how to play sudoku
Sudoku is a number-placement puzzle on a 9x9 grid. Fill every empty cell with a number from 1 to 9 so that no number repeats in any row, any column, or any of the nine 3x3 boxes marked by the thick borders.
You shouldn't need to guess. Every board has exactly one solution that can be reached by applying the rules below.
the rules
Every row holds 1 through 9, one of each.
Likewise, each column holds every number once.
The grid is split into nine 3x3 boxes. Each box holds every number once too.
a worked example
Let's walk through five moves on a real board to illustrate some techniques worth knowing.
We start with 34 given numbers and 47 blank cells.
Take the bottom-left box and ask where its 6 goes. Column 1 already has a 6, so the left column is out. Row 7 has one at column 8, so the box's top row is out.
The 6 must go in row 9, column 3. Sweeping a box this way is called cross-hatching, and the number it turns up is a hidden single.
We can do the same with columns. Column 9 needs a 2. Rows 1 and 5 already have their 2's, and the bottom-right box has one, which rules out the last three cells. Only row 6 is left.
Now, row 7 still wants a 2, a 4 and a 7. The 7 is already in column 9, the 2 already in this box, so only the 4 fits. A cell with one possible number left is a naked single.
When the easy moves dry up, write pencil marks: in every blank cell, note each number that still fits. Row 4 comes out like this.
Two cells in row 4 read 4 5. Between them they take the 4 and the 5, so nothing else in the row can be either. That is a naked pair, and it leaves row 4, column 8 with one mark: 3.
Those same two cells sit together in the middle box, so we can't have a 4 anywhere else in that box. That drops row 5, column 5 to a single 9.
Keep applying these rules to eliminate possibilities and fill in numbers. Here's the finished puzzle!
controls
Tap a cell to select it, then tap a number to write it in. The eraser clears the selected cell.
The pencil switches the number pad to small candidate marks, so you can note the numbers a cell could still hold. Tap the same number again to rub a mark out. They are notes to yourself: a board is solved on its full-size numbers alone.
If using a keyboard: arrow keys move between cells, 1 to 9 enter a number, and backspace clears a cell. Shift + a number writes a pencil mark.
tips
- Start where the grid is fullest. Work the row, column or box with the fewest blanks first. Fewer blanks means fewer places a missing number can go.
- Cross-hatch a box for a hidden single. Pick a box and a number, then look along every row and column that already holds that number. If one blank cell survives, the number goes there.
- Check a cell for a naked single. Take one blank cell and list what its row, column and box already hold between them. If that covers eight of the nine numbers, the last number must go in that cell.
- Use the pencil to make notes. This helps keep the possible numbers visible instead of in your head.