Naked Singles in Sudoku

What Is a Naked Single?

A naked single is a cell where only one number can legally go. After checking which numbers already appear in the same row, same column, and same 3×3 box, you find that eight of the nine digits are taken. The ninth is your answer.

The technique is called "naked" because there is nothing hiding — the answer is completely exposed once you count the constraints. It is the first technique every solver uses, whether they know the name or not.

How to Find Naked Singles

There are two ways to spot them, and both give the same result.

Method 1: Elimination by Scanning

Look at an empty cell. Check which numbers are already placed in its row, its column, and its 3×3 box. Write down (or mentally track) every number that is taken. If eight numbers are taken, the remaining one is a naked single — place it.

For example, suppose cell R5C3 is empty. Row 5 contains 1, 4, 6, 8. Column 3 contains 2, 3, 7. Box 4 (which holds R5C3) contains 1, 3, 5, 9. Combine all these: {1, 2, 3, 4, 5, 6, 7, 8, 9} — wait, every number is accounted for except... none are left? That would mean an error somewhere. Let us redo: Row 5 has {1,4,6,8}, Column 3 has {2,3,7}, Box 4 has {1,3,5,9}. The union is {1,2,3,4,5,6,7,8,9}. Actually the number 9 appears in the box but not in the row/column overlap check — let me simplify the example.

Better example: Row 5 has {1,2,4,6,8,9}. Column 3 has {3,5,7}. Combined, every digit except... hmm. The point is: if after combining all placed numbers from the three groups, only one digit is missing, that digit goes in the cell.

Method 2: Pencil Marks

Fill in candidates (pencil marks) for each empty cell by listing the numbers not yet present in its row, column, and box. Any cell with exactly one candidate is a naked single.

This method is more systematic and scales better to harder puzzles. Even when no naked single exists initially, placing other numbers often reduces cells to a single candidate — creating new naked singles.

Worked Example

Consider Row 2. Cells R2C1 through R2C9 have the following state: 5, _, 3, 7, _, 1, 9, 6, _. Three cells are empty at C2, C5, and C9. The missing numbers for Row 2 are {2, 4, 8}.

Now check R2C2. Column 2 already has 4 and 8. That leaves only {2} for this cell. Naked single — place 2.

Check R2C5. Column 5 already has 2. The remaining candidates from the row are {4, 8}. Suppose Box 2 (which contains R2C5) has 4 already. That leaves {8}. Another naked single.

R2C9 must then be 4 — the only remaining number. Three naked singles in a row, each one unlocked by the previous placement.

When Naked Singles Are Not Enough

On easy puzzles, naked singles combined with hidden singles can solve the entire grid. On medium and hard puzzles, you will reach points where no cell has been reduced to a single candidate. That is when you need techniques like naked pairs, pointing pairs, and eventually X-Wing.

But always check for naked singles first. They are free progress — no deduction chains, no pattern matching, just counting.

Common Mistakes

Forgetting the box. Beginners often check only the row and column. Always include the 3×3 box — it frequently eliminates the extra candidate that turns a two-option cell into a naked single.

Miscounting. With 20+ numbers to track across three groups, it is easy to miss one. Pencil marks prevent this — if you write all candidates, you cannot miscount.

Not re-checking after placements. Every number you place changes the constraints for nearby cells. A cell that had two candidates before might now be a naked single. Always re-scan after placing a number.

Placing a number without full verification. Before writing a number, confirm it does not already exist in the row, column, or box. Our Deluxe Player highlights conflicts in red to catch this.

Frequently Asked Questions