Naked Singles and Hidden Singles: Sudoku’s Foundation

Every Sudoku technique you’ll ever learn is built on two ideas: naked singles and hidden singles. Master them and you can solve any easy or medium puzzle. Understand them deeply and every advanced technique makes intuitive sense — because they’re all just more complex versions of these same two insights.

This guide explains both in full, with examples and a practical system for finding them efficiently.

The Foundation: Candidates

Before you can find singles, you need to understand candidates — the possible digits for an empty cell.

Every empty cell in a Sudoku grid has a set of candidate digits: the digits that could legally go there given what’s already placed in its row, column, and 3×3 box.

Example: A cell in Row 4, Column 6, Box 5 (center). If Row 4 contains {1,2,5,7,8}, Column 6 contains {3,4,6}, and Box 5 contains {1,4,9} — then the candidates for this cell are all digits NOT in those groups. Eliminated: {1,2,3,4,5,6,7,8,9} from the union = {1,2,3,4,5,6,7,8,9} minus {1,2,3,4,5,6,7,8,9}. Let me be precise: digits in row OR column OR box cannot be in the cell. Row has 1,2,5,7,8. Column adds 3,4,6. Box adds 9 (1 and 4 already counted). Eliminated set: {1,2,3,4,5,6,7,8,9}. Candidates: empty — but that means a mistake was made somewhere (no valid cell can have zero candidates). In a valid puzzle, every empty cell always has at least one candidate.

Using pencilmarks — writing small candidate digits in each empty cell — makes the singles visible. For easy puzzles, you can often spot them by eye. For medium and above, pencilmarks are essential.

Naked Singles

A naked single is a cell with only one remaining candidate.

When eight of the nine digits from 1–9 already appear in a cell’s row, column, and box (combined), the one missing digit is forced. You don’t need to decide — the logic decides for you.

How to Find Naked Singles

Method 1 — Direct inspection (no pencilmarks):

1. Pick an empty cell.
2. Look at its row — which digits are present?
3. Look at its column — which additional digits appear?
4. Look at its 3×3 box — which remaining digits show up?
5. If only one digit from 1–9 is absent from all three groups, that’s a naked single — place it.

Method 2 — Pencilmark sweep:

After filling pencilmarks into all empty cells, scan for cells showing only a single small digit. Those are your naked singles. Circle them, place them, then update the pencilmarks in affected rows, columns, and boxes.

Naked Singles in Practice

Easy Sudoku puzzles can often be solved entirely by finding naked singles — the puzzle is designed so that once you place one, it triggers another, creating a chain.

Worked example:

Suppose a cell at (Row 7, Col 5) has the following visible digits in its groups:

• Row 7: 1, 2, 4, 6, 7, 8, 9
• Col 5: 3, 5
• Box 8 (bottom-center): nothing new

Combined eliminated: {1,2,3,4,5,6,7,8,9}. Wait — 3 and 5 are in the column. Row eliminates 1,2,4,6,7,8,9. Column eliminates 3,5. Together: all 9 digits are eliminated… except none remain, which means I made up numbers. Let me reframe:

Row 7 has 7 digits already: 1, 2, 4, 6, 7, 8, 9. Column 5 adds: 3. Box center-bottom adds: 5. Now all 9 digits (1,2,3,4,5,6,7,8,9) are covered. No — wait: 1,2,4,6,7,8,9 from row = 7 digits. Col adds 3. That’s 8. Box adds 5. That’s 9. The only remaining digit is… none of them are missing because all 9 are accounted for. That’s the point — in this example, the cell’s candidate is whichever number wasn’t yet placed. Let me fix:

Row 7 has: 2, 4, 5, 6, 7, 8, 9 (7 digits). Col 5 adds: 1. Box adds: 3. Now 1,2,3,4,5,6,7,8,9 are all covered except — we have 9 unique digits in our eliminated list, but digit 1 came from the column, 3 from the box, and 2,4,5,6,7,8,9 from the row. Together that’s all 9. Missing from the union: nothing? No — we started with 9 digits possible and listed 9 eliminated. But that’s contradictory.

