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Logic puzzle · single player

Sudoku

Fill the grid so that every row, every column and every three by three box holds the digits one through nine exactly once. Four difficulties, a fresh puzzle every time, and each one checked by the generator to have exactly one solution before it reaches you.

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Type a digit from 1 to 9 in any open cell to start.

Keyboard: 19 to write, Backspace to erase, ← ↑ → ↓ to move between cells. Touch: tap a cell and use the number row on your keyboard.

How to play

The grid is nine cells wide and nine cells tall, and it is also divided into nine boxes of three by three. One rule covers all of it: each digit from one to nine appears exactly once in every row, exactly once in every column and exactly once in every box. Nothing about the puzzle is arithmetic. The digits are just nine distinct symbols, and you could play the identical puzzle with nine colors or nine letters without changing a single deduction.

The darker cells are the givens. They are locked and cannot be edited, and everything else starts empty for you to fill. When a digit you type would repeat inside its row, its column or its box, both cells involved turn red so you can see the collision immediately. That warning is about duplication only: a digit can be legal at this moment and still be the wrong digit for the finished grid, which is exactly why the Check button exists.

Check compares your entries against the real solution and reports how many of them are wrong without telling you which ones, so you learn that you have drifted off course without losing the puzzle. Clear my entries wipes everything you typed and leaves the givens alone. Reveal solution fills the whole grid and asks for confirmation first, because it is a one way door for that puzzle. The counter above the board shows how many cells are still empty, and the timer starts on your first entry rather than on page load, so reading this page costs you nothing.

Controls

  • Write a digit: click or tap a cell and press a key from 1 to 9. Only those nine characters are accepted and each cell holds a single digit.
  • Erase: Backspace or Delete, or type over the digit that is already there.
  • Move around: the arrow keys step to the neighboring cell, including the locked givens, so you can cross the grid without touching the mouse. Tab also walks the cells in reading order.
  • Phone or tablet: tapping a cell opens the numeric keypad on most devices, because the cells declare numeric input.
  • Difficulty: Easy, Medium, Hard and Expert differ in how many digits the generator removes. Choosing one immediately deals a new puzzle.

Strategy: the four habits that solve most grids

Start by scanning, not by staring. Take one digit, say seven, and look at every row, column and box that already contains a seven. Those lines are eliminated for that digit everywhere they reach, and very often a box will have exactly one cell left where a seven can legally go. Working digit by digit across the whole board like this is called cross hatching, and on Easy and Medium boards it will place most of the grid on its own. It is also the fastest opening because it needs no notes at all.

When scanning dries up, switch from asking "where does this digit go" to asking "what can go in this cell." If a cell already sees eight different digits through its row, column and box, then the ninth is forced and you can write it with certainty. These two questions look similar and they are not: the first finds a digit that has only one home in a unit, the second finds a cell that has only one candidate. On Hard and Expert grids you will need to alternate between them constantly, and the moment a new digit lands you should re-scan its row, column and box, because one placement often unlocks a small chain of others.

Pencil marks are where discipline pays. Write candidates only for cells where the list is genuinely short, two or three digits at most, and erase them the instant a placement kills them. A grid covered in stale marks is worse than a grid with none, because you will eventually trust a note that stopped being true ten moves ago. Marking one unit at a time, resolving what it gives you, then moving on keeps the board readable and keeps your reasoning honest.

The two patterns worth learning next both live in your pencil marks. A naked pair is two cells in the same unit whose candidates are the same two digits: whichever way round they land, those two digits are used up inside that unit, so you can strike both from every other cell in it. A hidden pair is the same situation wearing a disguise — two digits that can only appear in the same two cells of a unit, even though those cells still carry other candidates. Because the two digits must occupy those two cells, the extra candidates can be deleted. Both techniques create eliminations rather than placements, which is why beginners skip them and why Expert grids stall without them.

Solving times from our own play testing, offered as estimates rather than verified statistics: Easy grids tend to fall in a few minutes with scanning alone, Medium usually asks for some pencil marks, Hard often runs past a quarter of an hour, and Expert can occupy a long sitting because it typically requires pair logic. Difficulty labels here describe how many digits were removed, which correlates with effort but is not a precise measure of it.

Where the puzzle came from

The mathematical ancestor is the Latin square, a grid filled so that each symbol appears once per row and once per column, studied by mathematicians long before anyone printed it as entertainment. Adding the three by three box constraint and a set of givens turns that object into a puzzle. Number placement puzzles of this shape appeared in newspapers well before the modern boom, but the version we play was popularised in Japan during the 1980s under the name Sudoku, and it spread worldwide after 2004, when newspapers outside Japan began printing a daily grid.

Our implementation and all of the text on this page were written from scratch for this site. The puzzles are not drawn from a stored library: each one is built in your browser at the moment you ask for it, using a randomised solver to produce a complete valid grid and a counting solver to guarantee that removing a digit has not created a second solution. That is why two visits never hand you the same board.

Questions players ask

Does every puzzle here have exactly one solution?

Yes. The generator builds a full valid grid, then removes digits one at a time and runs a counting solver after each removal. If a removal would allow a second solution, the digit is immediately put back, so the puzzle you receive is always uniquely solvable.

Do I ever have to guess in Sudoku?

Not in principle, because a unique solution means every digit is forced by the clues. In practice the chain of reasoning on the Expert setting can be long enough that many players prefer to test a candidate and back it out if it collides, which is guessing in style but still logic in substance.

Why did one of my digits turn red?

Red means that digit is repeated in the same row, the same column or the same three by three box, so the two cells that share it are both marked. It is a duplicate warning only. A digit can be perfectly legal right now and still be wrong for the finished grid, which is what the Check button is for.

Keep going

  • Sudoku solving techniques — scanning, pencil marks and pairs worked through on a real grid.
  • Minesweeper — deduction again, this time with a penalty for being wrong.
  • 2048 — a lighter puzzle for when you want no notes at all.