Naked pairs and triples
A naked pair is two cells in the same row, column or box that have exactly the same two candidates. The two digits must go in those two cells, so they can be removed from every other cell of the unit. A naked triple is the same idea with three cells and three digits; each cell may show two or all three of them. The Bare Sudoku hint labels the resulting placement "Pair or triple".
When to use it
After the notes are complete and singles and locked candidates are exhausted. Naked pairs are very common in Hard puzzles, naked triples less so. Both are worth checking in every unit that still has five or more empty cells.
How to spot it
Look for cells with only two candidates and find another cell in the same unit with the same two. For triples, look at units with several two- and three-candidate cells and check whether three of them together use only three different digits. Cells with exactly the same candidates are easy to see once the notes are written; Fill notes in the game does that in one tap.
Example
Naked pair
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 3 | 8 | 47 | 2 | 5 | 467 | 469 | 49 | 1 |
| r2 | 257 | 6 | 2457 | 1 | 9 | 47 | 8 | 3 | 24 |
| r3 | 1 | 9 | 24 | 8 | 3 | 46 | 246 | 7 | 5 |
| r4 | 279 | 1 | 8 | 4 | 6 | 3 | 279 | 5 | 27 |
| r5 | 6 | 237 | 2379 | 79 | 1 | 5 | 2479 | 249 | 8 |
| r6 | 579 | 4 | 579 | 79 | 8 | 2 | 3 | 1 | 6 |
| r7 | 4 | 5 | 12 | 6 | 7 | 9 | 12 | 8 | 3 |
| r8 | 279 | 237 | 12379 | 35 | 24 | 8 | 12457 | 6 | 247 |
| r9 | 8 | 6 | 35 | 24 | 1 | 24 | 9 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- r9c5 and r9c8 in row 9 have exactly the same two candidates: 2 and 4.
- One of them must be 2 and the other 4. We do not know which, but both digits are used up by these two cells.
- So no other cell of row 9 can hold 2 or 4. Remove 2 from r9c2, 2 from r9c7, 4 from r9c7.
Naked triple
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 5 | 9 | 6 | 2478 | 27 | 2478 | 3 | 28 | 1 |
| r2 | 1 | 7 | 4 | 268 | 3 | 268 | 89 | 2589 | 58 |
| r3 | 3 | 2 | 8 | 9 | 1 | 5 | 4 | 6 | 7 |
| r4 | 2 | 356 | 7 | 46 | 8 | 3469 | 69 | 1 | 456 |
| r5 | 468 | 3568 | 35 | 1 | 26 | 23469 | 7 | 4589 | 4568 |
| r6 | 468 | 1 | 9 | 467 | 5 | 467 | 2 | 48 | 3 |
| r7 | 7 | 68 | 2 | 3 | 9 | 1 | 5 | 48 | 468 |
| r8 | 68 | 35 | 35 | 268 | 4 | 268 | 1 | 7 | 9 |
| r9 | 9 | 4 | 1 | 5 | 67 | 678 | 68 | 3 | 2 |
- Three cells of row 8 draw all their candidates from the same three digits, 2, 6, 8: r8c1 (6 8), r8c4 (2 6 8), r8c6 (2 6 8).
- The three digits must fill these three cells in some order. A cell does not need to show all three candidates; what matters is that none of the three cells has a candidate outside the set.
- Remove 2, 6, 8 from every other cell of row 8: 6 from r8c2, 8 from r8c2.
Common mistakes
- Taking two cells that share two candidates but also have a third one. For a naked pair, each cell must have exactly the two candidates and nothing else.
- Removing the digits from the pair cells themselves. The pair keeps its candidates; the eliminations go to the other cells of the unit.
- Requiring every cell of a triple to show all three digits. A cell with two of the three is fine, as long as no cell has a candidate outside the set.
In Bare Sudoku
Needed from level: Hard
In the game, the hint says: Pair or triple
Frequently asked questions
What is a naked pair in Sudoku?
Two cells in one unit that both have exactly the same two candidates. Those two digits are locked into those two cells, so they can be removed from the rest of the unit.
What is a naked triple?
Three cells in one unit whose candidates together are only three digits. Each cell may hold two or three of them. The three digits fill the three cells, so they can be removed from the other cells of the unit.
Does a naked pair place a digit?
Not by itself. It removes candidates, and the removal usually leaves a naked or hidden single. The hint in Bare Sudoku shows that single and names the technique that made it possible.
Can a naked pair be in a box and a row at the same time?
Yes. If the two cells share a row and a box, the pair eliminates in both units. Bare Sudoku handles them one unit at a time.
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