A naked single is the simplest move in sudoku, and most easy puzzles are nothing but naked singles from start to finish. If you've ever solved a sudoku without writing anything down, you were finding naked singles.
The definition
A naked single is a cell where eight of the nine possible digits are already in its row, column, or 3×3 box. That leaves exactly one digit that can go there. You place it and move on.
That's it. No pencil marks needed, no clever pattern matching. Just the realisation that for this one cell, every digit except one is ruled out.
How to find them quickly
New solvers look at one cell at a time and check every digit. That works, but it's slow. A faster method:
- Pick a cell that has lots of givens in its row, column, and box. Corner cells in a heavily-populated 3×3 box are good candidates.
- Mentally list which digits are already in the row. Then the column. Then the box. Combine them.
- If your combined list has eight digits, the cell is a naked single. The missing one goes there.
After a few games you'll do this in your head in a second or two. Don't write the candidates down for easy puzzles. it's overkill and slows you down.
A worked example
Imagine the cell at row 1, column 1. Row 1 already contains the digits 2, 4, 5, and 9. Column 1 contains 3 and 6. The top-left 3×3 box also contains 7 and 8 (in cells other than r1c1).
Add it up: 2, 3, 4, 5, 6, 7, 8, 9. Eight different digits, all of them off-limits for r1c1. The only one left is 1. Place it.
Now look around. The 1 you just placed eliminates 1 from the rest of row 1, column 1, and the top-left box. Often that creates another naked single nearby. Easy sudokus solve in a cascade like this. one placement opens the next.
When to look for them
After every placement. Always.
Every time you fill in a cell, the cells that can see it have one fewer candidate. If any of them was already down to two candidates, it's now a naked single. Don't move on until you've checked.
On easy puzzles you'll find naked singles for the whole solve. On medium and harder, they thin out, and you'll start needing hidden singles and pencil marks. But even at expert level, every chain of advanced moves usually ends with a naked single placement. They never go away.
Common mistakes
Forgetting the box. Beginners check row and column and skip the box. The box rules out three more digits on average, and often it's the box constraint that makes a cell a naked single. Always include it.
Stopping too soon. You found one naked single. Did you check whether placing it created another? Look at every cell in the newly-placed digit's row, column, and box before scanning elsewhere.
Pencil-marking when you don't need to. If a puzzle is full of naked singles, you don't need pencil marks. They're just cognitive overhead. Save them for puzzles where they actually unlock moves.
Why this is the foundation
Every other sudoku technique exists to create naked singles. Hidden singles place a digit, which generates new naked singles. Pointing pairs eliminate candidates, eventually leaving some cell with one candidate. a naked single. X-wing, swordfish, all of it, the same story.
Get fast at spotting naked singles and the rest of the game becomes easier. It's the same as drilling scales before playing music.
Practise it
The best practice for naked singles is easy sudoku. Easy puzzles are designed so that every move is either a naked single or a hidden single. Spend a week solving easy puzzles without writing pencil marks. By the end of the week, you'll spot most naked singles in under a second.
Once that feels automatic, move to medium and the same skill will save you from reaching for pencil marks too early.