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Become a Sudoku master

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Play with others Play soloRead the rules

A real position. The 8 has exactly one square left in the bottom-left box, and the first technique shows why.

New to sudoku?

Start here: one rule, one first move

Step 1 of 3

Look for a row, column or box with only one empty square. Row 5 is one.

The rule. Fill the empty squares so that every row, every column and every box (the squares inside the thicker lines) holds each digit exactly once. The board on the left is the 6×6 you are dealt first: the digits are 1 to 6, and a box is two rows by three. A 9×9 works the same way with 1 to 9. A row, a column or a box is called a unit, and two squares in the same unit see each other. The lessons use both words.

The givens. The digits already on the board when it is dealt. They never change, and every move you make follows from them.

Your first move. Find a row, column or box with only one empty square. Whichever digit it is missing goes there. The board on the left walks through one; press Next.

Then try it. A small board is the quickest way to make it stick. Solo deals an easy 6×6 on your first visit, and the techniques below take it from there.

Play soloLesson 1: the last empty square
The basics

Rules of the game

1

Fill every cell

Each empty square takes exactly one digit. The digits printed at the start are the givens. They never change, and everything you type goes into the empty squares.

2

No repeats in a row

Every digit appears exactly once in each row. On a 9×9 that means 1 to 9, once each, across the nine columns; on a 6×6 it is 1 to 6 across six.

3

No repeats in a column

The same rule turned on its side: read any column from top to bottom and you pass each digit exactly once.

4

No repeats in a box

Each box, the squares inside the thicker lines, must also hold every digit exactly once. This third rule is what makes sudoku sudoku, and it is where most deductions come from.

5

There is exactly one answer

Every board dealt here is checked to have exactly one solution, so the givens already decide every square and you never need to guess. Not every board gives way to the five techniques below; harder ones can need subtler reasoning. If you are stuck, a Hint either points at a single you missed or, when there is none, gives you a digit for a penalty.

6

Mistakes are shown, not punished

Type a digit that repeats one it can see and every square involved turns red at once, and clears the moment it is fixed. Nothing counts against you but the time it takes. One kind of mistake shows no red at all: a wrong digit that repeats nothing. Finding those is the Hint button's first job.

7

You win when the grid is full and clean

The game checks the whole board: every square filled, no rule broken. A board can look finished and still be wrong, so the last digit is judged like the first. Your time stops the moment the check passes and is credited to that puzzle.

8

No arithmetic anywhere

The digits are labels, not amounts. Nothing is ever added up, and a board of nine coloured shapes would play the same.

Get better

The techniques, in order

Five techniques, each with its own lesson. Learn them in this order, because each builds on the one before. The first three place a digit. The last two remove candidates instead, which is what you need once no single is left, and that happens more often as the givens thin out. The course walks the same five one page each, with the first move before them and pencil marks between. Some boards, expert ones especially, need reasoning beyond these. Every board below is a real position. The free hint knows the two singles: it points at one when the board has it, and it does not look for pairs.

Step 1 of 5

Pick a digit and a box: where can the 8 go in the bottom-left box? It has seven empty squares.

Lesson 2

Scanning

Where does the 8 go in the bottom-left box?

Pick a digit and a box, and let the copies already on the board do the work. Column 2 already has an 8, which rules out the box's middle column; column 1 has one too, which rules out its left column; and the 8 in row 9 rules out its bottom row. One square is left, at row 7, column 3, so the 8 goes there. Nothing to write down and nothing to guess: it is the first thing to try on any board, and on an easy one it takes you a long way.

Full lesson: scanning →

Step 1 of 4

Pick one empty square, row 7, column 6, and ask what it could hold.

Lesson 3

Naked singles

One square, one digit left.

Work the square instead of the digit. Take row 7, column 6, and look at everything it can see. Its row already has 3, 4, 5, 6 and 8; its column adds the 1 and the 2; its box adds the 7. That is eight different digits, so the square can only be a 9. No single unit was enough: the row alone still leaves four candidates.

Full lesson: naked singles →

Step 1 of 4

Ask where a digit can go: where can the 3 go in the centre box?

Lesson 5

Hidden singles

This square has four candidates, and the 3 still has only one home.

The previous technique asks what a square can hold. This one asks where a digit can go. Read the pencil marks across the centre box: none of its six empty squares is down to one mark, but the 3 appears in only one of them, row 6, column 6, which could also take a 2, a 4 or a 6. No other square in the box has room for a 3, so the 3 goes there. You would miss it entirely if you only ever looked square by square. Expect to need it once the easy openings are used up.

Full lesson: hidden singles →

Step 1 of 4

No single is left on this board. Read the pencil marks in the middle-left box.

Lesson 6

Naked pairs

Two squares own the 1 and the 6 between them, so the ringed square is a 4.

No single is left on this board. Read the middle-left box. Two of its empty squares, in column 3, show exactly the same two pencil marks, 1 and 6, and nothing else. Between them they must take both digits, so no other square in the box can hold a 1 or a 6. The ringed square was showing 4 and 6. Drop the 6 and only the 4 is left. This is the first technique that reasons about squares together instead of one at a time.