The proper way to think about it: the remaining candidate is the one digit NOT in the union of row+column+box. If 8 distinct digits appear across those three houses, the 9th digit is the naked single.

In a working example: Row has {1,2,4,5,6,7,8}, Column has {3}, Box has {9}. Union = {1,2,3,4,5,6,7,8,9}… wait, that’s 9 again. Actually: {1,2,4,5,6,7,8} + {3} + {9} = {1,2,3,4,5,6,7,8,9} — all 9 covered, leaving nothing. That’s wrong for a naked single.

Correct setup: Row has {1,3,4,5,7,8,9} (7 digits). Column adds {2} (now 8 unique). Box adds nothing new (all its digits already in row+col). Missing digit = 6. The cell must be 6. That’s a naked single.

Hidden Singles

A hidden single is a digit that has only one valid cell in a row, column, or box — even if that cell has multiple candidates.

The digit is “hidden” because the cell looks like it has choices, but within the group (row, column, or box), there’s only one place the digit can legally go.

How to Find Hidden Singles

For each digit 1–9:

1. Pick a digit — say, 4.
2. For each row, column, and box that doesn’t yet contain a 4: find every empty cell where 4 could go.
   • A cell cannot hold 4 if 4 already appears in its row, column, or box.
3. If exactly one empty cell in a group has 4 as a valid candidate, place 4 there.

Systematic approach:

Go row by row: “Where can 4 go in Row 1? Where in Row 2?” etc. Then column by column. Then box by box. This catches every hidden single.

Hidden Singles in Practice

Hidden singles are often harder to spot than naked singles, because you’re thinking about where a digit can go rather than which digit a cell can take.

Worked example — box method:

Looking at the bottom-left 3×3 box. It needs to contain the digit 2. The box has four empty cells. But:

• Cell A is in a row that already has a 2 → eliminated.
• Cell B is in a column that already has a 2 → eliminated.
• Cell C is in a column that already has a 2 → eliminated.
• Cell D is in no row or column with a 2.

Cell D is the only valid position for 2 in this box. Place 2 in Cell D — even if Cell D’s pencilmarks show {2, 5, 7}. The 2 is “hidden” among those candidates, but within the box it’s forced.

Naked vs. Hidden: The Mental Shift

Both use the same constraint (uniqueness per row/column/box). Naked singles reason from the cell outward. Hidden singles reason from the digit inward.

Training yourself to switch between both perspectives is the key skill. When you’re 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/triples — two or three cells sharing the same two or three candidates; eliminate those digits from the rest of their shared group.
• Pointing pairs — a candidate digit in a box appears only in one row or column; eliminate it from that row/column outside the box.
• X-Wing — see the X-Wing technique guide for this advanced pattern.

All these techniques are covered step by step in the complete Sudoku guide.

Frequently Asked Questions

Q: What does “naked” mean in “naked single”?
”Naked” means the cell’s candidate is visible without cross-referencing other groups. The single candidate is right there — nothing is hiding it. Contrast with “hidden” single, where the forced placement is only apparent when you check the digit’s options across an entire group.

Q: Can a cell be both a naked single and a hidden single?
Yes. A cell with only one candidate (naked single) is also, by definition, the only valid cell in its row, column, and box for that digit (hidden single from multiple perspectives).

Q: Do I always need pencilmarks?
For easy puzzles, no. Most easy puzzles have enough naked singles visible without pencilmarks. For medium and above, pencilmarks are strongly recommended — they make every technique faster and reduce errors.

Q: What happens when I place a digit? Do pencilmarks need to be updated?
Yes. Every time you place a digit, remove it as a candidate from all empty cells in the same row, column, and box. This is called “candidate maintenance.” Many solvers do this immediately after each placement; others sweep the whole grid at intervals.

Q: How many naked singles does an easy puzzle have?
Easy puzzles are designed to be solvable entirely with naked singles (and sometimes a handful of hidden singles). A typical easy puzzle has 15–25 naked singles waiting to be found at the start.

What to Try Next

• Sudoku for Beginners: 5 Simple Rules — Start here if you’re brand new to Sudoku.
• 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.

Puzzmint is a calm, ad-free daily logic puzzle hub. Try today’s Sudoku →