Hidden singles

A hidden single is a digit that has only one place it can go in a row, column or box. The cell may look like it could take several digits, which is why the single is “hidden”, but if every other cell in the unit is ruled out for that digit, the digit must go there.

This is the most important technique in sudoku. It is how almost every puzzle starts, and our solver uses it before anything else. Every easy puzzle on NineByNine can be solved with hidden singles and naked singles alone, and every harder puzzle still uses hidden singles for most of its steps.

Why it works

Each box must contain every digit once. Suppose a box has no 7 yet. Every 7 already placed elsewhere in the grid rules out a whole row and a whole column. If the 7s in neighbouring rows and columns cover every empty cell of the box except one, that last cell is the only place left for the box's 7. The same reasoning works for a row or a column: if a row is missing a 4 and every empty cell but one already has a 4 in its column or box, the 4 goes in the remaining cell.

The key difference from a naked single is the direction of the question. You are not asking what can go in one cell; you are asking where one digit can go in one unit. That makes hidden singles easy to find with a systematic scan, even when the grid is mostly empty.

How to spot it

• Scan one digit at a time. Pick a digit that already appears five or six times and check each box that is missing it.
• For each box, mentally draw lines through the rows and columns that already contain the digit. If only one empty cell survives, you have found it.
• Do the same for rows and columns that are nearly full: check where the missing digits can go.
• Select a placed digit: highlighting shows every copy of it on the grid, which makes the blocked rows and columns easy to see.

Common mistakes

• Checking only boxes. Hidden singles also appear in rows and columns, often late in a puzzle.
• Forgetting that a filled cell also blocks. The surviving cell must be empty; cells that already contain another digit are not candidates.
• Stopping too early. After placing a digit, go back: the new digit often creates another hidden single for the same digit in a neighbouring box.

Related techniques

With pencil marks, a hidden single is a digit that appears in the notes of only one cell in a unit. The same idea, extended to two digits that share the same two cells, is a hidden pair. And when a digit's possible cells in a box all lie in one row, you get a pointing pair: not quite a single, but enough to clear that digit from the rest of the row.

Stuck on a real puzzle? The sudoku solver names every technique it uses, step by step, and the hint button in the game teaches the same way.

How to practise

Play the three practice puzzles below in order. Each one reaches a point where hidden singles are the only way forward with the basic toolbox, so if you get stuck, that is the moment to look for the pattern. Try first without help. If you still cannot see a move, press Hint once: the first level names the technique, the second shows where to look, and only the third makes the move for you. After you finish, play a few easy puzzles without hints to make the habit stick.