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Sudoku is a logic-based number placement puzzle played on a 9×9 grid that is divided into nine 3×3 boxes. The puzzle starts with some cells already filled in as clues. Your task is to fill in every remaining empty cell with a digit from 1 to 9, following one simple rule applied three ways: every row must contain the digits 1-9 exactly once, every column must contain the digits 1-9 exactly once, and every 3×3 box must contain the digits 1-9 exactly once.
The goal is not arithmetic. Sudoku has nothing to do with addition or counting — the numbers are just nine distinct symbols. The puzzle is purely about deduction: given the clues you can see, where is each digit forced to go? Every well-formed Sudoku has exactly one solution, and that solution can always be reached by pure logic without guessing.
Modern Sudoku was invented in 1979 by Howard Garns, a retired American architect, and first published as "Number Place" in Dell Pencil Puzzles. It exploded globally in 2004 when Wayne Gould, a retired Hong Kong judge who had discovered the puzzle in Japan, convinced The Times of London to publish it. Within months, Sudoku appeared in newspapers around the world. Today it is the most-syndicated puzzle in newspapers worldwide and one of the most popular logic puzzles ever created.
Scanning is the most fundamental Sudoku technique and the first one any solver learns. The idea is simple: pick a digit, then look at every row, column, and 3×3 box where that digit already appears. Each appearance eliminates that digit from the rest of its row, column, and box. Wherever you find a unit that has been narrowed down to exactly one possible cell, you have placed that digit.
Most easy and many medium puzzles can be solved entirely by scanning. The technique is mechanical, requires no notation, and trains the spatial habit you'll need for every harder technique. Always exhaust scanning for all nine digits before reaching for anything more advanced.
Scan digits that already appear many times on the board first — the more clues a digit has, the fewer places it can still go. A digit that already appears six or seven times is often forced into its remaining cells almost immediately.
A naked single is a cell that has only one possible candidate digit left after every other digit has been eliminated by its row, column, and box. Naked singles are the easiest deduction in Sudoku: if eight of the nine digits are forbidden in a cell, the ninth must go there.
To find naked singles efficiently, use pencil marks. Fill each empty cell with the small candidates that remain valid, then watch for any cell that contains only one pencil mark. That cell is solved. Naked singles tend to cascade — placing one often eliminates candidates from neighboring cells, exposing more naked singles.
A hidden single is a digit that can only go in one cell within a row, column, or box — even though that cell may have several pencil-mark candidates of its own. The digit is "hidden" inside a busier cell, but it has nowhere else to go in its unit.
Hidden singles are slightly harder to spot than naked singles because they require you to look at the unit as a whole rather than at individual cells. The payoff is huge: hidden singles unlock most medium puzzles and many hard ones. After every solved cell, re-scan its row, column, and box for new hidden singles.
A naked pair happens when two cells in the same row, column, or box share the same two candidates and only those two. For example, if two cells in a row both have candidates "3 and 7" and nothing else, then 3 and 7 must occupy those two cells in some order. That means you can eliminate 3 and 7 from every other cell in the row, often opening up new naked or hidden singles elsewhere.
For really tough puzzles, the next step up is the X-Wing, a more advanced pattern that uses two rows and two columns simultaneously to eliminate a candidate. Don't worry about X-Wing until naked pairs and hidden pairs feel automatic — most puzzles you'll encounter never require it.
Desktop: Click any empty cell to select it, then type a number from 1 to 9 on the keyboard to place that digit. Right-click or hold a modifier key to add or remove pencil marks (candidate notes) without committing a final answer.
Mobile / Tablet: Tap a cell to select it, then tap a number from the on-screen keypad. Long-press on a number to switch between final-answer mode and pencil-mark mode for candidate tracking.
The game runs full-screen on phones and adapts to any screen size. Portrait orientation is recommended on mobile so the 9×9 grid stays large enough to read comfortably.
Once you've mastered the classic 9×9 grid, dozens of variants change the board size or add extra constraints to keep the puzzle fresh:
The classic 9×9 remains the standard everyone learns first. Master scanning, naked singles, hidden singles, and pairs on the classic before exploring variants.
To play Sudoku you fill in a 9 by 9 grid so that every row, every column, and every 3 by 3 box contains the digits 1 through 9 exactly once. The puzzle starts with some cells already filled in as clues, and your job is to deduce the rest using pure logic. You never guess and you never repeat a digit inside any row, column, or box.
The easiest technique is scanning. For each digit from 1 to 9, scan every row, column, and 3 by 3 box to see where that digit is forced to go. If a digit can only fit in one cell within a unit, it must go there. Combined with naked singles, scanning will solve most easy and medium puzzles without any advanced technique.
Every well-formed Sudoku has exactly one solution and can be solved by pure logic, but the techniques required can be very advanced. Easy puzzles need only scanning and naked singles. Hard puzzles can require naked pairs, hidden pairs, X-Wing, Swordfish, and other advanced patterns. You should never need to guess on a properly designed puzzle.
Modern Sudoku was invented in 1979 by a retired American architect named Howard Garns and first published under the name Number Place in Dell Pencil Puzzles. It became globally popular in 2004 when Wayne Gould, a retired Hong Kong judge who discovered the puzzle in Japan, convinced The Times of London to publish it. Today it is the most-syndicated puzzle in newspapers worldwide.
An easy Sudoku typically takes 5 to 10 minutes for an experienced player. Medium puzzles take 10 to 20 minutes. Hard and expert puzzles can take anywhere from 30 minutes to over an hour depending on how many advanced techniques are required. Speed solvers can finish easy grids in under two minutes. See our brain training science guide for cognitive research.
Yes. Killer Sudoku adds cage sums on top of the standard rules. Samurai Sudoku links five overlapping 9 by 9 grids. Hyper Sudoku adds extra constraint regions, and there are larger versions like 12 by 12 and 16 by 16. Each variant uses the same core deduction style but layers in extra constraints that demand more advanced techniques.
Put scanning, naked singles and hidden singles into practice now.
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