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Sudoku technique

Naked singles

The first technique, and the only one you can find without writing anything down. A cell with one candidate left is solved — the skill is in noticing that a cell has got there.

What a naked single is

A naked single is an empty cell with exactly one candidate left. Its row, its column and its box between them have ruled out eight of the nine digits, so the ninth is forced.

It is the most basic deduction in Sudoku and the one every solver finds on their own within a few boards. It is worth naming anyway, because the difference between a beginner and a fast solver is not whether they can spot one — it is whether they look in the right places for them.

Naked and hidden

The pair of terms confuses people, and the distinction is simple once said plainly.

Naked describes what you can see from the cell: this cell has one option. Hidden describes what you can see from the unit: this digit has one home. Both place a digit; they are two directions of the same question, and hidden singles are the harder and more valuable of the two precisely because the cell gives nothing away.

Where they appear

Naked singles cluster where the board is already dense. A box with seven digits in it, or a row crossed by two nearly-full columns, is where to look — not the empty quadrant that happens to be bothering you.

Every digit you place creates more of them, which is why solving a board feels like it accelerates. One placement removes a candidate from twenty other cells, and some of those cells were sitting on two.

2
7
6
3
7
7
1
7
6
8
1
5
2
8
4
2
5
7
8
2
3
4
9
2
3
8
6
8
4
1

Step 1 of 4

A real position

A genuine grid with a handful of digits placed. Somewhere in here is a cell that has already been decided without anyone deciding it.

A real position from a generated puzzle. Every elimination shown here was checked against that puzzle's actual solution.

The last free cell

The easiest naked single of all is a unit with one empty cell in it: eight digits present, one missing, no thought required. On an easy board, sweeping for rows, columns and boxes with a single gap will solve a surprising share of the grid before you have done anything that deserves to be called a technique.

When to stop looking for them

On easy and medium boards, naked and hidden singles are usually the entire solve. On harder grids they run out — and the moment they do is the moment to start writing candidates and looking for naked pairs, which do not place anything but create the singles that do.

One habit is worth building early: after every placement, glance at the twenty cells that just lost a candidate. That is where the next naked single almost always is, and it is far faster than starting a fresh sweep of the grid.

Other techniques

Try it on a real board

The free board on the home page has a notes mode, which is what every technique past hidden singles needs. Then take the same eye into a live match.