Techniques

Sudoku techniques

In order – from the technique that cracks every easy puzzle to the one you need for expert grids.

1. Naked single

A cell where only one digit is still possible. To find one, take an empty cell, go through its row, column and box, and rule out every digit already there. If exactly one is left, that's the answer.

Easy puzzles are made almost entirely of naked singles – which is why you can solve them in a single pass.

2. Hidden single

The reverse view: instead of asking “what fits in this cell?”, you ask “where in this box can this digit still go?”. If there is only one place, that's where it belongs – even if several other digits would still fit the same cell.

Hidden singles are the reason it pays to follow a single digit across the whole grid.

3. Candidate lists

From medium difficulty on, your head is no longer enough. Note every digit that is still possible in each empty cell – that's the foundation for all the techniques that follow. In neun., A does this for the whole grid at once.

Important: candidate lists have to stay up to date. When you place a digit, it disappears from the notes of every cell in the same row, column and box – here that happens automatically.

4. Naked pair

Two cells in the same unit that both have exactly the same two candidates – say only 4 or 7. Which digit ends up where is still open, but between them they claim these two cells. So neither the 4 nor the 7 can go in any other cell of that unit – strike them everywhere else.

The same works with three cells and three candidates (a naked triple).

5. Hidden pair

Two digits that, within a unit, appear only in the same two cells. Those cells then belong to the two digits – every other candidate in them can go.

6. Pointing pair

If, within a box, a digit only appears in cells of one row, then in that row it is guaranteed to sit inside the box – so you can strike it from the rest of the row. The same goes for columns. This is the first technique that links two units together.

7. X-Wing

For expert puzzles. In two different rows, a digit appears only in the same two columns. These four cells form a rectangle. However it plays out, one corner in each of the two columns will be filled. So the digit can be struck everywhere else in both columns.

From here on, Sudoku becomes pattern spotting. If you can reliably see an X-Wing, you can solve practically any puzzle that doesn't require guessing.

The order in practice

Always work down this list from the top, and start over at the top after every cell you fill. A single placed digit often sets off a chain of new singles – you only need the heavier techniques when the simple ones really have nothing left to give.

Still unsure about the basics? Read the rules. Otherwise, get back to playing.