Naked Pair
Two cells in a unit share the same two candidates.
A naked pair is two cells in the same row, column, or box that each hold exactly the same two candidates and nothing else — say both cells are limited to {1,2}. Because those two cells must take those two digits between them, no other cell in the shared unit can use either digit. The naked pair sudoku technique is one of the first true eliminating moves you learn after singles, and it clears candidates without you having to place a number first.
Worked example
Box 1 already holds the givens 3, 4, 5, 6, 7, 8 and 9, so only the digits 1 and 2 are left to fill its two empty cells, R1C1 and R1C2. Each of those cells therefore has candidates of exactly {1,2}, forming a naked pair that sits in both row 1 and box 1 at once. Since 1 and 2 must go into R1C1 and R1C2 in some order, you can strike both digits out of every other cell in row 1 and box 1 — for instance removing 1 and 2 from R1C4.
When to use it
Reach for a naked pair once basic singles dry up and you have started pencilling in candidates, because it needs an accurate candidate grid to spot. Scan each row, column, and box for two cells that have been whittled down to only two candidates, then check whether a second cell in the same unit carries that identical pair — here R1C1 and R1C2 both showing just {1,2} is the giveaway. It is most productive in units that are nearly full, like box 1 with seven givens, where a couple of cells are naturally squeezed to two options.
How to use it
- Spot two matching cells. Find two cells in the same unit that each have exactly the same pair of candidates, e.g. {3,7}.
- Lock the pair. Those two digits must occupy those two cells (in some order), so no other cell in the unit can use them.
- Eliminate from peers. Remove both digits from every other cell in the shared unit, often unlocking new singles.
Frequently asked questions
What is a naked pair in Sudoku?
A naked pair is two cells in one unit (a row, column, or box) that each contain exactly the same two candidates and no others. Those two digits are locked into those two cells, so they can be erased as candidates from every other cell in that unit. In the example, R1C1 and R1C2 are both restricted to {1,2}, so 1 and 2 come out of the rest of row 1 and box 1, such as R1C4.
How do I spot a naked pair when solving?
First fill in candidates, then look through each row, column, and box for a cell with only two candidates left. When you find one, check the other cells in its units for a second cell holding that exact same two-candidate set. R1C1 and R1C2 both reducing to {1,2} — because box 1's givens 3-9 leave nothing else — is a textbook sighting, and units that are almost complete are the easiest hunting grounds.
Does a naked pair have to be in the same box, or can it be in a row or column?
It can be in any single unit — a row, a column, or a box. The eliminations only apply to cells that share that unit with the pair. R1C1 and R1C2 happen to share both row 1 and box 1, so the pair clears 1 and 2 from all other cells in both units at once; a pair sitting only in a row would clear candidates along that row alone.