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Hidden pairs
Two digits with the same two possible cells.
Look for two digits that can go only in the same two cells of a row, column or box. Those cells may still contain other candidates.
When to use it
When two digits each appear as candidates in exactly the same two cells of a unit, those cells must contain those two digits. Remove every other candidate from those cells. This rule does not remove the pair’s digits from unrelated cells outside that unit.
How to find it
- 01
Choose a unit and find a digit with exactly two possible positions.
- 02
Find another digit whose only positions in that unit are those same two cells.
- 03
Keep those two digits in both cells; delete their other candidates.
Worked example
v1-expert-0002 · position before step 28
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, 7} |
| 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} |
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 r9c5 and r9c7. Follow these candidates: 2 and 4.
In row 9, each of the digits 2 and 4 can appear only in r9c5 and r9c7. Both cells are needed for those two digits, so their other candidates can be removed. The extra candidates inside the cells do not give those digits another place in the unit.
Candidates to remove
- Remove 5 from r9c5.
- Remove 5 from r9c7.
When the rule does not apply
In row 4, digit 3 can go only in c2 or c7, but digit 6 can go in c2, c7 or c9. The two shared positions do not form a hidden pair because 6 is not confined to them. Removing other candidates from c2 and c7 could delete a correct answer.
Do these positions establish a hidden pair of 3 and 6 in r4c2 and r4c7?
Show why
No. Digit 6 has a third possible position at r4c9. Both digits must be confined to the same two cells in the chosen unit.
Try another position
Try the technique on another puzzle.
v1-expert-0003 · position before step 18
View the cell table
| Cell | Value / candidates |
|---|---|
| r1c1 | {1, 5} |
| r1c2 | Placed: 7 |
| r1c3 | Placed: 8 |
| r1c4 | {1, 4, 6, 9} |
| r1c5 | {1, 4, 5} |
| r1c6 | Placed: 3 |
| r1c7 | Placed: 2 |
| r1c8 | {5, 6} |
| r1c9 | {5, 9} |
| r2c1 | {1, 3, 5} |
| r2c2 | Placed: 2 |
| r2c3 | Placed: 9 |
| r2c4 | {1, 6, 7} |
| r2c5 | Placed: 8 |
| r2c6 | {1, 6, 7} |
| r2c7 | {3, 7} |
| r2c8 | {3, 5, 6} |
| r2c9 | Placed: 4 |
| r3c1 | {3, 5} |
| r3c2 | Placed: 4 |
| r3c3 | Placed: 6 |
| r3c4 | {2, 7, 9} |
| r3c5 | {5, 7} |
| r3c6 | {2, 7, 9} |
| r3c7 | Placed: 1 |
| r3c8 | {3, 5, 8} |
| r3c9 | {3, 5, 7, 8, 9} |
| r4c1 | Placed: 7 |
| r4c2 | {1, 3, 5, 9} |
| r4c3 | {1, 5} |
| r4c4 | Placed: 8 |
| r4c5 | {1, 3} |
| r4c6 | {1, 2, 9} |
| r4c7 | Placed: 6 |
| r4c8 | Placed: 4 |
| r4c9 | {1, 2, 3} |
| r5c1 | {6, 8} |
| r5c2 | {1, 3, 8} |
| r5c3 | Placed: 2 |
| r5c4 | {1, 4, 6, 7} |
| r5c5 | {1, 3, 4, 7} |
| r5c6 | {1, 4, 6, 7} |
| r5c7 | Placed: 5 |
| r5c8 | Placed: 9 |
| r5c9 | {1, 3, 7, 8} |
| r6c1 | {6, 8, 9} |
| r6c2 | {1, 3, 8, 9} |
| r6c3 | Placed: 4 |
| r6c4 | {1, 2, 6, 7, 9} |
| r6c5 | {1, 3, 7} |
| r6c6 | Placed: 5 |
| r6c7 | {3, 7} |
| r6c8 | {1, 2, 3, 8} |
| r6c9 | {1, 2, 3, 7, 8} |
| r7c1 | {4, 8} |
| r7c2 | Placed: 6 |
| r7c3 | Placed: 3 |
| r7c4 | {1, 5, 7} |
| r7c5 | Placed: 9 |
| r7c6 | {1, 7} |
| r7c7 | {4, 8} |
| r7c8 | {1, 2, 5} |
| r7c9 | {1, 2, 5} |
| r8c1 | Placed: 2 |
| r8c2 | {1, 9} |
| r8c3 | Placed: 7 |
| r8c4 | {1, 4, 5} |
| r8c5 | Placed: 6 |
| r8c6 | Placed: 8 |
| r8c7 | {4, 9} |
| r8c8 | {1, 3, 5} |
| r8c9 | {1, 3, 5} |
| r9c1 | {4, 8, 9} |
| r9c2 | {1, 5, 8, 9} |
| r9c3 | {1, 5} |
| r9c4 | Placed: 3 |
| r9c5 | Placed: 2 |
| r9c6 | {1, 4} |
| r9c7 | {4, 8, 9} |
| r9c8 | Placed: 7 |
| r9c9 | Placed: 6 |
Try it yourself
Which action follows from this pattern? Check the candidates or reveal a hint.
Inspect r3c6 and r4c6. Follow these candidates: 2 and 9.
In column 6, each of the digits 2 and 9 can appear only in r3c6 and r4c6. Both cells are needed for those two digits, so their other candidates can be removed. The extra candidates inside the cells do not give those digits another place in the unit.
Candidates to remove
- Remove 7 from r3c6.
- Remove 1 from r4c6.
Compare techniques
After a hidden-pair elimination, the two cells become a naked pair. The starting evidence differs: a hidden pair is a restriction on where digits appear, not a short candidate list you can spot in isolation.
Compare with naked pairs