Sudoku

Sudoku technique

Hidden singles

A hidden single is a digit that has only one place left to go in a row, a column or a box. Every unit needs each digit once, so if only one cell can take it, that cell is settled. It is the most useful technique in Sudoku: easy puzzles are made almost entirely of hidden singles.

Why it is called hidden

The cell itself may have several candidates. Looked at on its own, it seems undecided. The single only shows when you look at the whole unit and ask where one particular digit can go.

That makes it the opposite of a naked single. A naked single starts with a cell and finds its only digit. A hidden single starts with a digit and finds its only cell.

In a box

Boxes are where hidden singles are easiest to see. In this starting position, take the digit 5 and the bottom-right box, which has four empty cells.

The 5 in column 7 rules out the empty cell at the top-left of the box. The 5 in column 9 rules out the one on the right-hand side. The 5 in row 9 rules out the one in the bottom row. That leaves row 7, column 8, and the 5 goes there.

With notes written in, that cell would show two candidates, 5 and 7. Nothing about the cell says which. The box does.

Three 5s outside the box cross off three of its empty cells. The fourth must be the 5.

In a row or column

Hidden singles turn up in rows and columns as well, and these are the ones people miss. In the same position, look at row 3 and the digit 2. The row has five empty cells.

Three of them are in the top-right box, which already has a 2. A fourth is in column 5, which has a 2 further down. Only row 3, column 4 is left.

A box hides nothing from a quick scan. A row can cross three boxes, so you have to check each empty cell against its own box and column.

In row 3, the 2 in the top-right box blocks three cells and the 2 in column 5 blocks one. The last empty cell takes the 2.

How to spot them

  • Scan digit by digit, box by box. The method is on the how to start page.
  • When boxes run dry, pick a row or column with three or four empty cells and ask where each missing digit can go.
  • With notes written in, look for a digit that appears as a note only once in a unit.

There are 27 units and nine digits, so there are plenty of places for a hidden single to be. When you seem stuck on an easy or medium puzzle, there is almost always one you haven’t looked at.

Common mistakes

  • Checking only rows and columns against a box and forgetting digits inside the box itself.
  • Stopping when two cells are left. Two possible cells is useful to remember, but it is not yet a placement.
  • Scanning boxes only. Rows and columns have hidden singles of their own.

When two cells are left for a digit in a box, and they share a row or column, you have found something else: a pointing pair.