The Square One field guide
How to play Sudoku.
Sudoku is not an arithmetic test. It is a process of noticing what can—and cannot—fit. This guide begins with the rules and builds through four useful solving techniques, without guessing.
The rules
Sudoku rules: use each number once.
A Sudoku board has nine rows, nine columns and nine 3×3 boxes. Complete the board so that each row, column and box contains every digit from 1 to 9 exactly once. The printed numbers are clues and cannot be changed.
You never need to calculate. Each answer follows from the positions already filled and the candidates still available.
Where to start
Start with candidates and pencil marks.
Pick a row, column or box that is already fairly full. Look at the missing digits, then test each empty square against the numbers in its crossing row, column and box. A digit that is already present in any of those three groups cannot go there.
Pencil marks record the candidates that remain. Keep them tidy and update them when you place a number. Good notes turn a busy board into a set of small, visible decisions.
Core techniques
Four Sudoku solving techniques.
One square, one possible number
Naked single
After checking its row, column and 3×3 box, a square has only one candidate left. That candidate must be the answer.For example, suppose a square’s row, column and box together rule out 1, 2, 3, 4, 6, 7, 8 and 9. Only 5 remains, so you can place 5 in that square.
One number, one possible square
Hidden single
A row, column or box may have several empty squares, but a particular number can fit in only one of them. The answer is hidden among other candidates.For example, a row still needs 2, 5 and 8. If only one empty square can contain 8, place 8 there—even if that square also has 2 and 5 pencilled in.
Two numbers locked into two squares
Naked pair
When two squares in the same row, column or box contain exactly the same two candidates, those numbers belong to that pair and can be removed from the other squares in the group.For example, two squares in a row each have exactly the candidates 2 and 7. Those squares must hold 2 and 7 in some order. Remove 2 and 7 from every other square in that row.
A candidate confined to one line
Box–line reduction
If every possible position for a number inside a 3×3 box falls on one row or column, that number cannot appear elsewhere on the same line outside the box.For example, all possible positions for 4 in the top-left box lie in the top row. That box must place its 4 in that row, so remove 4 as a candidate from the top row’s squares in the other two boxes.
Solving habits
When you feel stuck, change the question.
Instead of asking “What number goes here?”, choose a missing number and ask “Where can this number go in this row, column or box?” Moving between square-first and number-first thinking is often enough to reveal a hidden single.
Re-scan after every placement. One solved square changes three groups at once, so it may create a new single elsewhere. If no singles remain, inspect your candidates for pairs and box–line interactions before considering anything more complex.
Put it into practice
Try a free Sudoku puzzle.
Put these techniques into practice with today’s online Sudoku. Pencil marks, undo and checking are built in, so you can work through each step at your own pace.
Play today’s free SudokuKeep learning with the Square One app.
Enjoy unlimited offline Sudoku and four difficulty levels on iPhone, iPad and Android. On Apple devices, guided solving can explain a logical next step on your current board.
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