Naked singles and hidden singles explained

1 September 2026 · 7 min read

Singles are the only technique in Sudoku that actually writes a digit into the grid. Every other pattern — pairs, triples, X-wings — only removes candidates. They are useful because removing enough candidates creates a single. So however advanced your repertoire gets, the move that finishes the job is always one of these two.

They are also constantly confused with each other, which matters because they are found by looking at the board in opposite directions. If you have not played much Sudoku at all, start with the beginner’s guide — it covers the rules and the vocabulary this article assumes.

The difference in one line

• A naked single answers “what can go in this cell?” — and only one digit can.
• A hidden single answers “where can this digit go in this unit?” — and only one cell can hold it.

Naked singles are a property of a cell. Hidden singles are a property of a unit. That is the whole distinction, and it is why one is easy to see and the other is not.

Naked singles

A cell has a naked single when eight of the nine digits already appear among its peers — its row, its column and its box. The ninth is forced.

Below, look at row 3, column 7. Its row already holds 3, 1, 4 and 9. Its column holds 6 and 5. Its box holds 6, 5 and 9. Chase all three and everything except 2 is accounted for.

Nothing about that cell looks special from a distance, which is why the practical advice is not “look for naked singles” but “look at the cells with the most filled peers”. A cell in a nearly-complete box, on a nearly-complete row, is where they live. A cell in an empty corner of the grid will not have one.

If you keep pencil marks, naked singles find themselves: a cell with one mark left is one, by definition. That is the main reason marking up pays off.

Hidden singles

Now the other direction. Take a unit — a box is easiest — and a digit that unit is missing. Cross off every empty cell in it that already sees that digit somewhere along its row or column. If exactly one cell survives, the digit must go there, because the unit has to contain it somewhere.

In the grid below, look at the middle-right box (rows 4 to 6, columns 7 to 9). It has no 3 yet, and six empty cells. There is a 3 in row 3, column 7 — which knocks out the whole of column 7 inside the box. There is another 3 in row 9, column 8 — which knocks out column 8. That leaves exactly one cell: row 6, column 9.

Here is the part that catches people out: that cell still has other candidates. It is not down to one option. Looked at as a cell, it is unremarkable — you could stare straight at it while hunting naked singles and see nothing. The information lives in the box, not the cell.

Which is why the hidden single is the first real skill in Sudoku. Getting good at Sudoku is largely getting fast at these.

How to hunt hidden singles systematically

Wandering the grid does not work. Two orderings do, and it is worth having both:

1. By digit. Pick a digit, ideally one already placed six or seven times. Walk all nine boxes and check each one that is missing it. This is the faster sweep, because a heavily-placed digit constrains a lot of lines at once.
2. By unit. Pick the emptiest-looking box with the most surrounding digits, and try each missing digit in turn. Slower, but it catches what the digit sweep misses.

Boxes before rows and columns, in both cases. A box is three-by-three and you can hold it in your head; a row spans the width of the grid and your eye has to travel. This app’s Explain next step checks in the same order for the same reason — boxes first, then rows, then columns — so the explanation you get names the unit you would most plausibly have looked at.

Why hidden singles are harder — and how to make them easier

A naked single is visible from the cell. A hidden single requires you to hold a digit and a unit in mind at once and check up to nine cells against two lines each. That is genuinely more working memory.

Full pencil marks collapse the difference. Once every empty cell carries its candidates, a hidden single is just “this digit appears exactly once among the marks in this unit”, which is a counting job rather than a reasoning job. The trade is the time spent marking up, so the usual advice holds: mark up when scanning stops paying, not before.

The single that isn’t there

Two traps are worth naming, because both produce a wrong digit that feels right.

• Checking one line and stopping. “3 can’t be in these two cells because of column 7, so it goes in the third” — but you never checked whether the third cell was ruled out by its own row. A hidden single needs all other cells eliminated, not most of them.
• Stale pencil marks. A cell showing one mark is only a naked single if the marks are current. If you placed three digits since you last updated them, that single may be a leftover. This is the most common way a solve goes wrong.

When singles run out

On Easy and Medium puzzles they never really do. On Hard and above there comes a point where a full sweep finds nothing — and that is not a wall, it is a signal. It means the next move needs a technique that removes candidates so that a single can appear.

The cheapest of those, in the order worth trying them: naked pairs, then pointing pairs and box/line reduction, then hidden pairs. Each one deletes candidates; you then go back and sweep for singles again. That loop — eliminate, sweep, eliminate, sweep — is what solving a hard Sudoku actually consists of.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.