Naked Singles and Hidden Singles: Sudoku’s Foundation
Every Sudoku technique builds on two ideas: naked singles and hidden singles. Master them and you can solve any easy puzzle and make real progress on medium ones.
Candidates: The Starting Point
Every empty cell has a set of candidates — the digits from 1–9 that could legally go there.
A digit cannot be a candidate if it already appears in the cell’s row, column, or 3×3 box.
Example: A cell in Row 3, Column 7 shares a row with 1, 4, 5, 8 and a column with 2, 7, 9. Together those constraints eliminate seven digits, leaving 3 and 6 as candidates — write both as pencilmarks in the cell. You cannot place either digit yet. When further eliminations reduce any cell’s candidates to exactly one digit, that cell is a naked single — the technique defined in the next section.
Writing small candidate digits in each empty cell (called pencilmarks) makes the techniques below visible and fast.
Naked Singles
A naked single is a cell with only one candidate left.
When eight of the nine digits already appear somewhere in that cell’s row, column, and box, the one remaining digit is forced — there is no choice.
How to Find Naked Singles
Without pencilmarks:
- Pick an empty cell.
- Look at its row, column, and box.
- Count which digits from 1–9 are missing from all three combined.
- If only one digit is missing, place it.
With pencilmarks: After writing candidates in every empty cell, scan for any cell that shows only a single digit. That is your naked single — place it and update the surrounding pencilmarks.
Worked Example
Look at the blue target cell below (Row 5, Column 5). Three separate checks eliminate every candidate but one:
- Row 5: R5C1 holds 1, R5C7 holds 7, and R5C9 holds 3 → eliminate 1, 3, and 7
- Column 5: R1C5 holds 4 and R9C5 holds 9 → eliminate 4 and 9
- Center box: R4C4 holds 2, R6C4 holds 8, R6C6 holds 6 → eliminate 2, 6, and 8
With all constraints applied, only 5 remains. Place it in R5C5.
Easy Sudoku puzzles are often solved entirely this way. One naked single placement triggers the next, creating a chain.
Hidden Singles
A hidden single is a digit that can only go in one cell within a row, column, or box — even if that cell has other candidates too.
The digit is “hidden” because the cell looks like it has choices. But when you look at the whole group (row, column, or box), only one cell can take that digit.
How to Find Hidden Singles
Pick a digit — say, 4. For each row, column, and box that does not yet have a 4:
- Go through every empty cell in that group.
- Cross off any cell whose row or column already contains a 4.
- If only one cell remains, place 4 there.
Worked Example
Look at the top-left 3×3 box in the grid below. We need to place the digit 4.
- Cells in rows that already have a 4 are blocked (red ✕).
- Cells in columns that already have a 4 are also blocked (red ✕).
- Only one cell in the box has no 4 in its row or column — Row 2, Column 3 — that cell must be 4.
Naked vs. Hidden: The Key Difference
| Technique | Question you ask | How you think |
|---|---|---|
| Naked single | ”What digit must this cell be?” | Start from the cell |
| Hidden single | ”Where must this digit go?” | Start from the digit |
Both use the same rule: every digit appears exactly once in each row, column, and box.
Training yourself to switch between these two questions is the main skill. When you are stuck, change your question from “what goes here?” to “where does 4 go?”
After Singles: What Comes Next
Once naked and hidden singles are exhausted, look for:
- Naked pairs — two cells in the same group that share the same two candidates. Those two digits can be removed from all other cells in the group.
- Hidden pairs — two digits confined to the same two cells in a group, even if those cells still show other candidates. See the hidden pairs guide.
- Pointing pairs — a candidate digit appears only in one row or column within a box. Remove it from that row/column outside the box.
- X-Wing — see the X-Wing technique guide.
All these techniques are covered in the complete Sudoku guide.
Frequently Asked Questions
Q: What does “naked” mean in “naked single”?
It means the answer is right there in the cell — nothing is hiding it. The one remaining candidate is visible without cross-referencing other groups.
Q: Can a cell be both a naked single and a hidden single?
Yes. A cell with only one candidate is automatically the only valid cell for that digit in its row, column, and box — so it qualifies as both at once.
Q: Do I always need pencilmarks?
For easy puzzles, no. Most easy puzzles have naked singles visible by eye. For medium and above, pencilmarks are strongly recommended.
Q: What happens when I place a digit?
Remove it as a candidate from every empty cell in the same row, column, and box. Do this right away after each placement.
Q: How many naked singles does an easy puzzle have?
A typical easy puzzle has 15–25 naked singles waiting at the start.
What to Try Next
- Sudoku for Beginners: 5 Simple Rules — Start here if you are brand new to Sudoku.
- Sudoku Hidden Pairs: A Worked Example — The natural next step after singles, worked cell-by-cell.
- How to Solve Sudoku: Complete Guide — Intermediate and advanced techniques beyond singles.
- The X-Wing Technique Explained — The first advanced pattern to learn after mastering singles.
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