Sudoku is a logic puzzle played on a 9×9 grid. You fill the empty cells with the digits 1 to 9 so that every row, every column and every 3×3 box contains each digit exactly once. Some cells start filled in. Those are your clues, and there is only one way to fill in the rest.
The rules
The grid has 9 rows, 9 columns, and 9 boxes of 3×3 cells, marked off by the thicker lines.
- Each row holds the digits 1 to 9, once each.
- Each column holds the digits 1 to 9, once each.
- Each box holds the digits 1 to 9, once each.
That’s all. The order inside a row, column or box doesn’t matter, as long as nothing repeats. When the grid is full and no rule is broken, the puzzle is solved.
Because each area has nine cells and nine digits, “no repeats” and “every digit once” come to the same thing. That’s the whole trick of Sudoku: if a digit can’t go anywhere else in a row, column or box, it must go in the one place left.
A small example, solved
The rules work at any size. Here’s a 4×4 Sudoku: digits 1 to 4, with boxes of 2×2. It’s the quickest way to see how the reasoning goes. Rows are numbered from the top, columns from the left.
Step 1: find a row with one gap
Row 1 already has 3, 1 and 4. The only digit missing is 2, so it goes in the last cell.
Step 2: find the only place for a digit
Look at the top-left box. It needs a 2 and a 4, and its two empty cells are in row 2. The 4 can’t go in column 2, because column 2 already has a 4 (in row 3). So the 4 goes in column 1.
That fills in more of the grid at once:
- The top-right box now has 4, 2 and 3, so its empty cell is 1.
- Row 2 now has 4, 3 and 1, so its empty cell is 2.
Step 3: finish the bottom half
- Column 2 has 1, 2 and 4, so the gap in row 4 is 3.
- Column 3 has 4, 3 and 1, so the gap in row 3 is 2.
- Row 3 now needs 1 and 3. Column 1 already has a 3, so column 1 takes the 1 and the 3 goes in column 4.
- Row 4 needs 2 and 4. Column 4 already has a 2 (in row 1), so it takes the 4, and the 2 goes in column 1.
Every 9×9 puzzle is solved the same way, just with more to look at.
Two moves that start every puzzle
On a full-size grid, beginners make almost all their progress with two moves. They’re the same idea seen from two directions.
The only place for a digit
Pick a box and a digit the box is missing. Then look along the rows and columns that pass through the box: wherever that digit already sits in one of them, it rules out the whole line inside the box. If only one empty cell is left, the digit goes there.
This is often called cross-hatching or scanning, and it’s the fastest way into a fresh puzzle. Work through the digits 1 to 9 one at a time and check every box for each. It works for rows and columns too: a digit can have only one place left in a row or a column.
The only digit for a cell
Sometimes it’s easier to start from a cell. Every cell shares a row, a column and a box with 20 other cells. List the digits among those 20. If eight different digits are already there, the ninth is the only one the cell can take.
Here row 1 already has 2, 3, 4, 5, 6 and 9, column 3 adds a 1, and the top-left box adds a 7. That leaves 8. Scanning boxes for the 8 wouldn’t find this one yet, which is why it pays to switch between the two views.
Notes: pencil in what’s possible
When neither move finds anything, write in the digits each cell could still take. In the game, turn on Notes and tap digits to pencil them in small. Once a cell’s notes are down to one digit, or a digit’s notes in a row, column or box are down to one cell, you have your next move. Harder puzzles are solved almost entirely in the notes.
Common mix-ups
- Counting the diagonals. In classic Sudoku, only rows, columns and boxes count. A digit can repeat along a diagonal.
- Thinking you need maths. Nothing adds up. A 9 is no “bigger” than a 1 for solving purposes.
- Guessing to get unstuck. A wrong guess can sit unnoticed for twenty moves and then break the grid. If you’re stuck, look at one digit across all nine boxes, or fill in notes.