Sudoku

Sudoku is played on a 9×9 grid divided into nine 3×3 boxes, and the single rule is that every row, every column and each 3×3 box must contain the digits 1 to 9 exactly once — no repeats in any row, column or box. The 3×3 boxes are also called blocks or regions, and that one constraint is the whole game.

What are the givens?

Every puzzle begins with some cells already filled in. These are the givens (or clues), and they can never be changed. A well-made Sudoku has exactly one solution that can be reached by logic alone, with no guessing required — and every board on this page is generated and checked to guarantee it.

Is Sudoku a maths puzzle?

Because the numbers never add up or interact arithmetically, Sudoku is not really a maths puzzle: the digits 1–9 are just nine distinct symbols. You could play with nine letters or nine colours and the logic would be identical — what matters is where each symbol can and cannot go.

How few givens can a Sudoku have?

Mathematicians call a grid where each symbol appears exactly once per row and column a Latin square; Sudoku layers the 3×3-box constraint on top, which is what makes its deductions so rich. In a well-made puzzle the clues are placed symmetrically and pared to the minimum that still forces one answer — it has been proved that a proper 9×9 Sudoku needs at least 17 givens for a unique solution, though most printed boards use between 22 and 30. As a rule of thumb, the fewer the givens, the harder the solve.

Solve a Sudoku by applying a few techniques in order from simplest to hardest — scanning, naked singles, hidden singles, pencil marks, naked pairs and pointing pairs — always making every forced move first and working where the grid is most complete. The fastest way to improve is to learn these moves and apply them in that order.

The core solving techniques

• Scanning — pick a digit and scan the rows, columns and boxes where it already appears; often a box has only one cell left where that digit can legally go.
• Naked singles — a cell whose row, column and box already block eight of the nine digits has only one candidate left. Fill it in.
• Hidden singles — within a row, column or box a digit may have only one possible home, even if that cell still looks open. This is the most common move in easy and medium boards.
• Pencil marks — when scanning stalls, note the candidate digits in each empty cell; working from candidates turns a hard puzzle into a chain of small deductions.
• Naked pairs and triples — if two cells in a unit share the same two candidates, those digits are locked to those cells and can be removed from the rest of the unit.
• Pointing pairs — when a digit inside a box is confined to one row or column, it can be eliminated from the rest of that row or column outside the box.

In what order should you make moves?

Always make every forced move first — the cells that can only be one digit — before hunting for anything harder, and work where the grid is already most complete, because that is where the constraints bite hardest. Never guess: on a proper Sudoku there is always a logical next step.

When do you need X-Wing and Y-Wing?

The hardest boards occasionally call for pattern techniques such as the X-Wing or Y-Wing, where a digit’s candidates form a rectangle across two rows and columns and let you rule it out elsewhere. You will rarely need them below Hard, and you can always reach the answer here with careful singles, pairs and pointing pairs.

A worked example shows the techniques combining: find a hidden single where only one cell in a box can take a missing digit, then a naked single where one empty cell has every other digit blocked, then use pencil marks to strip candidates until the next forced move appears. A quick walkthrough makes the chain concrete.

Suppose the top-left box is missing the digit 5, and two of its three open cells already see a 5 somewhere in their row or column — only the third cell can take it. That is a hidden single, and it is usually the first kind of move to look for.

Now imagine a column whose filled cells and crossings already account for 1, 2, 3, 4, 6, 7, 8 and 9: the one empty cell must be 5, a naked single. Each digit you place removes a candidate from its row, its column and its box, which often unlocks the next forced move like a row of dominoes.

When no singles remain, switch to pencil marks. If two cells in a box can only be 3 or 7, then 3 and 7 are claimed — strike them from every other cell in that box, and a new single often appears elsewhere. Patient elimination, never guesswork, is what finishes even the hardest grid.

The three levels are all 9×9 — they differ only in how many givens you start with and which techniques you need: Easy has the most clues and falls to scanning, Medium removes clues and leans on pencil marks and pairs, and Hard gives the fewest clues and asks for advanced eliminations. No level is bigger; every Sudoku here is the same 9×9 grid.

