Singles

Singles are techniques that determine a digit placement by finding either an unfilled cell with only one possible candidate, or a digit with only one possible location in a house (row, column, or box). Singles directly place answer digits; most non-single techniques eliminate candidates through logical inference. When those eliminations leave a cell with only one candidate, or a digit with only one possible location in a house, the corresponding single technique can be used to place the answer digit.

Based on whether candidates need to be filled in first, singles can be divided into two categories:

• Direct: determine the placement using only the digits already placed on the board, without writing candidates.
• Indirect: write candidates first, then inspect the remaining candidates to determine the placement. These candidates may reflect eliminations made by other techniques.

Based on whether we examine the possible digits within a cell or the possible locations of a digit within a house, 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, the only missing digit must be placed in that cell.

	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 1–9, only one digit has not yet appeared, then that digit is the cell's naked single. (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 digit has only one possible location in a house)	Direct Hidden Single: Use cross-hatching to rule out positions until a digit can go in only one unfilled cell in a house.	Indirect Hidden Single: Inspect the remaining candidates in a house. A particular candidate appears in only one unfilled cell.