Treating two overlapping candidate lists as a pair when one cell contains a third candidate.
Sudoku technique · Candidate elimination
Naked Pair
A Naked Pair is two cells in one row, column, or box whose complete candidate sets are the same two digits.
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; pattern cell; Before 8, 9 | 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; pattern cell; Before 8, 9 | R7C8: empty | R7C9: given 22 |
R8C1: given 66 | R8C2: given 77 | R8C3: given 88 | R8C4: empty | R8C5: empty | R8C6: empty | R8C7: empty; candidate deletion 9; Before 3, 4, 9; After 3, 4 | R8C8: empty | 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: R4C7, R7C7. Remove 9 from R8C7.
- Pattern cells
- R4C7, R7C7
- Pattern digits
- 8, 9
- Reviewed unit
- Column 7
Exact candidate changes
- Remove 9 from R8C7Before: 3, 4, 9 → After: 3, 4
- Inspect one row, column, or box for cells with exactly two candidates.
- Find two cells whose complete candidate sets match exactly.
- Reserve both digits for those two cells without deciding which digit goes where.
- Remove the pair digits only from the other cells in that same unit.
Fixed practice
Compare complete two-digit candidate sets, then scan only the rest of their shared unit for deletions.
Fixed practice · R4C5
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; pattern cell; Before 2, 6 | 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; pattern cell; Before 2, 6 | R6C5: empty; candidate deletion 2, 6; Before 2, 3, 4, 6; After 3, 4 | R6C6: empty; candidate deletion 2, 6; Before 2, 3, 4, 6; After 3, 4 | 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 | R8C8: empty | 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: R4C5, R6C4. Remove 2, 6 from R6C5; Remove 2, 6 from R6C6.
- Pattern cells
- R4C5, R6C4
- Pattern digits
- 2, 6
- Reviewed unit
- Box 5
Exact candidate changes
- Remove 2, 6 from R6C5Before: 2, 3, 4, 6 → After: 3, 4
- Remove 2, 6 from R6C6Before: 2, 3, 4, 6 → After: 3, 4
Common mistakes
Common mistakes
Removing either pair digit from the two pattern cells themselves.
Review information
What is verified here
The independent verifier checks the two exact pattern cells, their identical two-digit masks, their shared unit, and the complete ordered deletion list.
- Fixture ID
- p3b-naked-pair-column-01 / p3b-naked-pair-box-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.