Introduction
Sudoku has been a fixture in newspapers since Wayne Gould convinced The Times of London to publish it in 2004. The puzzle itself traces back to Howard Garns' "Number Place" in 1979. Today, teachers, app developers, and puzzle enthusiasts need programmatically generated Sudoku grids. This tool generates puzzles at four difficulty levels and can also solve puzzles you paste in. The generator uses backtracking with a uniqueness check to ensure each puzzle has exactly one solution. Everything runs in your browser.
What this tool does
- Generates Sudoku puzzles at four difficulty levels: easy, medium, hard, and expert
- Each puzzle is guaranteed to have a unique solution (for easy and medium difficulties)
- Displays the generated puzzle in standard 9x9 grid notation with box separators
- Shows or hides the solution on demand
- Doubles as a solver: paste any 9x9 grid (using dots or zeros for blanks) to get the solution
How this tool works
The generator first creates a fully solved 9x9 grid using backtracking with randomized number selection. It then removes cells one by one, checking after each removal that the puzzle still has a unique solution. For easy and medium difficulties, a full uniqueness check runs after each cell removal. For hard and expert difficulties, the uniqueness check is skipped to allow faster generation with fewer clues, though this means some expert puzzles may have multiple solutions. The difficulty levels correspond to target clue counts: easy (45 clues), medium (35), hard (28), and expert (24). The minimum number of clues for a unique Sudoku solution is 17, as proven by McGuire, Tugemann, and Civario in 2012. When you paste a puzzle to solve, the solver uses the same backtracking algorithm to find the solution.
How Sudoku generation and solving works
Sudoku generation relies on two algorithms: grid filling and cell removal. Grid filling uses backtracking: place a number, check if it is valid (no duplicate in row, column, or 3x3 box), and recurse. If no number works, backtrack and try the next option. The numbers are shuffled at each step to produce different grids. Cell removal iterates through positions in random order, removing each cell and checking if the puzzle still has a unique solution. The uniqueness check counts solutions up to a limit of 2: if exactly 1 solution exists, the removal is accepted; otherwise the cell is restored. This is computationally expensive, which is why the check is skipped for hard and expert levels. The solver uses the same backtracking approach but without randomization, finding the first valid solution.
How to use this tool
- Select a difficulty level from the dropdown (easy, medium, hard, or expert).
- A puzzle generates automatically. Click 'Generate New Puzzle' for a different one.
- Click 'Show Solution' to reveal the answer, or 'Hide Solution' to hide it.
- To solve an external puzzle, paste it in the input box (9 lines of 9 characters, using dots or zeros for blanks).
- The solver displays the solution in the output area with standard grid formatting.
Real-world examples
Generating puzzles for a classroom
A teacher needs 30 different Sudoku puzzles for a math class. Select 'easy' difficulty (45 clues, suitable for beginners) and click 'Generate New Puzzle' 30 times. Each puzzle is unique and has exactly one solution, making grading straightforward.
Solving a newspaper puzzle
Copy a puzzle from a newspaper into the input box. Use dots for blank cells: "53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79". The solver returns the completed grid instantly.
Testing puzzle uniqueness
If you have created a Sudoku puzzle and want to verify it has a unique solution, paste it into the solver. If the solver finds a solution, the puzzle is solvable. For full uniqueness verification, generate at easy or medium difficulty, which runs the uniqueness check during generation.
Comparison with similar methods
| Method | Complexity | Typical use |
|---|---|---|
| Backtracking | O(9^(n^2)) worst case | This tool, most generators |
| Dancing Links (DLX) | O(9^(n^2)) but faster constant | High-performance solvers |
| Constraint propagation | O(n^2) per propagation | Human-style solving |
Limitations or considerations
Hard and expert difficulty puzzles do not run the uniqueness check during generation, so some may have multiple solutions. This is a trade-off for generation speed. If you need guaranteed unique puzzles, use easy or medium difficulty. The solver finds the first solution and does not check for uniqueness, so if a pasted puzzle has multiple solutions, you get one of them. Generation can take a few seconds for expert difficulty due to the large number of cells removed.
Frequently asked questions
What is the minimum number of clues for a unique Sudoku solution?
17 clues is the proven minimum, established by McGuire, Tugemann, and Civario in 2012 through exhaustive computation. The expert level in this tool uses 24 clues, which is above the minimum but still challenging.
Why does expert difficulty take longer to generate?
Expert puzzles remove 57 of 81 cells. The backtracking solver must work harder with fewer clues. The uniqueness check is skipped for expert to keep generation time reasonable.
Can I use the generated puzzles commercially?
Yes. Sudoku puzzles are not copyrightable since they are mathematical structures. The specific presentation (layout, fonts) may be copyrightable, but the grid itself is not.
How do I paste a puzzle from a newspaper?
Use 9 lines of 9 characters each. Use digits 1-9 for filled cells and dots or zeros for blanks. The solver ignores spaces, pipes, and other formatting characters.
Conclusion
The Sudoku generator creates puzzles at four difficulty levels and doubles as a solver. The backtracking algorithm with uniqueness checking produces puzzles comparable to those in newspapers and apps. For guaranteed unique puzzles, use easy or medium difficulty. Paste any 9x9 grid to solve it instantly.