Naked pairs: reserve two digits in two cells
A naked pair is two cells in the same unit with the same two candidates and no others.
Updated 2026-11-13
A naked pair is two cells in the same unit with the same two candidates and no others. Those digits occupy the pair in some order, so remove both digits from every other cell in that unit; the pair itself does not yet reveal the order.
Establish the pair before eliminating
Suppose cells A and B share a row and each has only two and seven as candidates. A must take one of those digits, and B must take the other because the row cannot repeat. Therefore no other cell in that row can contain two or seven.
The words “only” and “same unit” carry the proof. A cell with two, seven and nine is not one half of this naked pair. Two cells in unrelated rows and boxes do not reserve digits together merely because their notes match.
A worked candidate table
| Cell in the row | Before | After finding the pair |
|---|---|---|
| A | two, seven | two, seven |
| B | two, seven | two, seven |
| C | two, five, seven | five |
| D | five, nine | five, nine |
C becomes a naked single and can be filled with five. A and B remain unresolved. The useful result is outside the pair, so resist tapping a guessed value inside it.
Which peers can lose candidates?
If A and B share only a row, eliminate from the row. If they also sit in the same box, the pair reserves the digits in that box too, allowing a separate box elimination. You must justify each affected unit independently.
A cell that sees A but not B does not necessarily lose either digit. For example, a cell in A’s column cannot infer that the column’s two lies at A, because A might be seven. The pair supports eliminations only where both reserved digits are constrained together.
A repeatable search
Scan a unit for cells carrying exactly two notes. Compare the candidate sets rather than their visual positions. When two match, mark the pair mentally and check other cells for either digit. If no other cell contains those digits, the pair is real but currently offers no elimination.
After any removal, check whether another cell becomes a single or whether one digit has only one position left. A pair often contributes indirectly by exposing a simpler next move.
A useful counterexample
If three cells in a row all show only two and seven, the position is contradictory: three cells cannot be filled by two distinct digits without repetition. Do not call that a stronger pair. Recheck your earlier candidates and placements before continuing.
Work a pair that spans a row and a box
Take two cells A and B in the same row and the same box. Both have exactly three and eight as candidates. A third cell C is in their row but outside their box; D is in their box but on another row. E shares A's column only.
| Cell | Before | What the pair allows |
|---|---|---|
| A | three, eight | Keep both |
| B | three, eight | Keep both |
| C | one, three, eight | Keep one |
| D | three, six, eight | Keep six |
| E | three, nine | No change from this pair |
A and B reserve three and eight in their row, so C becomes one. They also reserve those digits in their box, so D becomes six. E sees only A, which could be either digit; therefore this pair alone cannot remove three from E.
- Establish the two matching candidate sets at A and B.
- Apply the row restriction to C and the box restriction to D separately.
- Place C's one and D's six, then update their own peers.
The new single at C may eventually affect E through another route, but that would be a separate deduction. Keep the direct reach of the pair distinct from the consequences of later placements.
Change one note and reconsider
Give B an additional candidate, nine. A still has three and eight, but B can now escape the pair by taking nine. Three or eight might then belong elsewhere in the row. The earlier deletions from C and D are no longer justified by these two cells.
You can still look for another pattern in the modified position. For example, a digit might have only one location somewhere else. What you cannot do is ignore B's nine to recover a shape you wanted to find. Naked pairs depend on the full candidate contents of the cells, not on selecting two matching marks from longer lists.
Where to play
Take the pair search into a puzzle in Ninefold. Its separate difficulty tracks let you choose a board that leaves time to compare candidate sets.