Sudoku

Sudoku is one of the world's most popular logic puzzles, challenging players to fill a 9x9 grid so that every row, column, and 3x3 box contains the digits 1 through 9. No maths is required, just clear thinking and patience. Our free online Sudoku lets you play instantly in your browser without any download or sign-up.

How to Use the Sudoku Tool

1. Select a difficulty level: Easy, Medium, Hard, or Expert.
2. Click any empty cell in the grid to select it.
3. Type or click a number (1-9) to place it in the selected cell.
4. Use the Notes mode to pencil in candidate numbers when you are unsure.
5. Keep going until every cell is filled correctly. The puzzle will confirm when you have solved it.

How the Game Works

The Sudoku grid is a 9x9 square divided into nine 3x3 boxes. At the start, some numbers are pre-filled as clues. Your job is to fill the remaining cells so that every row contains the digits 1 to 9 with no repeats, every column contains the digits 1 to 9 with no repeats, and every 3x3 box contains the digits 1 to 9 with no repeats. Each puzzle has exactly one valid solution. You never need to guess if you use logic correctly, though harder puzzles require more advanced techniques.

Tips for Winning

• Start with rows, columns, or boxes that already have the most numbers filled in. Fewer empty cells means fewer possibilities to consider.
• Use the process of elimination: if eight of the nine digits are accounted for in a row, the missing one must go in the remaining cell.
• Scan the grid for a single digit at a time. Find every 7 on the board, for example, and work out where the remaining 7s must go.
• Use pencil marks (notes) to track which numbers are still possible in each cell. Cross them off as you confirm placements elsewhere.

Difficulty Levels Explained

Easy puzzles give you more starting clues and can usually be solved using basic elimination alone. Medium puzzles require you to combine row, column, and box scanning. Hard and Expert puzzles use advanced techniques like naked pairs, hidden triples, and X-wings. If you are new to Sudoku, start on Easy and work your way up as your confidence grows.

Frequently Asked Questions

Do I need to be good at maths to play Sudoku? Not at all. Sudoku is purely a logic puzzle. The digits 1 to 9 are used as symbols, and you could replace them with any nine distinct symbols and the puzzle would work exactly the same. No addition, multiplication, or arithmetic is involved.

Can a Sudoku puzzle have more than one solution? A properly constructed Sudoku puzzle has exactly one solution. If you find a puzzle with multiple valid completions, it is technically considered flawed. All puzzles on this site are verified to have a unique solution.

What is the fastest way to get unstuck? If you are stuck, try switching your focus to a single digit and hunting for where it can legally go across the whole grid. Alternatively, review your pencil marks and look for a row, column, or box where only one cell can hold a particular number.

Is there a time limit? No. Play at your own pace. A timer runs so you can track your speed and try to beat your personal best, but there is no penalty for taking longer.

What a complete grid contains

A finished 9 by 9 grid holds 81 cells, arranged into 9 rows, 9 columns and 9 boxes. Each of the nine digits appears exactly nine times. That balance is what makes the puzzle work as pure logic. A digit placed anywhere removes eight options from its row, its column and its box, so the grid narrows itself as you fill it.

The counting gets large quickly. The number of ways to arrange one row without repeats is 9 factorial, or 362,880. The number of complete valid grids is 6,670,903,752,021,072,936,960, which is roughly 6.67 sextillion. Bertram Felgenhauer and Frazer Jarvis published that figure in 2005. It divides by 362,880 exactly, giving 18,383,222,420,692,992.

Clue counts attract more argument than they deserve, but one number is settled. A puzzle needs at least 17 clues to have a single solution. Gary McGuire, Bastian Tugemann and Gilles Civario proved this in 2012 by searching exhaustively for a 16 clue puzzle and finding none. The proof is published as arXiv:1201.0749.

A 26 clue puzzle solved without guessing

The grid below has 26 clues and 55 empty cells. It has exactly one solution, and two techniques finish it. Every step is checked against the rules rather than guessed.

The full solution, so you can check your own work at the end:

Not one cell starts with a single candidate, so the first move cannot be a forced value. The 55 empty cells begin with this spread of candidates:

The whole puzzle falls in 55 deductions. Thirty of them are naked singles, where a cell has one candidate left. Seventeen are hidden singles found in a row, six are hidden singles found in a column, and two are hidden singles found in a box.

Reading the first two deductions

A naked single is easy to see once you have pencil marks. A hidden single is the one that catches people out, because the cell often still shows several candidates.

Take row 1 of the puzzle. The givens are 9, 3, 7 and 5. That leaves five empty cells, with these candidates after scanning each cell's column and box:

Look for digit 1. It appears in exactly one of those five candidate sets, the one at column 5. Every other empty cell in the row has ruled 1 out, because a 1 already sits in its column or its box. So row 1, column 5 is 1. That is a hidden single, and it is the first move of the puzzle.

Fifteen deductions later, the same grid reads:

Now take the empty cell at row 2, column 6. Its row already shows 1, 2, 3, 5, 7 and 8. Its column already shows 2, 4, 5, 7 and 9. Its box already shows 1, 2, 3, 5, 7, 8 and 9. Between the three units, every digit from 1 to 9 is accounted for except 6. The cell holds one candidate, and it is 6. That is a naked single, and it needs no technique at all once the pencil marks are written down.

The two moves show the difference in practice. A hidden single asks which cell in a unit can hold a digit. A naked single asks which digit a cell can still hold. Working both in the same pass is what keeps a puzzle moving.

How the difficulty labels map to technique

Difficulty is set by the techniques a puzzle requires, not by how many clues it shows. The 26 clue puzzle above sits at the easy end of the scale, because singles alone solve it. Harder puzzles remove the singles and force you to reason about combinations.

A puzzle built only from singles can look busy while staying simple. A puzzle with few clues and no singles can look calm while requiring every technique on that list. When you get stuck, count the candidates in the emptiest row or box first. The move you are looking for is usually where the candidates are thinnest.

The two papers behind the grid count

The 17 clue minimum is proved in McGuire, Tugemann and Civario, "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem", arXiv:1201.0749, submitted January 2012. The total grid count is from Felgenhauer and Jarvis, "Enumerating possible Sudoku grids", published in 2005, and is sequence A107739 in the OEIS. The worked puzzle on this page was generated and solved by an exhaustive solver, which confirmed a single solution and recorded each of the 55 deductions in order.

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