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Sudoku Hidden Singles: Find the Only Place for a Digit

A hidden single is a digit that has only one place left in a row, column or box. Pick a box and a digit it’s missing, rule out every empty cell that already sees that digit, and if one cell is left, the digit goes there. It’s the first technique in Sudoku and the one you’ll use most: on PeerPuzzles, every Easy level can be finished with hidden singles alone.

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This is the first of the Sudoku techniques. We call it “the only place for a digit” in the rules and how to solve pages.

The rule

  1. Choose a row, column or box, and a digit it doesn’t have yet.
  2. Rule out every empty cell there that already sees the digit, through its own row, column or box.
  3. If exactly one cell is left, the digit goes in it.

In a box, the digits that do the ruling out sit in the rows and columns passing through it. This is often called cross-hatching.

The only place for a 2 in the top-middle box The top-middle box has five empty cells. The 2 in row 1 rules out the empty cell in row 1. The 2 in column 5 (row 6) rules out column 5, and the 2 in column 6 (row 9) rules out column 6. Only row 3, column 4 is left, so the 2 goes there. 5 2 9 3 6 4 7 5 8 3 4 7 2 5 7 1 3 8 5 1 2 6 3 9 1 2 7 3 5 4 6 8 2 3 4 5 7 1 1 2 2
The top-middle box needs a 2. The 2s in row 1, column 5 and column 6 rule out four of its five empty cells.

It works the same in a row or column, where the ruling out comes from crossing columns (or rows) and from boxes.

The only place for a 9 in row 5 Row 5 has five empty cells. Columns 3, 6 and 8 already have a 9, and so does the box holding column 9, which rules out four of them. The 9 goes in the one cell left, row 5, column 5. 5 3 7 6 9 1 9 2 1 4 7 5 9 2 1 2 5 4 3 3 7 9 5 7 3 7 2 1 5 9 9 4 9
Row 5 needs a 9. Columns 3, 6 and 8 have one, and so does the box holding column 9. One cell is left.

Why “hidden”

The cell doesn’t look forced. In the Hard puzzle below, each of the first five cells filled could still take more than one digit when you look at the cell alone. What pins each one down is the row or box: the digit has nowhere else to go. Compare a naked single, where the cell itself is down to one digit.

The simplest hidden single is a row, column or box with one empty cell: the missing digit has only one place. That’s sometimes called a full house.

In a real puzzle

Every technique page follows the same Hard puzzle. It opens with five hidden singles, in a box, a row, a box, and twice in the centre box. Then they run out, and the next three moves are pointing pairs.

The first five moves: all only places The Hard puzzle after its first five moves, in colour: 9 at row 2, column 5; 2 at row 4, column 5; 3 at row 5, column 3; 1 at row 6, column 6; and 5 at row 6, column 5. After these, no digit has only one place left. 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
The Hard puzzle’s first five moves, all hidden singles, in colour. After these, no digit has only one place left anywhere.

That’s the pattern for the whole solve. The note techniques only rule digits out; nearly every digit is still placed by a hidden single. Of the 55 digits this puzzle needs, 53 are hidden singles (20 of them full houses), and just 2 are naked singles.

How to find them fast

  • Go digit by digit. Start with the most common digit on the grid and check every box for it, then move to the next.
  • Scan two boxes out of three. If a digit is in two boxes of a band, the third box’s digit is in the row that’s left. See the tip.
  • Don’t forget rows and columns. Some hidden singles only show in a row or column, like the 9 in row 5 above. Its box and its column haven’t narrowed it down yet.
  • Look where you just placed. A new digit rules out cells in its row, column and box, and that’s where the next hidden single usually is.

Next steps

Questions

Why is it called a hidden single?

Because the cell itself doesn’t give it away. Looked at on its own, the cell could still take several digits. It’s only when you look along its row, column or box that one digit turns out to have nowhere else to go.

What's the difference between a hidden single and a naked single?

A hidden single starts from a digit: it has one place left in a row, column or box. A naked single starts from a cell: it has one digit left. They find different moves, so it pays to use both.

Is a full house a hidden single?

Yes, the simplest kind. When a row, column or box has one empty cell, the missing digit has only one place left. Some guides call this a full house or last digit.