Singles
Singles are techniques used to determine the digit for a cell by observing that only one candidate remains. In other words, they are techniques that directly produce a digit placement. By contrast, most non-single techniques only eliminate candidates through logical inference. Eventually, when a cell is reduced to just one candidate, some form of single is still needed to complete the placement.
Based on whether candidates need to be filled in first, singles can be divided into two categories:
- Direct: the single can be found by inspecting the grid without writing candidates.
- Indirect: the single can only be seen after candidates have been filled in.
Based on whether the relevant information is immediately visible or hidden, singles can also be divided into Naked Singles and Hidden Singles.
- Naked Single: a cell has exactly one possible candidate, so the information is visible directly in that cell.
- Hidden Single: a cell may have multiple candidates, but in one of its houses (row, column, or box), one particular candidate appears in only one cell. The information is therefore hidden and takes more observation to spot.
There is also a special case of the Naked Single: when a house (row, column, or box) has only one unfilled cell left. By the rules of Sudoku, that cell must contain the only missing digit.
| Direct (without filling in candidates) | Indirect (after filling in candidates) | |
|---|---|---|
| Naked Single (the cell has only one candidate) | Direct Naked Single: Inspect the peer cells of a cell. If, among digits (Special case) Full House/Last Digit: A house has only one unfilled cell left. | Indirect Naked Single: Inspect the candidates of a cell. If only one candidate remains, then that digit is the cell's naked single. |
| Hidden Single (a candidate appears only once in a house) | Direct Hidden Single: Use cross-hatching to eliminate possibilities until a digit can go in only one cell in a house. | Indirect Hidden Single: In a house, a digit can go in only one cell. |