Re-scan with New Digits and Find Hidden Singles

With your pencil marks complete, the puzzle enters a new phase. You must now re-scan, but this time you are looking for two things: new Naked Singles (cells where your pencil marks show only one candidate) and, more importantly, Hidden Singles. A Hidden Single occurs when a candidate number appears only once in a row, column, or box. For example, if in a particular row, the digit '4' is only penciled in one cell (even though that cell has other candidates like '4' and '7'), then that cell must be '4'. The '4' is hidden among other notes. Check each row, column, and box for digits 1-9 to find these. Every Hidden Single you find and place becomes a new given, allowing you to erase that digit as a candidate from its related units and update your pencil marks.

• Scan by 'unit' (row/column/box) and by 'digit.' Look down a column and ask, 'Where can 8 go in this column?'
• After placing any new number, immediately erase that digit as a candidate from its row, column, and box to keep your pencil marks accurate.

Step 5: Stop and Assess the Remaining Puzzle

Repeat the cycle of Step 4—update pencil marks, scan for Naked and Hidden Singles, place numbers—until you make a full pass without finding any new singles. This is a natural stopping point for the opening phase. The puzzle is now 'candidate-rich.' You will likely see many cells with 2 or 3 pencil marks left. Congratulations! You have successfully simplified the puzzle using basic logic alone. The remaining challenge requires identifying patterns among these pencil marks, such as pairs and triples, which will be covered in later guides like our walkthrough Part 3. At this stage, take a moment to note if any rows, columns, or boxes are nearly complete, as these will be key areas for the next techniques.

Building Fast, Accurate Opening Habits

Speed in Sudoku comes from routine, not rushing. The most efficient solvers automate the scan-place-update cycle. First, always perform the full 1-9 digit scan at the start. Second, never delay pencil marking; as soon as the easy placements slow, fill in all candidates. Third, after placing a number, make it a reflex to eliminate that digit from pencil marks in its row, column, and box. Fourth, scan systematically: check all rows for Hidden Singles, then all columns, then all boxes. This prevents you from staring at the grid randomly. Practicing this structured approach on easy puzzles builds muscle memory, making you faster on harder ones where this phase is just the warm-up. For more foundational strategies, see our guide on solving Sudoku for beginners.