Sudoku
The grid below is built while the page loads. A complete solution is generated first, then digits are taken away one at a time, and each removal is kept only if exactly one solution still remains. Tap a cell and use the pad underneath, or click a cell and type. Nothing is downloaded and no puzzle is stored anywhere, which is why reloading gives you a different board rather than the same one back.
Every page in this section
- Hard SudokuHard Sudoku, playable in the page
- Medium SudokuMedium Sudoku, playable in the page
- Easy SudokuEasy Sudoku, playable in the page
- Expert SudokuExpert Sudoku, playable in the page
- Printable SudokuPrintable Sudoku, playable in the page
- Daily SudokuDaily Sudoku, playable in the page
- Mini Sudoku (6x6)Mini Sudoku (6x6), playable in the page
- Very Hard SudokuVery Hard Sudoku, playable in the page
- Sudoku SolverSudoku Solver, playable in the page
- Sudoku for Kids (4x4)Sudoku for Kids (4x4), playable in the page
- How Sudoku WorksHow Sudoku Works, playable in the page
- Sudoku TechniquesSudoku Techniques, playable in the page
Twenty cells are watching every square you fill
A nine-by-nine grid contains twenty-seven units: nine rows, nine columns and nine boxes. Every cell belongs to exactly three of them, and the cells it shares a unit with are its peers. The tempting count is twenty-four – eight along the row, eight down the column, eight in the box – but two of those box cells are already in the row and two more are already in the column, so the real figure is twenty. That single number is most of what the puzzle is: writing one digit tells twenty other squares what they cannot be, and every deduction you will ever make is a consequence of that.
The badge above the grid reports what the board earned
This page asks the generator for a middling puzzle, but the word in the strip above the grid is not the request – it is the grade the finished board came out at after its own solver had worked through it. The two usually agree. When they do not, the badge tells you the truth rather than the intention, which is worth knowing before you decide a puzzle is beating you: some of them really are a step above what the page went looking for.
Red means it clashes, which is not the same as wrong
Two different things can be true about a digit you have just written. It might contradict something already visible – the same digit in its row, its column or its box – and the board turns those cells red as you type, because a contradiction can be spotted without knowing the answer. Or it might sit perfectly happily with everything on screen and still not be the digit in the solution. That second kind is invisible, it is the one that quietly wastes twenty minutes, and it is what Check exists for: Check compares your filled cells against the solution and reports how many disagree. It deliberately does not say which, because being told the count is a nudge and being shown the cells is the answer.
There are 6,670,903,752,021,072,936,960 finished grids
The number of ways to fill a nine-by-nine grid legally was settled by exhaustive computation in 2005, and it runs to twenty-two digits. A good deal of it is bookkeeping: any finished grid can be relabelled in 362,880 ways by swapping which symbol means what, and on top of that the rows inside a band, the columns inside a stack, and the bands and stacks themselves can all be permuted without breaking a rule. Strip every one of those symmetries out and roughly 5.47 billion genuinely different grids remain. Both figures are far past anything a website could store, which is the practical reason the puzzle here is built for you on the spot instead of dealt out of a library.
Where to go from here
The grades are separate pages because they mean separate things on this site, each one named after the hardest deduction it forces: easy, medium, hard and expert. The same engine also draws smaller boards – a six-by-six and a four-by-four – and if you want the deductions themselves rather than another grid, they are set out in order on techniques.