Every empty cell in a Sudoku starts with nine possible digits. Each given number in the same row, column or 3x3 box removes one of them. When eight have been removed and a single digit remains, that cell is a naked single. There is nothing to work out. The digit is forced, so you write it in.
The name comes from the older pencil-and-paper habit of writing small candidate numbers in each cell. A cell whose pencil marks have been whittled down to one digit shows that digit "naked", with nothing else beside it. Some books call the same thing a forced cell or a sole candidate.
Easy puzzles on this site (40 or more givens) can be finished with naked singles and its close cousin, the hidden single, and nothing else. Medium puzzles need them constantly between the harder moves. Learn to see them without pencil marks and your solving speed roughly doubles.
Worked example
This is a real easy puzzle. Use the buttons to step through two naked singles and one cell that is not a single yet.
How to spot a naked single without pencil marks
Pick an empty cell and run through 1 to 9 in your head, glancing at the row, column and box for each. With practice this takes two or three seconds. Two shortcuts make it faster:
- Start with crowded cells. A cell whose row, column and box already hold 18 or more digits between them is the most likely to have one candidate left. Empty regions can wait.
- Count the missing digits in the unit first. If a row has only two blanks, each blank has at most two candidates. Check the column and box of each blank and one of them usually collapses to a single.
On this site, turning on Notes shows the small candidate marks; the Hint button will place a single for you if you are stuck, and it costs you score rather than the puzzle.
Naked single or hidden single?
The two beginner techniques look at the same board from opposite directions. A naked single starts from a cell and asks "which digits can still go here?" A hidden single starts from a digit and asks "where in this row, column or box can it still go?" If the answer is one cell, the digit is placed even though that cell may show several candidates.
Most solvers scan for hidden singles first because they need no pencil marks, then switch to naked singles when the board fills up and cells start running out of options. Neither is better; a fast solver alternates between them without noticing.
Common mistakes
- Checking only the row and column. The 3x3 box is the constraint people forget. Always check all three units.
- Trusting stale pencil marks. If you placed a digit and did not update the notes in its row, column and box, a cell may look like it has two candidates when it really has one. On this site, placing a digit clears that digit from the notes of every peer automatically.
- Mistaking a lonely mark for a single. A cell showing one pencil mark is only a naked single if you actually wrote down every candidate for that cell. If you only marked the digits you happened to be thinking about, the cell might have others you never noted.
Why this is enough for easy puzzles
The generator behind the Easy Sudoku page keeps removing clues from a full grid only while the remaining puzzle can be finished by singles alone. That is what "easy" means here, not a number pulled from the air. So on an easy board there is always at least one naked or hidden single available at every moment, right up to the last cell. If you cannot find one, it is there; look at the most-filled box again.
Medium puzzles (33 to 39 givens) still lean on singles for most placements but will stall once or twice, at which point you need naked pairs or pointing pairs to break the logjam.
Easy boards are built so that singles alone finish them. Turn on Notes and watch cells collapse to one candidate.
Frequently asked questions
A naked single is an empty cell where only one digit is still possible, because the other eight already appear in that cell's row, column or 3x3 box. The remaining digit must be placed there.
Yes. Sole candidate, forced cell, single candidate and naked single all describe the same situation. Different books and apps use different names.
Easy puzzles, yes. The easy boards on this site are generated so that naked and hidden singles are always enough. Medium and harder puzzles reach positions where no cell has a single candidate, and you need pairs, pointing pairs or more advanced patterns.
No. Checking 1 to 9 against the row, column and box takes a few seconds per cell once you are used to it. Pencil marks (the Notes button here) help when the board is crowded and several cells are down to two or three candidates.
A naked single is found by looking at one cell and seeing only one digit fits. A hidden single is found by looking at one digit and seeing only one cell in a row, column or box can take it. The hidden single cell may still show other candidates in pencil marks.