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Naked pairs
Two cells with the same two candidates.
Two cells in one row, column or box with exactly the same two candidates reserve those digits for the pair.
When to use it
If exactly two cells in a unit each have the same two candidates {a, b}, remove a and b from every other cell in that unit. Do not remove either candidate from the pair itself.
How to find it
- 01
Find a cell with exactly two remaining candidates.
- 02
Find a second cell in the same unit with exactly that pair.
- 03
Keep the pair intact. Remove its digits from the other cells of the shared unit.
Worked example
v1-expert-0001 · position before step 19
View the cell table
| Cell | Value / candidates |
|---|---|
| r1c1 | {2, 4, 5, 8} |
| r1c2 | {2, 4, 5, 8} |
| r1c3 | {3, 5, 8} |
| r1c4 | {3, 5} |
| r1c5 | Placed: 6 |
| r1c6 | Placed: 9 |
| r1c7 | {3, 5, 7} |
| r1c8 | {5, 7} |
| r1c9 | Placed: 1 |
| r2c1 | {5, 9} |
| r2c2 | Placed: 1 |
| r2c3 | Placed: 6 |
| r2c4 | {3, 5} |
| r2c5 | Placed: 2 |
| r2c6 | Placed: 7 |
| r2c7 | Placed: 4 |
| r2c8 | Placed: 8 |
| r2c9 | {3, 5, 9} |
| r3c1 | {5, 9} |
| r3c2 | Placed: 7 |
| r3c3 | {3, 5, 9} |
| r3c4 | Placed: 1 |
| r3c5 | Placed: 8 |
| r3c6 | Placed: 4 |
| r3c7 | Placed: 2 |
| r3c8 | Placed: 6 |
| r3c9 | {3, 5, 9} |
| r4c1 | {5, 7, 9} |
| r4c2 | {5, 9} |
| r4c3 | Placed: 2 |
| r4c4 | {6, 9} |
| r4c5 | Placed: 4 |
| r4c6 | Placed: 8 |
| r4c7 | {1, 3, 5, 6, 7, 9} |
| r4c8 | {1, 5, 7, 9} |
| r4c9 | {3, 5, 6, 7} |
| r5c1 | Placed: 6 |
| r5c2 | {4, 5, 8, 9} |
| r5c3 | {5, 8, 9} |
| r5c4 | Placed: 7 |
| r5c5 | Placed: 3 |
| r5c6 | Placed: 1 |
| r5c7 | {5, 8, 9} |
| r5c8 | {4, 5, 9} |
| r5c9 | Placed: 2 |
| r6c1 | {4, 7, 8, 9} |
| r6c2 | Placed: 3 |
| r6c3 | Placed: 1 |
| r6c4 | {6, 9} |
| r6c5 | Placed: 5 |
| r6c6 | Placed: 2 |
| r6c7 | {6, 7, 8, 9} |
| r6c8 | {4, 7, 9} |
| r6c9 | {6, 7, 8} |
| r7c1 | {2, 3, 5, 8} |
| r7c2 | {2, 5, 8} |
| r7c3 | Placed: 7 |
| r7c4 | Placed: 4 |
| r7c5 | Placed: 9 |
| r7c6 | {3, 6} |
| r7c7 | {1, 5, 6, 8} |
| r7c8 | {1, 2, 5} |
| r7c9 | {5, 6, 8} |
| r8c1 | Placed: 1 |
| r8c2 | Placed: 6 |
| r8c3 | {8, 9} |
| r8c4 | Placed: 2 |
| r8c5 | Placed: 7 |
| r8c6 | Placed: 5 |
| r8c7 | {8, 9} |
| r8c8 | Placed: 3 |
| r8c9 | Placed: 4 |
| r9c1 | {2, 3, 5, 9} |
| r9c2 | {2, 5, 9} |
| r9c3 | Placed: 4 |
| r9c4 | Placed: 8 |
| r9c5 | Placed: 1 |
| r9c6 | {3, 6} |
| r9c7 | {5, 6, 7, 9} |
| r9c8 | {2, 5, 7, 9} |
| r9c9 | {5, 6, 7} |
Work through the example
Inspect the supporting cells and candidate removals. This panel keeps the intermediate state; the original-puzzle link starts from the givens.
Inspect r2c1 and r3c1. Follow these candidates: 5 and 9.
r2c1 and r3c1 share column 1, and each has exactly these candidates: 5 and 9. The two cells must use those digits in some order. Other cells in the unit cannot use either digit.
Candidates to remove
- Remove 5 from r1c1.
- Remove 5 from r4c1.
- Remove 9 from r4c1.
- Remove 9 from r6c1.
- Remove 5 from r7c1.
