Sudoku
Guide
English

Basic Techniques: Singles

Hidden singles and naked singles. Easy and Medium puzzles need nothing else.

On this page
  1. One idea first
  2. Hidden single
  3. Naked single
  4. When to start taking notes
  5. Next steps

One idea first

Every solving technique answers one of two questions: what can go in this cell? Where can this number go? Singles are the two most basic answers:

  • Start from a number: if a number has only one place left in a row, column or box, that is a hidden single.
  • Start from a cell: if a cell has only one possible number left, that is a naked single.

Hidden single

Look at one number at a time, say 7. For each box, ask: "Where can the 7 go in this box?" Every 7 outside the box crosses out its row and column. If only one cell in the box is left, it must be 7.

1122334455667788994327973984429323914943817846282635349
Look at box 4: once the 2s outside the box cross out their rows and columns, only the highlighted cell can hold 2.

The same idea works for a row or column: if the 7 in a row has only one cell left, place it. Boxes are the easiest place to spot this, though, which is why the in-game hints look at boxes first.

Scanning order

  1. Start with the number that appears most often on the grid. It has the fewest places left, so it is the easiest to find.
  2. Sweep one number through all nine boxes. Each time you place one, sweep again, because the new number crosses out more cells.
  3. When a number gives you nothing more, move on to the next.

Naked single

Now start from an empty cell instead: list the numbers already present in its row, column and box. If eight of the nine numbers are there, the missing one is the answer.

1122334455667788992964395948316512895618456251412571263
Look at row 3, column 4: its row, column and box already contain the other eight numbers, so only 8 fits.

The more numbers are filled in, the more naked singles appear. That is why the second half of a puzzle often goes cell after cell.

When to start taking notes

Easy puzzles rarely need notes; scanning is enough. In Medium puzzles the singles are better hidden. When scanning finds nothing, you can:

  1. Pick the row, column or box with the fewest empty cells and write the possible numbers of each cell as notes.
  2. Look for a cell with only one note left (a naked single), or a number that appears in the notes of only one cell in that area (a hidden single).

"Auto notes" does it all in one go. From Hard upward you will always need notes: every technique on the next page works by removing them.

Next steps

Up nextIntermediate Techniques: Boxes and Pairs →
Play nowBack to the guide