How to Play Sudoku
Quick Overview
Sudoku is a logic-based number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids (also called "boxes" or "regions") contain all of the digits from 1 to 9 without repetition.
Basic Rules
The rules of Sudoku are straightforward:
- Fill in the grid so that every row, column, and 3×3 box contains the numbers 1 through 9 exactly once.
- Some numbers (called "givens") are already filled in to start the puzzle.
- You can't change the given numbers.
- There is only one valid solution to each puzzle.
Example Sudoku puzzle
How to Start Solving
1. Scan rows, columns, and boxes
Look for rows, columns, or boxes with several numbers already filled in. The more numbers filled in, the easier it is to determine what's missing.
2. Look for single candidates
Find empty cells that can only contain one possible number. If a cell has only one possible value based on what's already in its row, column, and box, you can confidently fill it in.
3. Use elimination
For each empty cell, consider which numbers are already present in the same row, column, and box. The remaining numbers are your candidates for that cell.
4. Work back and forth
After filling in a cell, re-scan the affected row, column, and box to see if any new cells now have only one possible value.
Basic Solving Techniques
Sole Candidate
If a cell has only one possible number that can go in it (after considering its row, column, and box), that number must be the answer for that cell.
If a cell can only contain the number 7 because 1-6 and 8-9 are already present in its row, column, or box, then 7 is the answer.
Unique Candidate
If a number can only go in one cell within a row, column, or box, then that number belongs in that cell.
If in a particular row, the number 4 can only go in one specific cell (because other cells in that row already have constraints preventing 4), then that cell must contain 4.
Candidate Lines
If a number can only appear in one row (or column) within a 3×3 box, then that number cannot appear in that same row (or column) in other boxes.
If in a 3×3 box, the number 9 can only be placed in cells that are all in the same row, then 9 cannot appear elsewhere in that row outside the box.
Advanced Techniques
Pairs and Triples
If two cells in the same row, column, or box can only contain the same two numbers, those numbers can be excluded from other cells in that row, column, or box.
This extends to triples as well: if three cells can only contain the same three numbers, those numbers can be excluded from other cells.
X-Wing
If a candidate number appears exactly twice in each of two different rows, and these candidates are aligned in the same columns, then this number can be eliminated from other cells in those columns.
Y-Wing (XY-Wing)
This involves three cells forming a "Y" shape, where the central cell has two possible values, and each of the other cells shares one possible value with the central cell but has a different second value.
Swordfish and Jellyfish
These are extensions of the X-Wing technique to three or four rows and columns.
Sudoku Variants
Diagonal Sudoku
In addition to the standard rules, the two main diagonals (from top-left to bottom-right and from top-right to bottom-left) must also contain the numbers 1-9 exactly once.
Killer Sudoku
The grid is divided into "cages" (irregularly shaped regions), and the sum of the numbers in each cage must equal a specified value. Standard Sudoku rules still apply.
Jigsaw Sudoku
Instead of 3×3 boxes, the grid is divided into irregularly shaped regions of 9 cells each. Each region, along with each row and column, must contain the digits 1-9.
Samurai Sudoku
Five 9×9 Sudoku grids are overlapped to form a larger puzzle. The overlapping regions must satisfy the constraints of both grids they belong to.
Tips for Beginners
- Start with easier puzzles (usually rated by difficulty) and gradually work your way up
- Use pencil marks to note possible candidates for each cell
- Don't guess! Sudoku puzzles can always be solved through logic
- If you get stuck, take a step back and look at the entire puzzle
- Check your work regularly to avoid compounding errors
- Practice regularly – your pattern recognition will improve over time
- When you're stuck, try applying a different technique