- Remove 5 from r9c1.
- Remove 9 from r9c1.
When the rule does not apply
r1c1 has {2, 8}, while r1c4 has {2, 8, 9}. This is not a naked pair: r1c4 might be 9, so the two cells do not reserve both 2 and 8. A third cell with exactly {2, 8} in the same unit would instead signal an inconsistent candidate state, not a choice of any two cells.
Can {2, 8} and {2, 8, 9} alone justify removing 2 from another cell in the row?
Show why
No. The extra 9 prevents the second cell from being restricted to the pair. A valid deduction would need additional evidence.
Try another position
Try the technique on another puzzle.
v1-expert-0002 · position before step 27
View the cell table
| Cell | Value / candidates |
|---|---|
| r1c1 | Placed: 1 |
| r1c2 | {4, 6, 7} |
| r1c3 | {4, 7} |
| r1c4 | Placed: 9 |
| r1c5 | {4, 5, 6, 7} |
| r1c6 | {4, 5, 6} |
| r1c7 | Placed: 3 |
| r1c8 | Placed: 2 |
| r1c9 | Placed: 8 |
| r2c1 | Placed: 5 |
| r2c2 | {4, 9} |
| r2c3 | {3, 4, 8, 9} |
| r2c4 | Placed: 2 |
| r2c5 | {3, 4, 8} |
| r2c6 | {4, 8} |
| r2c7 | Placed: 1 |
| r2c8 | Placed: 7 |
| r2c9 | Placed: 6 |
| r3c1 | Placed: 2 |
| r3c2 | {6, 7} |
| r3c3 | {3, 7, 8} |
| r3c4 | Placed: 1 |
| r3c5 | {3, 6, 7, 8} |
| r3c6 | {6, 8} |
| r3c7 | Placed: 9 |
| r3c8 | Placed: 5 |
| r3c9 | Placed: 4 |
| r4c1 | Placed: 9 |
| r4c2 | {4, 5} |
| r4c3 | {4, 5} |
| r4c4 | {6, 8} |
| r4c5 | {6, 8} |
| r4c6 | Placed: 2 |
| r4c7 | Placed: 7 |
| r4c8 | Placed: 3 |
| r4c9 | Placed: 1 |
| r5c1 | Placed: 7 |
| r5c2 | Placed: 8 |
| r5c3 | Placed: 1 |
| r5c4 | Placed: 5 |
| r5c5 | Placed: 9 |
| r5c6 | Placed: 3 |
| r5c7 | Placed: 6 |
| r5c8 | Placed: 4 |
| r5c9 | Placed: 2 |
| r6c1 | Placed: 3 |
| r6c2 | Placed: 2 |
| r6c3 | Placed: 6 |
| r6c4 | Placed: 4 |
| r6c5 | Placed: 1 |
| r6c6 | Placed: 7 |
| r6c7 | {5, 8} |
| r6c8 | {8, 9} |
| r6c9 | {5, 9} |
| r7c1 | {4, 6} |
| r7c2 | Placed: 3 |
| r7c3 | {5, 9} |
| r7c4 | {6, 8} |
| r7c5 | {2, 4, 5, 6, 8} |
| r7c6 | Placed: 1 |
| r7c7 | {2, 4, 5, 8} |
| r7c8 | {8, 9} |
| r7c9 | Placed: 7 |
| r8c1 | {4, 6} |
| r8c2 | {5, 7, 9} |
| r8c3 | Placed: 2 |
| r8c4 | {3, 6, 7, 8} |
| r8c5 | {4, 5, 6, 8} |
| r8c6 | {4, 5, 6, 8} |
| r8c7 | {4, 5, 8} |
| r8c8 | Placed: 1 |
| r8c9 | {3, 5, 9} |
| r9c1 | Placed: 8 |
| r9c2 | Placed: 1 |
| r9c3 | {5, 7} |
| r9c4 | {3, 7} |
| r9c5 | {2, 4, 5} |
| r9c6 | Placed: 9 |
| r9c7 | {2, 4, 5} |
| r9c8 | Placed: 6 |
| r9c9 | {3, 5} |
Try it yourself
Which action follows from this pattern? Check the candidates or reveal a hint.
Inspect r4c4 and r7c4. Follow these candidates: 6 and 8.
r4c4 and r7c4 share column 4, and each has exactly these candidates: 6 and 8. The two cells must use those digits in some order. Other cells in the unit cannot use either digit.
Candidates to remove
- Remove 6 from r8c4.
- Remove 8 from r8c4.
Compare techniques
A hidden pair starts with two digits confined to two cells, which may contain other candidates. A naked pair starts with two cells already restricted to two digits. The elimination targets are different.
Compare with hidden pairs