Looking only for cells with two candidates; Hidden Pairs are found by counting digit positions.
Sudoku technique · Candidate elimination
Hidden Pair
A Hidden Pair appears when two digits can occur in only the same two cells of a row, column, or box, even though those cells show other candidates.
Learning order
Topic relationships
These links express the same learning and proof relationships used throughout the library.
- Uses candidate language fromCandidate Notes
Verified example
Work through the example
R1C1: given 11 | R1C2: given 22 | R1C3: given 33 | R1C4: given 44 | R1C5: given 55 | R1C6: empty | R1C7: given 77 | R1C8: empty | R1C9: empty |
R2C1: given 44 | R2C2: given 55 | R2C3: given 66 | R2C4: given 77 | R2C5: empty | R2C6: empty | R2C7: given 11 | R2C8: empty | R2C9: given 33 |
R3C1: given 77 | R3C2: given 88 | R3C3: given 99 | R3C4: empty | R3C5: empty | R3C6: empty | R3C7: empty | R3C8: empty | R3C9: empty |
R4C1: empty | R4C2: given 33 | R4C3: given 44 | R4C4: given 55 | R4C5: empty | R4C6: given 77 | R4C7: empty | R4C8: empty | R4C9: empty |
R5C1: given 55 | R5C2: given 66 | R5C3: given 77 | R5C4: given 88 | R5C5: given 99 | R5C6: given 11 | R5C7: empty | R5C8: empty | R5C9: given 44 |
R6C1: empty | R6C2: given 99 | R6C3: given 11 | R6C4: empty | R6C5: empty | R6C6: empty | R6C7: given 55 | R6C8: empty | R6C9: given 77 |
R7C1: given 33 | R7C2: given 44 | R7C3: given 55 | R7C4: empty | R7C5: given 77 | R7C6: empty | R7C7: empty | R7C8: empty | R7C9: given 22 |
R8C1: given 66 | R8C2: given 77 | R8C3: given 88 | R8C4: empty | R8C5: empty | R8C6: empty | R8C7: empty; pattern cell; Before 3, 4 | R8C8: empty; pattern cell; candidate deletion 1, 5, 9; Before 1, 3, 4, 5, 9; After 3, 4 | R8C9: empty |
R9C1: given 99 | R9C2: given 11 | R9C3: given 22 | R9C4: given 33 | R9C5: empty | R9C6: empty | R9C7: given 66 | R9C8: given 77 | R9C9: empty |
Pattern cells: R8C7, R8C8. Remove 1, 5, 9 from R8C8.
- Pattern cells
- R8C7, R8C8
- Pattern digits
- 3, 4
- Reviewed unit
- Row 8
Exact candidate changes
- Remove 1, 5, 9 from R8C8Before: 1, 3, 4, 5, 9 → After: 3, 4
- Choose one unit and count the candidate positions for each missing digit.
- Find two digits whose only positions are the same two cells.
- Reserve those cells for the two digits without deciding their order.
- Remove every non-pair candidate from the two pattern cells.
Fixed practice
Count where each digit can go in one unit; compare location pairs rather than candidate-list lengths.
Fixed practice · R2C8
R1C1: given 11 | R1C2: empty | R1C3: given 33 | R1C4: given 44 | R1C5: empty | R1C6: given 66 | R1C7: empty | R1C8: given 88 | R1C9: given 99 |
R2C1: empty | R2C2: empty | R2C3: empty | R2C4: empty | R2C5: empty | R2C6: given 99 | R2C7: given 11 | R2C8: empty; pattern cell; candidate deletion 4, 7; Before 2, 3, 4, 7; After 2, 3 | R2C9: empty |
R3C1: empty | R3C2: given 88 | R3C3: empty | R3C4: given 11 | R3C5: empty | R3C6: given 33 | R3C7: empty | R3C8: given 55 | R3C9: given 66 |
R4C1: empty | R4C2: empty | R4C3: given 44 | R4C4: empty | R4C5: given 66 | R4C6: empty | R4C7: empty | R4C8: given 99 | R4C9: empty |
R5C1: given 55 | R5C2: empty | R5C3: given 77 | R5C4: empty | R5C5: empty | R5C6: empty | R5C7: empty | R5C8: empty; pattern cell; candidate deletion 4, 6; Before 2, 3, 4, 6; After 2, 3 | R5C9: empty |
R6C1: empty | R6C2: empty | R6C3: empty | R6C4: given 22 | R6C5: given 33 | R6C6: empty | R6C7: empty | R6C8: empty | R6C9: given 77 |
R7C1: given 33 | R7C2: given 44 | R7C3: given 55 | R7C4: given 66 | R7C5: empty | R7C6: empty | R7C7: empty | R7C8: given 11 | R7C9: given 22 |
R8C1: empty | R8C2: empty | R8C3: empty | R8C4: empty | R8C5: empty | R8C6: empty | R8C7: given 33 | R8C8: empty | R8C9: empty |
R9C1: empty | R9C2: empty | R9C3: empty | R9C4: given 33 | R9C5: given 44 | R9C6: empty | R9C7: empty | R9C8: empty | R9C9: given 88 |
Pattern cells: R2C8, R5C8. Remove 4, 7 from R2C8; Remove 4, 6 from R5C8.
- Pattern cells
- R2C8, R5C8
- Pattern digits
- 2, 3
- Reviewed unit
- Column 8
Exact candidate changes
- Remove 4, 7 from R2C8Before: 2, 3, 4, 7 → After: 2, 3
- Remove 4, 6 from R5C8Before: 2, 3, 4, 6 → After: 2, 3
Common mistakes
Common mistakes
Removing the pair digits from other cells instead of removing extra digits from the pair cells.
Review information
What is verified here
The independent verifier recomputes both digits’ only positions, the two exact pattern cells, and every non-pair candidate removed from those cells.
- Fixture ID
- p3b-hidden-pair-row-01 / p3b-hidden-pair-column-01
- Engine version
- legen-sudoku-engine/1.3.0
- Verification status
- Independent candidate-elimination verifier passed
- Facts reviewed
- 2026-07-18
Technique terminology and examples are tied to the published engine version. See the review information below for scope and dates.