Tap New for a fresh board at any level, or play the shared Daily to get the same puzzle as everyone else that day.

Once the classic 9×9 feels comfortable, the same one-of-each idea powers a whole family of variants — Killer, Mini, X-Sudoku, Hyper and Samurai — each adding a twist on top of the basic fill-every-region rule. They all share Sudoku’s DNA.

• Killer Sudoku adds dotted “cages” that must sum to a given total, blending Sudoku with light arithmetic.
• Mini Sudoku (6×6, with 2×3 boxes) is a gentler, faster version — great for beginners and children.
• X-Sudoku adds the two long diagonals as extra regions that must also hold 1–9.
• Hyper and Samurai Sudoku add shaded inner regions or overlap several grids into one giant puzzle.

They all share Sudoku’s DNA — fill a grid so each region uses every symbol once — which is the same deductive skill the rest of this collection trains, from Kakuro (Sudoku with sums) to Futoshiki (a Latin square with inequalities). Learn Sudoku well and the others come faster.

The core Sudoku vocabulary is short: a given (clue) is a fixed starting digit, a candidate is a digit that could still go in a cell, a unit is any row, column or 3×3 box, and singles and pairs name the patterns you exploit to fill the grid. A few words come up in every strategy guide.

• Given (clue) — a digit printed at the start; it is fixed and cannot be changed.
• Candidate — a digit that could still legally go in a cell.
• Unit — any single row, column or 3×3 box; each unit must hold 1–9 exactly once.
• Naked single — a cell with only one candidate remaining.
• Hidden single — a digit with only one possible cell left in a unit.
• Naked pair — two cells in a unit sharing the same two candidates, which can then be cleared from the rest of that unit.
• Pointing pair — a digit confined to one row or column inside a box, letting you eliminate it from that line outside the box.

You do not need the jargon to play — tap a cell and pick a number — but the names make every strategy guide easier to follow.

Most Sudoku frustration comes from a few avoidable habits — guessing, ignoring the 3×3 boxes, skipping pencil marks and rushing — and fixing each one removes the errors before they cascade. They are easy to break once you can name them.

• Guessing. Place a digit you are not certain of and a single error can cascade for dozens of cells before it surfaces. There is always a logical move — find it instead.
• Ignoring the boxes. Beginners scan only rows and columns, but the 3×3 box is an equal constraint and often holds the key to a hidden single.
• Skipping pencil marks. Holding every candidate in your head works on easy boards and breaks down on hard ones; write them in.
• Rushing. Place the forced moves first and re-scan after each one — the grid changes with every digit you add.

Sudoku endures because it is fair, portable and endlessly renewable: every board has one answer reachable by reason alone, so progress always feels earned, and the deductive skills it builds carry straight over to the rest of this collection. There is no luck to blame and nothing to unlock.

A quick Easy grid is a five-minute reset on a commute; a Hard one is a satisfying half-hour of deep focus. It also makes a gentle daily habit: the shared Daily gives you the same board as everyone else and a small streak to keep. Best of all, the deductive muscles Sudoku builds — scanning, elimination and thinking a few steps ahead — carry straight over to the rest of this collection, which makes it the ideal first stop before trying Slitherlink, Nonogram or Kakuro.

Although the name is Japanese, the modern puzzle was born in the United States in 1979, when the American architect Howard Garns published it as “Number Place” in Dell magazines — a 9×9 grid with the now-familiar one-of-each rule. Its global journey ran through Japan and Britain from there.

How did it become “Sudoku” in Japan?

It found its real home in Japan. In 1984 the publisher Nikoli introduced it as sūji wa dokushin ni kagiru (“the digits must be single”), soon shortened to Sudoku (数独). Nikoli added the two touches that define the modern puzzle: a limited, symmetric set of givens and a guaranteed unique, logically solvable answer.

How did Sudoku go global?

Sudoku went global in 2004, when a New Zealander, Wayne Gould, wrote a program to generate boards and persuaded The Times of London to print them. Within a year it was a worldwide newspaper fixture, and it is still the most popular logic puzzle in the world — the gateway that brings most people to the wider family of Japanese grid puzzles.