Sudoku technique

Hidden Single

Within a zone (row, column, or box), a digit has only one cell left where it can go — even if that cell still accepts other digits too. It’s “hidden” among its neighbors: you have to scan the whole zone to spot it.

A puzzle that requires it

Level Easy — the puzzle is shown twice: right below, and again in the demo that follows.

6	9						8	1
1	8		9				4
5	2	4				7
9	6	8			7		1	3
3		1	8	9	6	2		5
7	5		3			6	9	8
		6				9	5	4
	3				1		2	7
2	7						3	6

Demonstration

State of the grid right when the technique applies, after 15 earlier deductions.

Demo

Demo — watch first, you'll play right after.

Technique's pattern
Cell solved by the technique
Solved earlier
Given (clue)

6	9						8	1
1	8		9				4	2
5	2	4	1			7	6	9
9	6	8			7	4	1	3
3	4	1	8	9	6	2	7	5
7	5	2	3	1	4	6	9	8
8	1	6				9	5	4
4	3				1	8	2	7
2	7					1	3	6

Singleton caché

Dans la zone surlignée, un chiffre n'a plus qu'une place possible : la case entourée — même si elle accepte encore d'autres candidats.

Placement:

the 6 in L2C5

Your turn: puzzle 1 →

A Hidden Single appears when a digit has only one possible cell left in a zone: a row, a column or a box. That cell may still accept other digits. The candidate is “hidden” among them, and you find it by looking at the digit rather than at the cell.

The principle

In every row, every column and every box, the digits 1 to 9 each appear exactly once. If a digit is still missing from a zone, it has to go somewhere in that zone. When every empty cell but one is closed to it, because its row, its column or its box already contains it, only one place remains: the digit goes there.

It does not matter what else the cell accepts. If it has several candidates, they no longer count: the zone demands that digit, and that cell is the only one that can take it.

How to spot it

Start from a digit and a zone. Take a digit that is already well represented on the grid, then a box where it is missing. The digit is already placed on some of the rows and columns that cross this box: those rows and columns are blocked for it. Then look at the empty cells of the box that escape those blocks. If only one is left, that is the Hidden Single.

Run the same search on rows and columns: in a row where a digit is missing, go through the cells one by one, ruling out those whose column or box already contains that digit.

If you keep notes, the method gets simpler: in a zone, look for a digit that appears in the notes of only one cell. Even if that cell carries several other candidates, this is the digit it has to take.

A worked example

Picture a box where one digit is still missing. That digit is already placed on two of the three rows crossing the box, and on two of the three columns. The cells on those rows and columns are therefore closed to it. Only one cell sits where the remaining row and the remaining column meet, and if it is empty the digit goes there.

But the box needs this digit, and no other cell can supply it. The cell takes the digit, and its other candidates disappear.

Common mistakes

The first mistake is to confuse the Hidden Single with the Naked Single. In the naked one, the cell has a single candidate. In the hidden one, the cell often has several, and it is the digit that has only one place. If you look for a cell with one candidate, you will walk right past it.

Another trap is to look only at boxes. A Hidden Single also turns up in a row or in a column, and many players sweep only one of the three zones. Finally, notes work against you if they are wrong: a candidate struck by mistake can make you believe a digit has only one place. Before you place, check against the grid itself.

When to use it

The Hidden Single is expected from the Easy and Medium levels, which rest on the two singles. An Easy puzzle is finished by alternating both: a Naked Single when a cell is obvious, a Hidden Single when it no longer is.

When no single shows up, even after sweeping each digit in each zone, it is time for the elimination techniques. The first in the catalog is the Pointing Pair, expected at the Hard level.

Frequently asked questions

What is the difference between a Hidden Single and a Naked Single?

The Naked Single starts from the cell: it has only one candidate left. The Hidden Single starts from the digit: within a zone it has only one possible cell, even if that cell accepts other digits.

Do I need to pencil in candidates to find a Hidden Single?

Not necessarily. You can sweep a digit through a box by looking at the rows and columns where it is already placed. Notes make the search faster and safer when many cells are open.

Where should I look first?

Start with the digits that are most present on the grid: they block many rows and columns, so they leave few open cells in each zone. Nearly full zones are good candidates too.