Naked Singles in Sudoku
The naked single is the most fundamental technique in sudoku. Every other method — hidden singles, naked pairs, pointing pairs — builds on top of the logic introduced here. Master this technique first and you can solve any easy puzzle and most medium ones.
What Is a Naked Single?
A naked single occurs when an empty cell has only one possible digit remaining after all elimination is applied. After checking the cell's row, column, and 3×3 box, eight of the nine digits (1–9) have been ruled out, and exactly one remains. That remaining digit is the answer.
The name "naked" refers to the fact that the single candidate is fully visible — it's the only option left in that cell when you look at it directly. This contrasts with a hidden single, where the logic involves looking at a group rather than a single cell.
How to Find Naked Singles
For any empty cell, follow these steps:
- List all digits already present in the cell's row. Eliminate those from consideration.
- List all digits already present in the cell's column. Eliminate those too.
- List all digits already present in the cell's 3×3 box. Eliminate those as well.
- Count the remaining digits. If exactly one remains — that's your naked single.
Example: The green cell in the diagram is our naked single. Its row (blue) already contains 1, 3, 7, 9 — four digits eliminated. Its column (green tint) contributes 6 and 2 — two more. Its 3×3 box (amber) adds 4 and 8 — two more. Together, eight digits are ruled out: 1, 2, 3, 4, 6, 7, 8, 9. Only 5 remains. That cell must be 5.
Scanning Efficiently for Naked Singles
Checking every empty cell one by one is slow. Instead, use these shortcuts:
Target dense rows and columns first. A row with seven or eight filled cells only has one or two empty cells. Those empty cells are likely to be naked singles. Start there.
Work from recently placed digits. When you fill in a cell, the cells sharing its row, column, and box now have one more constraint. Check those cells immediately — they're the most likely candidates for new naked singles.
Use digit counting. Count how many of each digit (1–9) are already on the board. Digits that appear eight times only need to be placed once more — and that last cell is very likely a naked single.
Naked Singles and Pencil Marks
On harder puzzles, use pencil marks to track candidates. Write the remaining possible digits as small numbers inside each empty cell. A cell that starts with four candidates and gets reduced to one (as neighboring digits are placed) reveals itself as a naked single automatically — you'll see a cell with only one pencil mark.
This is why maintaining pencil marks carefully matters: stale or missing marks can hide naked singles from view.
When Naked Singles Run Out
On easy puzzles, naked singles alone are sufficient to solve the entire grid. On medium and hard puzzles, you'll reach a point where no cell has exactly one candidate remaining. This is when you advance to the next technique: hidden singles.
The transition from naked singles to hidden singles is the key skill jump between easy and medium solving.
Practice
The best way to internalize naked singles is to solve easy puzzles until finding them feels automatic. At that point, your eyes will naturally jump to constrained cells without consciously running through the three-group check.