Naked Singles is one of the most fundamental Sudoku solving techniques and the natural next step after Last Remaining Cell. A Naked Single occurs when an empty cell has only one possible candidate digit remaining after considering all the constraints from its row, column, and 3x3 box. Even if the row, column, and box each have multiple empty cells, the intersection of their constraints may leave just one valid digit for a particular cell.
To find Naked Singles, examine an empty cell and list all digits from 1 to 9 that do NOT appear in its row, column, or box. If only one digit remains, that cell is a Naked Single and the digit can be placed immediately. This is different from Last Remaining Cell because you are analyzing constraints from three units simultaneously rather than looking for a unit with only one empty cell.
Naked Singles appear frequently in easy and medium puzzles and form the backbone of basic Sudoku solving. Developing the ability to quickly spot Naked Singles by scanning rows, columns, and boxes simultaneously will dramatically speed up your solving. This technique also introduces the concept of candidates (possible digits for a cell), which is essential for understanding more advanced strategies later on.
Try It Yourself
Walk through each step of the naked singles technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look at cell (0,0) — it is empty. We need to determine what digit can go here by checking the constraints from its row, column, and the top-left 3x3 box.
Step-by-Step Guide
Select an empty cell to analyze.
Check which digits (1-9) already appear in the same row.
Check which digits already appear in the same column.
Check which digits already appear in the same 3x3 box.
Combine all used digits to find the complete set of eliminated values.
If only one digit from 1-9 is not eliminated, that digit is the Naked Single.
Place the digit in the cell and look for more Naked Singles triggered by this placement.
Imagine you are at a dinner table and each seat has a name card. After everyone else sits down, the constraints from every direction leave only one name for your seat — no guessing needed.
A cell in Sudoku is simultaneously constrained by three units. When the union of digits already placed in its row, column, and box accounts for eight of the nine possible values, only one value satisfies all three constraints at once. This is a direct consequence of constraint intersection: each unit independently forbids certain digits, and the intersection of all permitted sets yields a single element, making the placement logically necessary.
When to use: After pencil marking an area, look for any cell whose candidate list has been reduced to a single digit. That cell can be solved immediately.
Common Mistakes to Avoid
Confusing Naked Singles with Last Remaining Cell. Naked Singles come from three-unit constraint intersection, not from a unit having one empty cell.
Ask yourself: am I checking that this cell has one candidate (Naked Single) or that this unit has one empty cell (Last Remaining Cell)?
Forgetting to check the 3x3 box constraints and only looking at the row and column, leaving extra false candidates.
Always check all three units — row, column, and box — before concluding that a cell has a single candidate.
Not re-scanning for new Naked Singles after placing a digit, missing a chain reaction of easy placements.
Each time you place a digit, re-examine cells in the same row, column, and box — a new Naked Single may have just appeared.
More Examples
See naked singles applied in different puzzle configurations to strengthen your pattern recognition.
Highlighted cells show the naked singles pattern
Practice Puzzles
Apply the naked singles technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- A cell has only one candidate in its pencilmarks
- Action:
- Place that candidate as the cell's value
- Look for:
- Cells with a single pencilmark remaining