How to Solve Sudoku Step by Step: A Complete Walkthrough
Solving Sudoku follows a repeatable process: scan for singles, mark candidates, find pairs, and apply advanced techniques. This logical progression, from the easiest to the most complex patterns, allows you to solve puzzles of all difficulty levels. This walkthrough provides a clear, step-by-step method you can apply to any puzzle, starting with the simple rules and building up to more complex deductions. If you need a refresher on the rules, check out our guide on [How to Play Sudoku](/blog/how-to-play-sudoku).
Step 1: Understand the Grid and Basic Rules
Before you place a single digit, confirm you know the puzzle's layout and core constraints. A standard Sudoku grid has 81 cells arranged in a 9x9 square, divided into nine 3x3 boxes. Every row, column, and 3x3 box must contain the digits 1 through 9 exactly once. All puzzles start with a set of given numbers that provide the starting logic. For example, if a row already has the numbers 1, 2, 3, 4, 5, 6, and 7, you know the two empty cells must be 8 and 9.
Step 2: Scan for Naked Singles (The Easiest Move)
Your first and most frequent action is to scan for Naked Singles. Look at each empty cell and check all other cells in its row, column, and box. If eight of the nine digits are already present in those 'peer' cells, the ninth digit is the only possible candidate for that cell. This is the simplest logical deduction. For instance, if a cell's row, column, and box collectively contain the numbers 1, 2, 3, 4, 5, 6, 7, and 9, then the cell must be an 8. Fill it in immediately and repeat this scan after every placement, as new singles will appear.
- Always scan the entire grid after placing a number. Each new digit creates new information.
Step 3: Find Hidden Singles (Looking Within a Unit)
When no more Naked Singles are visible, switch your focus to individual units: rows, columns, and boxes. Look for a digit that can only go in one specific cell within that unit. This is a Hidden Single. For example, within a particular 3x3 box, if the digit '3' is not yet placed, check which cells could possibly hold it based on the rows and columns. If only one cell remains as a possible location for the '3' within that box, you have found a Hidden Single and can place the digit. This technique often reveals the next move when scanning for Naked Singles fails.
Step 4: Mark Pencil Marks (Candidate Notation)
For harder puzzles, you need to start noting all possible candidates for each empty cell. This is called 'pencil marking'. For each empty cell, write small digits (1-9) that are not already present in its row, column, or box. Systematic pencil marking reveals patterns that are impossible to see otherwise. It transforms the puzzle from a visual search into a logic puzzle based on candidate elimination. This step is crucial for applying the advanced techniques that follow.
Step 5: Look for Pairs and Triples
With candidates noted, search for subsets. A Naked Pair is two cells in the same unit (row, column, or box) that share the exact same two candidates. Since those two digits must occupy those two cells, you can eliminate those two candidates from all other cells in that same unit. Similarly, look for Pointing Pairs, where if a candidate appears only in one row or column within a box, you can eliminate it from the rest of that row or column outside the box. Finding these patterns systematically cleans up your pencil marks, often revealing new singles.
Step 6: Apply Advanced Techniques (Like X-Wing)
For the toughest puzzles, you may need pattern-based strategies. The X-Wing is a classic advanced technique. It occurs when a candidate is confined to two rows and two columns, forming a rectangle. If the candidate appears as a possibility in only two cells in each of those two rows (and those cells line up in columns), you can eliminate that candidate from all other cells in those two columns. Mastering techniques like X-Wing requires practice with pencil-marked grids but is the key to solving the most challenging puzzles without guessing.
- Advanced techniques like X-Wing are pattern recognition tools. Practice identifying the shape on solved puzzles first.
Key Facts
- ▪Sudoku is solved by placing digits 1-9 so each row, column, and 3x3 box contains each digit exactly once.
- ▪A Naked Single is a cell where only one digit is possible because all other eight digits are already in its row, column, and box.
- ▪A Hidden Single is a digit that has only one possible cell left within a specific row, column, or 3x3 box.
- ▪Pencil marking, or noting all possible candidates for empty cells, is essential for solving medium and hard puzzles.
- ▪A Naked Pair is two cells in the same unit sharing the same two candidates, allowing you to eliminate those candidates from other cells in that unit.
- ▪A Pointing Pair occurs when a candidate in a box is restricted to one row or column, letting you eliminate it from the rest of that row or column outside the box.
- ▪The X-Wing technique uses a rectangular pattern of a candidate across two rows and two columns to perform eliminations.
- ▪The solving process is iterative: place a digit, then re-scan the grid, as each new placement changes the possibilities for other cells.
- ▪All Sudoku puzzles can be solved through pure logic without guessing, using a progression of techniques from simple to complex.
Frequently Asked Questions
What is the first thing I should do when solving a Sudoku?
Scan the entire grid for Naked Singles, cells where only one digit can go because the other eight are already in its row, column, and 3x3 box.
What is the difference between a Naked Single and a Hidden Single?
A Naked Single is obvious from looking at one cell's peers. A Hidden Single requires checking a specific digit's placement within a single row, column, or box to see it has only one possible cell.
When should I start using pencil marks?
Start pencil marking when you can no longer find any Naked or Hidden Singles through simple scanning. This is typically at the medium difficulty level.
What is the most important rule in Sudoku?
The fundamental rule is that every row, column, and 3x3 box must contain all digits from 1 to 9 exactly once. Every solving technique is derived from this constraint.
Do I need to learn advanced techniques like X-Wing?
For easy and medium puzzles, basic techniques are enough. Advanced techniques like X-Wing are necessary to solve hard and expert-level puzzles logically.