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Sudoku Naked Singles: The Only Digit Left for a Cell

A naked single is a cell that has only one possible digit left. Its row, column and box between them already hold every other digit, or your notes have ruled the others out. Put that digit in. Easy puzzles never need it, but on Hard puzzles it’s the second most important technique there is.

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This is the second of the Sudoku techniques. The how to solve page calls it “the only digit for a cell”.

The rule

  1. Choose an empty cell.
  2. List the digits in its row, its column and its box (20 cells in all).
  3. If eight different digits are there, the ninth goes in the cell.

With notes, it’s simpler still: when a cell’s notes are down to one digit, that’s the digit.

The only digit for row 8, column 8 A hard puzzle part-way through. No digit has only one place left anywhere, but row 8, column 8 already sees 1, 2, 3, 4, 5, 6, 7 and 9, so it must be 8. 1 6 8 3 4 9 4 6 5 8 1 6 4 2 7 8 6 4 7 1 5 5 2 1 7 6 2 4 1 6 4 6 8 4 6 4 6 7 4 8
Row 8, column 8 of a Hard puzzle sees every digit but 8. It’s the only move on the whole board.

What it adds over hidden singles

A hidden single looks for a digit with one place. A naked single looks for a cell with one digit. Usually they find the same moves, but not always. In the position above, no digit has only one place left in any row, column or box, so scanning finds nothing. The only way forward is to look at the cell.

That’s why naked singles matter on harder puzzles. On PeerPuzzles, 45 of the 50 Medium levels need one, and 40 of the 50 Hard levels. No Easy level does.

Naked singles from notes

A cell can become a naked single without any new digit on the grid, when a note technique rubs digits out of its notes.

Only digit in the Hard puzzle: row 9, column 4 Row 9, column 4 could be 4 or 9 from the digits around it. The centre box pointing its 4s down column 4 rules out the 4, so it must be 9. 4 9 3 5 4 2 7 2 3 5 2 1 3 5 9 2 2 9 7 8 8 1 8 6 7 6 8 1 9 2 3 5 1
In the Hard puzzle, row 9, column 4 could be 4 or 9. A pointing pair rules out the 4, so it’s 9.

In the Hard puzzle every technique page follows, row 9, column 4 starts with two options: 4 or 9. The centre box’s 4s all lie in column 4, so the 4 in this column must be in the centre box, which rules out the 4 in row 9. That leaves 9: a naked single, and the puzzle’s first new digit in three moves. Next, the puzzle turns to box/line reduction.

How to find them fast

  • Look at crowded cells. A cell whose row, column and box are all busy is the most likely to be down to one digit.
  • Check two-note cells after every elimination. When a note technique removes a digit, any cell it leaves with one note is a naked single.
  • Count, don’t guess. List the digits the cell sees, out loud if it helps. Missing one is the easiest way to get this wrong.

Next steps

Questions

Why is it called a naked single?

Because it’s out in the open. Once the cell’s notes are written down, there’s one digit in them, plain to see. Some guides call it a sole candidate.

Do I need notes to find naked singles?

Not always. A cell that already sees eight different digits is a naked single without any notes. But many naked singles only appear once notes have been narrowed by other techniques, so on Hard puzzles notes help a lot.

Should I look for naked or hidden singles first?

Hidden singles first. They’re quicker to scan for and they’re all you need on Easy. Switch to naked singles when the scanning runs dry.