Sudoku Techniques

Scanning (cross-hatching)

Pick a digit, say 5. Mark every row and column that already contains a 5, then look at each box. If those lines leave only one free cell in a box, the 5 goes there. Repeat for every digit. This simple technique solves most of an easy Sudoku.

Naked and hidden singles

• Naked single: a cell with only one candidate left after you rule out every digit in its row, column and box.
• Hidden single: a digit that can go in only one cell of a row, column or box, even though that cell has other candidates. The unit needs that digit somewhere, so it must go there.

Naked and hidden pairs

• Naked pair: two cells in a unit that contain only the same two candidates, for example {3, 7}. These digits must fill those two cells, so remove 3 and 7 from every other cell in the unit.
• Hidden pair: two digits that appear as candidates in only the same two cells of a unit. Those cells must hold those digits, so delete all their other candidates.

Triples and quads

The pair idea extends to three or four cells. In a naked triple, three cells share a combined set of only three candidates, so those digits can be removed from the rest of the unit. A hidden triple is the reverse: three digits confined to three cells, letting you erase every other candidate from those cells. These appear mostly in hard and expert puzzles.

Pointing pairs and triples

If every candidate for a digit inside a box lies in a single row or column, that digit must go in that line within the box. Remove the digit from the rest of that row or column outside the box.

Box-line reduction

The mirror image of pointing pairs. If every candidate for a digit in a row or column lies inside one box, the digit must go in that box on that line. Remove it from the other cells of the box.

X-Wing and Swordfish

Look for a digit that has exactly two possible cells in each of two rows, with those cells sharing the same two columns. The digit must occupy opposite corners of the rectangle, so you can remove it from every other cell in those two columns. The same pattern works with rows and columns swapped.

Swordfish is the same logic over three rows and three columns, and it is harder to spot.

XY-Wing

An XY-Wing uses three cells with two candidates each: a pivot with {X, Y} and two wings with {X, Z} and {Y, Z}. The pivot must see both wings. Whichever way the pivot resolves, one wing becomes Z, so any cell that sees both wings cannot contain Z.

Which technique to try first

Try the cheapest technique first and move down the list only when it stops working. For the bigger picture on how to combine them, read our Sudoku strategies guide, then use the Sudoku solver to check your reasoning.

Sudoku Techniques FAQ

What is a naked single in Sudoku?

A cell where only one candidate digit remains once you rule out everything already in its row, column and box.

What is the difference between naked and hidden pairs?

In a naked pair, two cells contain only the same two candidates. In a hidden pair, two digits appear as candidates in only the same two cells of a unit, although those cells may contain other candidates too.

What is an X-Wing in Sudoku?

An X-Wing is a pattern where a digit has exactly two possible cells in each of two rows and those cells line up in the same two columns. It lets you eliminate that digit from the rest of those two columns.

Which techniques do I need for hard Sudoku?

Hidden singles, full pencil notes, naked and hidden pairs and pointing pairs cover most hard puzzles. Expert puzzles can also need box-line reduction, X-Wing and XY-Wing.