Sudoku Written by Brian Hamilton and Karan Hamilton.
Brian and Karan are the puzzle lovers and game makers behind Sudoku Online Puzzles. You can learn more on the About page.
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If you have just learned the rules, you already know everything a naked single needs: a digit can’t appear twice in a row, a column or a box. Pick an empty cell and cross off every digit its row, column and box already show. Sometimes only one digit is left. That digit is the cell’s answer, and a cell in that state is called a naked single.
It is the first technique every solver learns, and on easy puzzles it is very nearly the only one. We played 200 boards from each level of our classic sudoku the way a careful beginner would, taking a naked single whenever there was one. On Easy, naked singles placed 8,166 of the 8,200 digits. The example below is one of those boards.
What is a naked single in sudoku?
A naked single is an empty cell with only one candidate left: one digit that could still go there. Every cell needs a digit, so that one goes in. “Naked” means nothing hides it. You will also see it called a sole candidate, a lone number, a singleton, a forced digit or, in some apps, an obvious single.
Without pencil marks, a naked single is a cell whose row, column and box between them already show eight different digits. With pencil marks, it is a cell with one mark left. The easiest of all is the last empty cell in a row, column or box, sometimes called a full house: the house shows the other eight digits, so the missing one goes in.
Rows, columns and 3×3 boxes are all houses, and each holds 1 to 9 exactly once. A candidate is a digit that none of a cell’s three houses contains yet, and writing candidates small in the cell is called pencil marking. We name cells by row, then column, counting from the top left, so R2C6 is row 2, column 6. Boxes are numbered the same way: 1 to 3 across the top, 7 to 9 along the bottom.
The naked single is the smallest of a family. Two cells in a house holding the same two candidates and no others are a naked pair; three cells sharing three candidates are a naked triple. Those cross candidates out of other cells. A single places a digit.
How do you find a naked single?
Pick an empty cell and count the different digits it can see. The figures below use a real Easy puzzle from our generator, at the very start, before anything has been written in. Take R2C6, in box 2 at the top middle:
- Row 2 shows 7, 4, 6, 8 and 5. Five digits ruled out.
- Column 6 shows 8, 2, 6, 3 and 4. Two of those are new: 2 and 3.
- Box 2 shows 8, 1, 4, 6 and 2. One is new: 1.
Between them, the three houses show every digit from 1 to 8. Only 9 is left, so R2C6 is 9.
All three houses were needed. Stop after the row and the column and you are left with 1 or 9; it is the 1 at R1C5, inside the box, that settles it. Checking two houses and moving on is the usual way to walk straight past a naked single.
This Easy puzzle is waiting in our Sudoku Helper. Next Hint, pressed twice, does the rest: the first press writes the pencil marks, the second names the naked single in R2C6.
What happens after you place a naked single?
Every digit you place is one more digit for the cells in its row, column and box to see. In the second figure, placing the 9 in R2C6 takes the 9 out of R1C6, R2C7 and R7C6, and R2C7, which could have been 3 or 9, is left with 3: a new naked single. Place that and another appears. On this board naked singles fill all 41 empty cells, one after another, and nothing else is ever needed.
Only cells that share a row, column or box with the digit you just placed can lose a candidate, so that is where a new naked single turns up, if one does. About half the time one does: across our 200 Easy boards, 3,970 of the 8,166 naked singles (49%) created at least one new one, taking them in reading order as our helper does.
On our level pages, press Start Notes to fill in every candidate. From then on, each correct digit you place clears itself from the notes in its row, column and box, so a new naked single shows up as a cell with one note left.
Where should you look for naked singles first?
Without pencil marks, naked singles take more finding than you might expect. Proving one means accounting for all nine digits around a cell, and most cells don’t pass: a fresh Easy board from our generator has a median of 8 naked singles among its 41 empty cells, and many Hard and Expert boards start with none (the table below has the counts). That is why many solvers find hidden singles first when working by hand. Three habits cut the search down:
- Start with the fullest rows, columns and boxes. A house with one gap is a full house, and in a house with two or three gaps each cell has only a few digits left to rule out.
- Try cells where a busy row crosses a busy column. R2C6 saw 13 clues across its three houses, plenty to cover eight digits.
