Naked single and hidden single: the two moves behind every sudoku

Every number you write in a sudoku is forced by some reasoning. The simplest kinds of reasoning, the ones that solve an easy sudoku all on their own, are two, and they're called singles: the hidden single and the naked single. They look alike, but they look at the grid from two opposite sides. Knowing how to tell them apart helps you find moves you didn't see before.

The hidden single: one number, one place

You start from a number and a unit (a row, a column or a box). The number has to go in the unit, but all its cells except one are ruled out: the number goes in the only one left. It's what you find with scanning.

It's called “hidden” because the cell, on its own, could also hold other numbers: it's the number that has no alternatives, not the cell.

The naked single: one cell, one number

Here you start from an empty cell. Look at all the numbers already in its row, its column and its box. If together they make eight different numbers, only one is left for the cell: the one that's missing.

It's “naked” because it's out in the open: if you write notes, the cell has just one candidate.

And the last free cell

There's also a case simpler than all the others: a unit that's missing just one number. It's called a full house. It's a naked single and a hidden single at once, and it's worth looking for first, because you see it right away.

Which one to look for first

The two singles are looked for in different ways:

	Hidden single	Naked single
You start from	a number	a cell
You look at	where the number can't go	which numbers the cell can't have
You find it with	scanning, by eye	checking the row, column and box
In easy sudoku	it's the most frequent	it comes up when scanning stops

The practical advice: scan all the numbers until you find something. When that stops working, go through the cells with the most numbers around them, that is, the ones in the fullest rows, columns and boxes: that's where naked singles hide.

With pencil marks

If you use notes, the two singles become easy to read:

• a naked single is a cell with a single note;
• a hidden single is a number that, in the notes of a row, a column or a box, appears only once.

The second is easier to miss, because the cell also has other notes. Get used to going through the units number by number.

How far they take you

On Sudokumania a sudoku is easy precisely when it can be solved with singles alone: our solver checks it for every puzzle. In medium and hard ones the singles are still most of the moves, but every now and then you need techniques that remove candidates without writing numbers, and we show them in the next guides.