Singles
Singles are the bread and butter of Sudoku solving. Every Sudoku puzzle relies on singles — they're the foundation of all solving techniques.
What is a Single?
A single is when a cell has exactly one possible number. There are two types:
- Naked Single: A cell with only one candidate remaining
- Hidden Single: A cell that's the only place for a number in its row, column, or box
Both result in placing a number, but you find them differently.
Naked Singles
A naked single occurs when a cell has only one possible candidate.
Visual Example
How we know A4 must be 9:
- The box already has: 1, 2, 3, 4, 5, 6, 7, 8
- Only 9 is missing from the box!
- Therefore, A4 = 9
How to Find Naked Singles
- Look at an empty cell
- Check its row — which numbers are already placed?
- Check its column — which numbers are there?
- Check its box — which numbers exist?
- If only one number remains possible, that's a naked single!
With Pencil Marks
When you've filled in candidate notes, naked singles are easy to spot:
Any cell with only one candidate is a naked single. Place that number!
Hidden Singles
A hidden single occurs when a number can only go in one cell within a row, column, or box — even if that cell has multiple candidates.
Visual Example
What's happening:
- This row needs a 7 somewhere
- Check each empty cell: can it hold 7?
- Only cell F has 7 as a candidate
- So 7 MUST go in cell F!
The Hidden Part
The single is "hidden" because the cell has other candidates (2, 4, 8). You discover it by asking:
"Where can 7 go in this row?"
Instead of:
"What can go in this cell?"
Hidden Single in a Box
Finding it:
- This box needs a 3
- Check each empty cell: can it hold 3?
- Cells A, C, G: only have 1,4,7 or 5,7 — no 3!
- Cell D: has 3,5,7 — 3 is here!
- So 3 MUST go in cell D
Naked vs. Hidden: The Difference
| Aspect | Naked Single | Hidden Single |
|---|---|---|
| Definition | One candidate in the cell | One cell for the number in a unit |
| How to find | "What can go here?" | "Where can this number go?" |
| With notes | Cell has one candidate | Number appears in one cell |
| Visibility | Easy to see | Requires checking |
Example:
Finding Hidden Singles: Method
Row Scanning
- Pick a number (start with 1)
- Look at each row
- Find which cells can hold that number
- If only one cell works, place it there
- Repeat for 2, 3, 4, ... 9
Column Scanning
Same process, but for columns:
- Pick a number
- For each column, find where it can go
- If only one cell works, place it
Box Scanning
Same process for 3x3 boxes:
- Pick a number
- Check each box
- Find the only cell that can hold it
Systematic Approach
For efficient solving:
- Scan for hidden singles (each number 1-9)
- Check for naked singles (cells with few candidates)
- Repeat after each placement — new singles often appear!
Practice: Find the Singles
Exercise 1: Find the naked single
Answer
No naked singles here — all empty cells have multiple candidates.
But check for hidden singles:
- 1: cells D, G, I — not unique
- 3: cells D, G only
- 5: cells D, G, I — not unique
Hidden single on 3: Actually, 3 appears in D and G, so no hidden single on 3 either.
This row needs information from columns or boxes to make progress!
Exercise 2: Find the hidden single
Answer
Check where each missing digit can go:
- 1: cells A1, A4 — appears in 2 cells
- 2: cells A1, B1, A4, B7 — appears in 4 cells
- 3: cells A1, B1, A4, B7 — appears in 4 cells
- 5: cells A1, B1, A4 — appears in 3 cells
Hidden single on 1! Looking at the candidates:
- A1 has [1,2,3,5]
- A4 has [1,3,5]
Only cells A1 and A4 can hold a 1 in this box. That's 2 cells, not 1... so no hidden single on 1.
But wait — check the columns too. If column A already has a 1 in another row outside this box, then only one of A1 or A4 could have 1!
Key insight: This exercise shows that hidden singles often require checking row/column constraints outside the box. In a real puzzle, additional constraints would narrow it down further.
Common Mistakes
Mistake 1: Missing row/column/box constraints
Always check ALL THREE constraints for naked singles. A number might seem possible until you check all of them.
Mistake 2: Stopping too early
After placing a single, immediately check for new singles created by that placement.
Mistake 3: Overlooking hidden singles
If you're stuck, systematically check where each number 1-9 can go. Hidden singles are often missed!
Mistake 4: Not updating candidates
When you place a number, remove it from candidates in the same row, column, and box.
Priority: When to Use Singles
Singles should be your first technique — always!
- Before anything else — check for singles
- After any elimination — check for new singles
- When stuck — systematically scan for hidden singles
- Easy puzzles — rely almost entirely on singles
Quick Reference
Naked single:
- Cell has only one candidate
- Place that number directly
- Found by checking what CAN go in a cell
Hidden single:
- Number can only go in one cell of a unit
- Place it in that cell (ignore other candidates)
- Found by checking WHERE a number can go
Systematic finding:
- For each unit (row, column, box)
- For each number 1-9
- Count cells where it can go
- If exactly one cell → place it!
What's Next?
Once you've mastered singles:
- Naked Pairs — Two cells claiming two candidates
- Hidden Pairs — Two candidates restricted to two cells
- Pointing Pairs — Box/line intersection techniques