- After every placement, look in that digit’s row, column and box first.
Pencil marks change the job. Once every cell has its candidates written in, a naked single is a cell with one mark, which you can spot at a glance. They also show naked singles the clues alone can’t. On harder puzzles a pointing pair or a naked pair can cross marks out, and a cell can be left with one candidate even though its row, column and box show fewer than eight digits. In our replays that happened 43 times among 8,705 naked singles on Hard and 160 times among 8,431 on Expert, and never on Easy or Medium.
Can you solve a whole sudoku with naked singles alone?
On our Easy level, almost always; on the harder levels, less and less often. These are the 200 boards per level we played:
| Level (clues) | Naked singles at the start | Boards starting with none | Solved by naked singles alone | Digits naked singles placed |
|---|---|---|---|---|
| Easy (40) | 8 | 0 | 192 of 200 | 8,166 of 8,200 |
| Medium (32) | 3 | 6 | 94 of 200 | 9,154 of 9,800 |
| Hard (26) | 1 | 57 | 13 of 200 | 8,705 of 11,000 |
| Expert (22–25) | 1 | 94 | 0 of 200 | 8,431 of 11,575 |
Each level means 200 boards from our own generator, solved simplest move first with our helper’s techniques, so a naked single was taken whenever one existed. “At the start” is the median number of cells whose row, column and box show eight different digits before anything is written in. Measured in October 2026.
Forty clues are enough for naked singles to finish 192 of our 200 Easy boards on their own; the other eight run dry at least once and need 34 hidden singles between them. By Expert, no board finishes without hidden singles. At the far end, 499 of the first 500 puzzles in our Extreme bank start with no naked single at all, and no other move our helper knows either.
We checked every 4×4 sudoku with exactly one solution, all 13,579,680 of them, for our 4×4 Sudoku page: naked singles alone finish every one. On our 6×6 puzzles they finish every Easy board but one in 10,000. The 4×4, the first grid on our Sudoku for Kids page, is pure naked-single practice.
What is the difference between a naked single and a hidden single?
They ask opposite questions. A naked single starts from a cell: which digits can go here? If the answer is one, you place it. A hidden single starts from a digit and a house: where can the 6 go in column 1? If the answer is one cell, the 6 goes there, even when that cell could otherwise take several digits. Both are certain, and neither is a guess.
Between them they placed every digit on our four classic levels; the other techniques only cross candidates out. As the clues thin, the work shifts: hidden singles placed 34 digits on Easy, 646 on Medium, 2,295 on Hard and 3,144 on Expert. Fewer cells can see eight different digits, but a digit still often has only one place left in a house. From Medium up, you need both: on Medium, 106 boards in 200 need at least one hidden single, and every Expert board does.
Stuck with no naked singles left? What to try next
This is one of the eight Easy boards where naked singles ran out. After 13 of them, 28 cells are still open and not one is down to a single candidate.
When it happens to you, work through these in order:
- Check the houses of the last digit you placed. A naked single you missed is most likely there.
- Look for hidden singles. Take one digit at a time and ask where it can go in each row, column and box. The board above had five. One was all it needed; after it, naked singles did the rest.
- Make sure your pencil marks are complete, then look for moves that cross marks out: pointing pairs, box/line reduction and naked pairs. Some of our Hard and Expert boards need them, and none needs anything more: 177 of our 200 Hard boards and 132 of 200 Expert boards finish with singles alone. Hidden pairs, X-Wings and chains only come into play on our Evil and Extreme puzzles.
One warning sign: if a cell has no candidates left, or two cells in the same house are down to the same single digit, a digit placed earlier is wrong. Go back over your last few moves rather than pushing on. For the order to learn everything else in, see our sudoku strategies for beginners and the full guide to sudoku techniques.
Where can you practise naked singles?
Easy is the place: 192 of our 200 boards there needed nothing else. Solve a few without notes, counting digits as in the first figure, since that is the skill that carries over to paper; then try Start Notes and watch for cells with one mark. When Easy feels quick, Medium adds the hidden singles.
Open the Sudoku Trainer and choose Naked Single. It has ten positions from our generator, gentlest first. Click the cell you think is the naked single and press Check; save Find Pattern for after you have tried.