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Naked singles

A naked single is a cell with only one possible digit left. Learn how to spot one by checking its row, column and box together.

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A real example from a sudoku.ie puzzle. The only number that fits in row 6, column 1 is 3. Every other number already appears in its row, column or box. Yellow cells make the pattern. Green shows the number you can write in.

What it is

A naked single is an empty cell where only one digit is possible. Every other digit from 1 to 9 is already used somewhere in that cell’s row, column or box. So the one digit left over must go in the cell.

It is called “naked” because, once you have your notes written in, the answer is sitting there in plain sight: a cell with a single candidate. It is one of the two kinds of single, along with the hidden single, and between them they solve every Easy puzzle.

How to spot it

Look for cells that are crowded in. A cell whose row, column and box are all nearly full is a strong candidate. Good places to check:

  • a row or column with only two or three empty cells,
  • the cells where a busy row crosses a busy column,
  • a box with only a few gaps.

If you keep pencil marks, naked singles are easy to find: any cell with one note left is a naked single. Without notes, you need to count the digits that a cell can “see” across its row, column and box.

A worked example

Look at the cell at row 4, column 7. It sits in box 6, which covers rows 4 to 6 and columns 7 to 9.

  • Row 4 already contains 1, 2, 5 and 9.
  • Column 7 already contains 3, 6 and 8.
  • Box 6 already contains 2, 4 and 9.

Now list every digit the cell can see: 1, 2, 3, 4, 5, 6, 8 and 9. Some of them appear twice (the 2 and the 9 are in both row 4 and box 6), but that does not matter. What matters is that eight different digits are ruled out.

The only digit missing from that list is 7. So row 4, column 7 must be 7.

A tip for counting: run through 1 to 9 in order and ask, for each one, “can this cell see it?” Saying them in order stops you skipping one.

Why it matters after every move

Each time you place a digit, the cells around it lose a candidate. A cell that had two options a moment ago might now have one. So whenever you fill a cell, glance along its row, down its column and around its box. That is where new naked singles appear. Following this chain of placements is often how a whole puzzle unravels.

A common mistake

The usual slip is checking only the row and column and forgetting the box. In the example above, the 4 is only in box 6. If you missed the box, you would think 4 and 7 were both possible and walk past an easy placement. Worse, if you missed a digit and wrote in the wrong one, the error might not show up for many moves.

Another mistake is trusting old notes. If you placed a digit nearby and did not update the notes, a cell might look like it has two candidates when it really has one, or one when it really has none left. Keep your notes up to date.

When you will need it

Naked singles are one of the two techniques used on Easy puzzles on sudoku.ie (Monday’s daily is Easy). They appear on every puzzle at every level, and even the hardest Expert grid finishes with a run of them. Once you can spot naked singles reliably, move on to hidden singles.