How to play sudoku

Nine short lessons, one idea at a time. Each one explains the idea, walks through an example on a real board, then gives you a board to try it yourself.

1 The one rule

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Sudoku is a 9 by 9 grid, split into nine boxes. You fill it with the numbers 1 to 9.

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Sudoku is a 9 by 9 grid, split into nine boxes. You fill it with the numbers 1 to 9.
This is a row. It has 1 to 9, each one exactly once.
This is a column. Same rule: 1 to 9, once each.
This is a box, inside the thick lines. Same rule again.
That's the only rule. Every row, every column and every box gets 1 to 9 once. No repeats.

2 The last gap

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The easiest place to start: a row, column or box with only one empty square.

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The easiest place to start: a row, column or box with only one empty square.
Row 5 has eight numbers and one gap.
Count them off: 1, 2, 4, 5, 6, 7, 8, 9. The one missing is 3.
So the gap has to be 3. Nothing else is left for it.

3 Rule squares out

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This trick finds most of the moves in an easy puzzle. Where can the 5 go in the top-left box?

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This trick finds most of the moves in an easy puzzle. Where can the 5 go in the top-left box?
Start with the 5s you can already see.
Row 1 already has a 5. A row can't have two, so no other square in row 1 can be 5.
Row 3 has a 5 too. Rule that row out as well.
Column 2 has a 5 further down. Rule it out.
And column 3.
Only one square in the box is left, so the 5 has to go there. This is called cross-hatching.

4 Only one fits

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Sometimes one square is boxed in from every side. Look at the middle square.

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Sometimes one square is boxed in from every side. Look at the middle square.
Its row already has 9, 2, 4 and 5.
Its column has 7, 1 and 6.
Its box has 3 and 4.
Put together, that rules out 1, 2, 3, 4, 5, 6, 7 and 9. Eight numbers.
Only 8 is left, so the square has to be 8.

5 One find leads to the next

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Every number you place is a new clue. One find often leads straight to the next.

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Every number you place is a new clue. One find often leads straight to the next.
Let's find the 5 in the top-left box.
Because row 1 already has a 5, the box's 5 can't be in row 1.
Columns 2 and 3 have 5s further down, so rule those out too.
That leaves two squares, and one of them already has a 7. So the 5 goes in the other one.
Now that new 5 does some work. Rows 1 and 2 both have a 5, which means the top-middle box has to put its 5 in row 3.
Columns 4 and 5 already have 5s down below, so it can't go there either.
So it has to go here. Because of the first 5, we found the second.

6 Two gaps, two numbers

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When a row has two gaps left, you can often work out which number goes where.

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When a row has two gaps left, you can often work out which number goes where.
Row 8 has two empty squares.
The row is missing 7 and 9. So one square is 7 and the other is 9. Write both in small.
Now look up column 8. It already has a 7, so this square can't be 7.
Which means it has to be 9.
And that leaves 7 for the other gap. Two numbers placed from one clue.

7 Pencil marks

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Harder puzzles don't hand you a move. That's when you write small notes, called pencil marks.

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Harder puzzles don't hand you a move. That's when you write small notes, called pencil marks.
Take this square. Its row, column and box already use 1, 4, 5, 6, 7 and 9.
So only 2, 3 and 8 could go here. Write those in small.
Do the same for every empty square in the box.
Now look for a number that shows up only once. 8 is only in one square's notes.
The box still needs its 8, and this is the only square that can take it. So 8 goes there, even though that square had 3 choices.

8 Pairs

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Pencil marks let you spot pairs. This board is smaller, 6 by 6, so the idea is easier to see.

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Pencil marks let you spot pairs. This board is smaller, 6 by 6, so the idea is easier to see.
These two squares in box 6 can only be 3 or 4.
One of them is 3 and the other is 4. We don't know which yet, but between them they use up both.
So no other square in box 6 can be 3 or 4. Cross those notes out.
That's called a naked pair: two squares with the same two choices claim both numbers.

9 Pointing pairs

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One more pattern with notes. This one points from a box out along a row or column.

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One more pattern with notes. This one points from a box out along a row or column.
In box 2, the 5 can only go in these squares.
They're all in row 1. So box 2's 5 is somewhere in row 1, we just don't know where.
Which means no other square in row 1 can be 5. Cross those out. That's a pointing pair.

You're ready

Rule squares out, look for the last gap, check what fits, and follow the chain. That covers any Easy or Medium puzzle. Hard and Expert use a few more tricks, and the hint names each one when you need it.

Start today's puzzle

Teaching a younger kid? The kids board uses animals on smaller grids. Kids sudoku