How to Solve Sudoku: 4 Techniques, Step by Step

Sudoku has simple rules, and you do not need to be good at math. Every puzzle on this site can be solved with the four techniques below, one step at a time, without guessing. Each technique matches one of our four levels, and each level also uses the techniques that come before it.

The rules

Fill every empty square with a number from 1 to 9 so that:

1. each row has the numbers 1 to 9, once each,
2. each column has the numbers 1 to 9, once each,
3. each 3×3 box (outlined with thick lines) has the numbers 1 to 9, once each.

Keep a pencil and eraser nearby. Many people write small notes in the corner of a square to remember which numbers could still go there.

Technique 1: Look inside one box (Beginner)

Pick one 3×3 box and a number it is still missing. Look at the rows and columns that pass through the box. If the number already appears in one of those rows or columns, it cannot go in that part of your box. When only one empty square in the box is left, the number goes there.

Example. The top-left box has no 7 yet. It has five empty squares: two in its top row, two in its middle row and one in its bottom row. Farther along the top row of the grid, there is already a 7, so neither empty square in the box's top row can be 7. Farther along the middle row there is also a 7, which rules out the two squares in the middle row. Only the square in the bottom row is left, so the 7 goes there.

Technique 2: Look along a row or column (Easy)

This works like Technique 1, but along a whole row or column instead of a box. Pick a row and a number that row is still missing. Check each empty square in the row. If the number is already in that square's column or 3×3 box, it cannot go there.

Example. The fifth row is missing 2, 4 and 9, and has three empty squares. Where can the 4 go? The column above the first empty square already has a 4. The second empty square sits in a box that already has a 4. That leaves only the third square, so the 4 goes there.

Technique 3: "It must be in this row of the box" (Medium)

Sometimes you cannot place a number yet, but you can still narrow things down.

Example. In the middle-left box, the 6 could go in only two squares, and both are in the box's top row. You do not know which one yet. But you do know this box's 6 will be somewhere in that row. A row can hold only one 6, so no other square in that same row can be 6, including the squares in the two boxes to the right. Cross 6 off those squares. Often this leaves one of those boxes with only one place for its 6, and you can fill it in with Technique 1.

The same idea works for columns.

Technique 4: Pairs (Hard)

A pair is two squares that must hold the same two numbers between them.

Example. In one row, you check two empty squares and find that each can only be a 3 or an 8, because every other number is already in its row, column or box. These two squares will take the 3 and the 8, one each, even if you do not know which is which yet. That means no other square in that row can be a 3 or an 8. Cross them off the rest of the row. Often a square that had several choices is now down to just one.

Pairs work the same way in a column or a 3×3 box. Small pencil notes make pairs much easier to spot.

If you get stuck

• Go back to Technique 1 and check each box for each number from 1 to 9. It often turns up something new.
• Take a short break. A fresh look helps.
• Page 2 of every puzzle has a hint that points to the spot where most people get stuck. The full answer is below the hint, so cover it with a sheet of paper if you only want the hint.

Ready to try? Start with Beginner puzzles, or see all four levels.