What Sudoko gives you to apply these techniques
Advanced techniques rely on candidates, the digits still possible in each cell. In Sudoko you pencil them in yourself with Notes mode (N key). The game helps in three ways:
- it refuses an impossible note, a digit already present in the row, column or box, and flashes the cells that block it;
- it removes a digit automatically from the notes of its row, column and box as soon as you place it correctly;
- it lets you note a digit in several cells with a single drag (or Shift + drag on a computer).
The game does not fill in candidates for you, and the eliminations described below are done by hand, with the erase button (labelled Effacer) or by tapping the noted digit again.
Techniques that place a digit
The naked single
A cell has only one candidate left: its row, column and box already contain the other eight digits. With notes it jumps out, because the cell shows a single digit. Without notes, count what the cell "sees".
The hidden single
A digit has only one possible spot left in a row, column or box, even if that cell has other candidates. This is what scanning finds: you look for the spot of a digit rather than the digit of a cell. Our guide on how to play Sudoko walks through an example step by step.
Techniques that eliminate candidates
The naked pair
Two cells in the same group share exactly the same two candidates. Those two digits are reserved for them and disappear from the other cells of the group. An example on one row:
| Cell | Candidates |
|---|---|
| Column 1 | 3, 8 |
| Column 4 | 3, 8 |
| Column 6 | 1, 3, 6, 8 |
| Column 9 | 1, 6, 8 |
Columns 1 and 4 form a 3-8 pair. Strike 3 and 8 elsewhere: column 6 drops to 1, 6 and column 9 to 1, 6, which creates a new pair.
The hidden pair
Two digits appear only in the same two cells of a group, among other candidates. If in a box the 2 and the 7 are only possible in two cells noted 2, 4, 7, 9 and 2, 5, 7, those two cells must hold the 2 and the 7: strike their other candidates.
The naked triple
Same idea as the pair, with three cells and three digits. Three cells noted 1, 4, then 4, 9, then 1, 9 share the digits 1, 4 and 9, even though none contains all three. Those digits disappear from the other cells of the group.
Box and line interactions
Pointing
In a box, all the candidates for a digit line up on the same row (or column). The digit will therefore be on that row, inside the box, so you can strike it from the rest of the row, in the other two boxes. Depending on the number of cells, this is called a pointing pair or a pointing triple.
Example: in the top-left box, the 5 is only possible on row 2, in columns 1 and 3. Row 2's 5 must be in that box, so strike it from columns 4 to 9 of row 2.
Box/line reduction
This is pointing in reverse. In a row, all the candidates for a digit sit in the same box. That row's digit is therefore in that box, and you can strike it from the box's other cells, on its other two rows.
The X-Wing
X-Wing is the best-known advanced technique. A digit has only two possible spots in one row, and the same two columns in another row:
| Row | Possible columns for 7 |
|---|---|
| 2 | 3 and 8 |
| 6 | 3 and 8 |
In row 2, the 7 is in column 3 or 8. In row 6 as well. Whichever option holds, the two 7s occupy columns 3 and 8, one in each. So you can strike the 7 from every other cell in columns 3 and 8. The pattern also works with rows and columns swapped.
Which techniques for which grid?
In Sudoko, difficulty depends on how many digits are given at the start: around 36 for an easy grid, 28 for a medium one and 22 for a hard one, which is Sunday's. That does not guarantee that a specific technique is required. In practice:
- easy grids fall to singles;
- medium grids sometimes need a pair or a pointing move;
- hard grids can require several eliminations in a row, and rarely an X-Wing.
Every grid has a single solution and can be solved without guessing. For practical advice on pace, notes and the joker, read our Sudoko tips.