If two cells in the same row, column or box have exactly the same two candidates, those two digits must go in those two cells. You don't know which way round yet, but you can remove both digits from every other cell in that unit. Three cells sharing three candidates, a naked triple, work the same way.
A naked pair is the natural next step after naked singles. A single is one cell with one candidate; a pair is two cells that between them have only two candidates.
It's called naked because it is in plain sight: you see it by reading the pencil marks of the two cells, nothing else.
A naked pair
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In row 5, R5C4 and R5C5 can only hold 5 and 7. Those two cells will use up both digits, so they can be removed from every other cell in row 5: R5C2. That leaves R5C2 with only one candidate: 8.
A naked triple
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In column 6, R3C6, R4C6 and R7C6 hold only 1, 3 and 8 between them, though no single cell has all three. Three cells, three digits: they take all of them, so 1, 3 and 8 can be removed from the rest of column 6: R6C6, R8C6 and R9C6. That leaves R9C6 with only one candidate: 5.
A naked quad
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In row 8, R8C2, R8C3, R8C5 and R8C6 hold only 1, 4, 7 and 8 between them. Four cells, four digits: they take all of them, so 1, 4, 7 and 8 can be removed from the rest of row 8: R8C7, R8C8 and R8C9. That leaves R8C8 with only one candidate: 9.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Look for a cell with exactly two candidates.
2Scan its row, column and box for another cell with the very same two candidates.
3When you find one, remove both digits from every other cell in the unit they share. Two cells that share a box and a row clear both.
4For triples, look for three cells in one unit whose candidates together are only three digits. Each cell can show two or three of them.
5Check the cells you just cleaned for new singles.
Why it works
Two cells in one unit must hold two different digits. If both can only be one of the same two digits, one cell takes each, and there is no third option. The unit needs each of those digits exactly once, so both are already spoken for and no other cell there can take them.
The same counting works for three cells and three digits, and even four (a naked quad), though quads are rare and hard to see.
Common mistakes
Pairing cells that don't share a row, column or box. Two cells with 5/7 in different units prove nothing.
Treating 5/7 and 5/7/9 as a pair. Both cells must have exactly the two digits; that combination only counts as part of a triple.
Expecting every cell of a triple to show all three digits. 1/3, 3/8 and 1/8 make a perfectly good naked triple.
Questions
What is the difference between a naked pair and a hidden pair?
A naked pair is two cells that can only hold two digits. A hidden pair is two digits that can only go in two cells, and those cells may still show other candidates, which is what hides it. Naked pairs clean the rest of the unit; hidden pairs clean the two cells themselves.
Do the two cells have to be next to each other?
No. They only have to share a row, column or box. Anywhere in that unit counts.
What is a naked triple?
Three cells in one unit whose candidates, taken together, are only three digits. Each cell can show two or three of them. Those three digits are then removed from the rest of the unit.
We use one strictly necessary cookie to keep you signed in, and your browser's local storage to save game progress (your puzzles and best times) on this device. Analytics runs cookie-free by default — accepting lets us measure visits in more detail.