Full lesson: naked pairs →

Step 1 of 4

Where can the 6 go in the top-middle box? Read the marks of its five empty squares.

Lesson 7

Pointing pairs

The 6 cannot leave the top row of its box, so it cannot be anywhere else in that row.

Read the top-middle box for the 6. It has exactly two possible squares there, and both sit in row 1; the box's other empty squares have no 6 among their marks. Wherever the 6 ends up, it is in row 1 inside that box, so it cannot be in row 1 outside it. The ringed square, in column 8, was showing 4 and 6. The 6 goes, and the 4 is left. The box told you something about the row. Look for this whenever a digit's marks inside a box line up, and the same idea runs the other way: a digit confined to one box along a line can be cleared from the rest of that box.

Full lesson: pointing pairs →

After these five

The pair ideas grow. A hidden pair is two digits that can only go in the same two squares of a unit, so whatever else those squares were showing can be erased. A triple is the same argument with three squares and three digits. An X-wing is a digit whose only squares in two rows sit in the same two columns, which clears it from those columns everywhere else. None of them needs a new kind of thinking, only more marks on the board at once. That is the real reason to keep your notes accurate on an expert 9×9, and more so on a 12×12 or 16×16.

Avoid these

Common mistakes

Guessing to get unstuck

Every board here has exactly one solution, so a digit that merely seems to fit can still be wrong, and everything you build on it is wrong with it. Go back to the fullest boxes and lines, or bring your notes up to date.

Trusting a board with no red

Red only marks a digit that repeats one it can see. A wrong digit that repeats nothing shows no red at all. If the board stops making sense, that is the first thing the Hint looks for: it rings the wrong digits, for a 30-second penalty.

Letting notes go stale

Placing a digit clears it from the marks of every square that can see it, but no deduction is applied for you: marks a pair has ruled out stay until you clear them yourself, and stale marks hide the singles you are looking for.

Starting on the biggest board

A 16×16 has the same rules and far more to hold in your head. Learn on a 4×4 or a 6×6 (a new room is dealt a 6×6 unless its host picks another) and move up when the techniques feel automatic.

Reading the level as a promise

Difficulty counts the givens, not the techniques a board needs. Two boards at the same level can feel quite different, and a hard one that goes quickly is not a sign that you missed something.

On this board

Notes, shapes and difficulty

Notes are the whole game above easy

Tap Notes in the control bar (or press N) and typing a digit writes a small pencil mark instead of an answer. Use it the moment scanning stops finding digits. Once a square's remaining candidates are written down, the techniques above become things you can read off the board rather than work out again on every pass. Placing a digit removes it from the marks of every square that can see it, the bookkeeping you would do by hand, and that digit and every mark it took are one Undo step. Erase clears a square's marks along with its digit. Notes are saved with your board and are private: no watcher sees them at any setting.

Full lesson: pencil marks →

What difficulty actually changes

Not the size of the grid, but how many givens you start with. Each of the four levels, easy to expert, removes more of the solved grid's digits, and always stops before the board could have a second solution. Fewer givens usually means a longer chain of reasoning before a digit goes in, and a hard board is more likely to stall until you have worked a pair or something subtler. That is why hard boards feel stuck rather than slow. But the level counts givens, not techniques: it is a rough guide to how a board will feel, not a promise of which techniques it needs.

Playing solo

Solo is your own private board with the same rules, clock and controls. Every puzzle you play there is remembered: how many times you have solved each board and level, and your best time on each. New puzzle deals the next one with whatever board and level you pick, at any moment, even mid-puzzle. Come back to a puzzle you finished and the next one of the same kind is already dealt. Come back to one you left half done and it is waiting, paused, exactly as you left it.

A board is named by its box

Grid size alone is ambiguous: 2×3 and 3×2 boxes both make a 6×6. So every board here is named by the box that tiles it. The rules never change, only how much you are holding at once.

  • 2×24×4 gridThe four-digit board. Small enough to teach the three rules in a minute, and the fastest board here to race.
  • 2×36×6 gridRectangular boxes, two rows by three columns, so a scan has to look both ways. The first board where scanning stops feeling automatic, and the one a new room is dealt unless its host chooses another.
  • 3×39×9 gridThe classic. Nine digits, nine boxes, and the shape every technique on this page is written for.
  • 3×412×12 gridTwelve digits over 3×4 boxes. Long enough that notes stop being optional.
  • 4×416×16 gridSixteen digits over 4×4 boxes. A different kind of puzzle: the deductions are the same, but holding them in your head is not.
Play together

Playing with others

On Puzzled you can race other people through the same deal, live. A room is a table with up to twelve seats, playing a series of puzzles at a time, with standings, chat and watchers. Everything about playing here (the control bar, the keyboard and the phone, what a hint costs, rooms, series, watching and the standings) has its own page.

Playing sudoku on Puzzled →
Questions

Frequently asked

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