Sudoku technique

Naked Pair

Two cells in the same zone share exactly the same two candidates between them. Those two digits are reserved for them: nothing else in the zone can take them, even without knowing which cell gets which.

A puzzle that requires it

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

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

Demonstration

State of the grid right when the technique applies, after 10 earlier deductions.

Demo

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

Technique's pattern
Candidates removed
Solved earlier
Given (clue)

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

Paire nue

Ces 2 cases n'acceptent que 5, 7. À elles deux elles épuisent ces chiffres : personne d'autre dans la zone ne peut les prendre.

Candidates removed:

the 7 from cell L5C2
the 7 from cell L5C3
the 7 from cell L5C4
the 5, 7 from cell L5C8

Your turn: puzzle 1 →

The Naked Pair relies on two cells of the same zone that have, between them, only the same two candidates. Those two digits are reserved for them, even though you do not yet know which goes where. You can therefore erase them from every other cell of the zone: the Naked Pair eliminates elsewhere.

The principle

A zone is a row, a column or a box. Suppose two of its cells have exactly the same two candidates, say 4 and 7, and no other. One of the two cells will take the 4 and the other the 7. You do not know which, but it does not matter: between them, they use up those two digits.

In the other cells of the zone, 4 and 7 are therefore impossible. Remove them from their candidates. The Naked Pair does not touch its own cells, which stay as they are: it cleans the neighboring cells of the zone.

The argument makes no assumption about how the two digits split: it only needs the set to be closed. That closure is called a naked subset of size two. Naked Triples and Naked Quads extend the same idea to three and four cells.

How to spot it

You need candidate notes. Go through a zone and look for two cells that each have only two candidates, and the same ones. Two cells with different candidates do not form a Naked Pair, nor do two cells where one carries a third candidate.

Once you have found the pair, look at the other empty cells of the zone and erase the two digits from their notes. If the two cells of the pair are also in the same box, or on the same row, you can repeat the elimination in that second zone.

After the elimination, a neighboring cell may be left with one candidate, or a digit may have only one place in the zone. Check right away: that is where the Naked Pair unlocks the grid.

A worked example

On row 3, three cells are still empty: R3C4, R3C7 and R3C8. The row already holds 3, 7, 8, 4, 6 and 1: the three missing digits are 2, 5 and 9.

The cells R3C4 and R3C7 are left with only 2 and 9 as candidates. One of them will take the 2, the other the 9 — we do not know which. But between them, they hold those two digits: that is the Naked Pair 2-9 on row 3.

The third empty cell, R3C8, used to have 2, 5 and 9 as candidates. Remove the 2 and the 9: only the 5 remains, a Naked Single, which we place at once.



3	7	8	4	6	1

Naked Pair 2-9 on row 3: the two yellow cells share digits 2 and 9; in the red cell, candidates 2 and 9 are eliminated, 5 is left alone.

Eliminations and placements

The Naked Pair removes the digits 2 and 9 from the other empty cells of the zone. In our example, that reduces R3C8 to a single candidate, 5, which gets placed right away.

In general, a Naked Pair does not place a digit on its own: it thins out the notes, and a Naked or Hidden Single, a fresh pair, or a box-line interaction tends to surface next. The chain of consequences is what moves the grid forward.

Common mistakes

Confusion number one is with the Hidden Pair. The Naked Pair is recognized by its cells: two cells that have only two candidates, the same ones. It eliminates those digits in the other cells of the zone. The Hidden Pair, on the contrary, is recognized by its digits, and it cleans its own cells, not those of its neighbors.

Another trap is to think a Naked Pair needs two cells that look identical at a glance. The two cells must have exactly the same two candidates, not one more. Finally, incomplete notes create false pairs. If a cell lost a candidate by mistake, the pair you think you see can lead to a wrong elimination.

One last pitfall, less often mentioned: forgetting to extend the elimination to a second zone. When the two cells share both a row and a box, the pair eliminates in both zones, not just the row where you spotted it.

Related patterns

The Naked Triple extends the pair to three cells whose combined candidates make up only three digits. Those three digits are reserved for the triple; remove them from every other cell of the zone. Each cell of the triple need not carry all three digits — the union just has to hold three.

The Hidden Pair is the inside view of the same idea: two digits can only land in two cells of the zone. Those cells monopolize the two digits, and every other candidate inside them disappears. Hunt for it when no Naked Pair is obvious.

The Naked Single is the limit case: one cell has a single candidate left. It is the most direct deduction in sudoku, and a Naked Pair often triggers one on a neighbor.

When to use it

The Naked Pair is expected at the Hard level, along with the Pointing, Claiming and Hidden Pairs. It is often the easiest of the four to see: you just look for cells with two candidates.

It prepares the ground for wider techniques, such as the Naked Triple, which follows the same reasoning with three cells and three digits. To practice, Hard puzzles are a good ground: the engine only allows pairs and box-line interactions at that level, so a Naked Pair often stays the most visible deduction.

Frequently asked questions

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

The Naked Pair eliminates elsewhere: two cells have only the same two candidates, and those digits disappear from the other cells of the zone. The Hidden Pair cleans its own cells: two digits fit in only two cells, and every other candidate in those two cells disappears. In the first case you hunt for cells, in the second for digits.

Do the two cells of a Naked Pair have to be adjacent?

No. They only have to belong to the same zone, meaning the same row, the same column or the same box. Other cells can sit between them.

Does a Naked Pair place a digit?

Not on its own. It removes two candidates from the neighboring cells. Those eliminations can then leave a Naked or Hidden Single, which lets you place a digit.

What if two cells have only two candidates, but not the same ones?

That is not a Naked Pair. Both cells must have exactly the same two candidates. With only partly shared candidates, this technique concludes nothing.

Can a Naked Pair act in two zones at once?

Yes. If the two cells of the pair are in the same box and on the same row (or column), you erase the two digits from the other cells of the box and from the other cells of the row. Two zones cleaned for one pair.