Sudoku is a 9×9 grid split into nine 3×3 boxes. Some squares start with a digit; you fill in the rest. There are four rules, and everything else is technique.
Rules
- Fill the 9×9 grid so every row holds the digits 1 to 9 once each.
- Every column also holds 1 to 9 once each.
- The thick lines split the grid into nine 3×3 boxes (numbered 1 to 9, left to right, top to bottom). Each box holds 1 to 9 once each too.
- The digits you start with are fixed. Tap an empty square, then a number. Turn on Notes to pencil in the digits a square might hold.
Your first moves
Start with the digits that already appear most often. Take one, say 7, and look at a box that has no 7 yet. The 7s in the neighbouring boxes rule out every square in their row and column. Often only one square in the box is left: that is the 7. Go through all nine digits this way, then start again; each digit you place opens up new ones.
When scanning stops working, write notes: the digits each empty square could still hold. Every technique below works on those notes.
A worked example
The first three moves, as our solver finds them:
- Row 2, column 5 can only be 9: the other eight digits are all in its row, column or box.
- Row 2, column 6 can only be 2: the other eight digits are all in its row, column or box.
- Row 2, column 1 can only be 3: the other eight digits are all in its row, column or box.
Everything after that is more of the same: this puzzle needs nothing but singles, which is what makes it easy.
Techniques, from easiest to hardest
Every example below comes from a real puzzle on this site, at the moment our solver used the technique. Small digits are notes; red ones are the notes the technique removes.
Naked single
A square where eight of the nine digits already appear in its row, column or box. The ninth must go there.
Hidden single
A digit that has only one possible square left in a row, column or box. The square may still look open to other digits; this one has nowhere else to go.
Pointing pair and box/line reduction
If a digit's only options inside a box all lie in one row (or column), that row gets its digit from this box, so the rest of the row can't have it. The mirror image is the box/line reduction: if a digit's options in a row all fall inside one box, the rest of that box can't have it. Medium puzzles need one of these at least once.
Naked and hidden pairs and triples
Two squares in the same row, column or box that can only hold the same two digits (a naked pair) will take those two digits between them, so the other squares in that unit can't have them. A hidden pair is the reverse: two digits that can only go in the same two squares of a unit, so those squares can't hold anything else. Triples work the same way with three squares and three digits. Hard puzzles need at least one.
X-Wing
Two rows where a digit can only go in the same two columns. The two rows need one each and can't share a column, so between them they use that digit's places in both columns. Every other square in those two columns loses the digit. It works the same with rows and columns swapped.
XY-Wing
Three squares with two notes each: a pivot with AB, and two wings it can see, one with AC and one with BC. If the pivot is A, the first wing is C; if the pivot is B, the second wing is C. Either way one wing is C, so any square that sees both wings can't be C.
Swordfish
The X-Wing with three rows and three columns: a digit that, in three rows, can only go in the same three columns. Those rows take the digit's places in all three columns, so the rest of the columns lose it.
What each level needs
| Level | Digits given | What it takes |
|---|---|---|
| Easy | 36–40 | Only naked and hidden singles |
| Medium | 28–34 | At least one pointing pair or box/line reduction; nothing harder |
| Hard | 24–32 | At least one naked or hidden pair or triple; nothing harder |
| Expert | 24–30 | One or two X-Wing or XY-Wing steps |
| Evil | 24–26 | A Swordfish, or three or more X-Wing / XY-Wing steps |
Common mistakes
- Guessing when stuck. A wrong guess can sit unnoticed for twenty moves. On these puzzles there is always a logical move; look for it, or tap Hint.
- Stale notes. Every time you place a digit, remove it from the notes in its row, column and box. (The game does this for you.)
- Checking only rows. Most early moves come from boxes. Scan box by box first.
Questions
What is the goal of sudoku?
To fill every empty square so that each row, each column and each 3×3 box contains the digits 1 to 9 exactly once.
Is sudoku a math puzzle?
No arithmetic is involved. The digits are just nine different symbols; the puzzle would work the same with letters or colours.
Do I ever need to guess?
Not on this site. Every puzzle here can be finished with the techniques on this page. On harder puzzles elsewhere you may meet ones that need more advanced chains, but a well-made sudoku never needs trial and error.
Where do I start?
Pick the digit that already appears most often and look for the boxes still missing it. For each of those boxes, check which of its empty squares that digit can reach. When only one is left, fill it in.
How many digits does a sudoku need to have one solution?
At least 17. That was shown in 2012 by an exhaustive computer search. Our puzzles start with 24 to 40.