Requiring all three candidate lists to be identical; valid lists can be different non-empty subsets whose union is three digits.
Sudoku technique · Candidate elimination
Naked Triple
A Naked Triple is three cells in one row, column, or box whose non-empty candidate sets are all subsets of the same three digits and whose combined union is exactly those three 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: empty | R1C2: given 11 | R1C3: given 66 | R1C4: empty | R1C5: empty | R1C6: empty | R1C7: given 22 | R1C8: empty | R1C9: empty |
R2C1: given 99 | R2C2: given 88 | R2C3: empty | R2C4: empty | R2C5: empty | R2C6: empty | R2C7: empty | R2C8: given 66 | R2C9: empty |
R3C1: empty; pattern cell; Before 2, 4, 7 | R3C2: empty; pattern cell; Before 2, 7 | R3C3: empty; candidate deletion 4; Before 3, 4; After 3 | R3C4: given 66 | R3C5: empty; pattern cell; Before 4, 7 | R3C6: empty | R3C7: empty; candidate deletion 4, 7; Before 1, 3, 4, 7, 9; After 1, 3, 9 | R3C8: given 55 | R3C9: empty; candidate deletion 4; Before 1, 4, 8, 9; After 1, 8, 9 |
R4C1: empty | R4C2: empty | R4C3: given 99 | R4C4: given 44 | R4C5: given 33 | R4C6: empty | R4C7: empty | R4C8: empty | R4C9: empty |
R5C1: empty | R5C2: given 33 | R5C3: empty | R5C4: empty | R5C5: given 99 | R5C6: given 66 | R5C7: empty | R5C8: empty | R5C9: empty |
R6C1: empty | R6C2: empty | R6C3: empty | R6C4: empty | R6C5: empty | R6C6: given 77 | R6C7: empty | R6C8: empty | R6C9: empty |
R7C1: empty | R7C2: empty | R7C3: empty | R7C4: given 77 | R7C5: given 11 | R7C6: given 44 | R7C7: empty | R7C8: given 22 | R7C9: given 33 |
R8C1: given 33 | R8C2: empty | R8C3: given 77 | R8C4: empty | R8C5: given 66 | R8C6: empty | R8C7: given 88 | R8C8: empty | R8C9: empty |
R9C1: given 11 | R9C2: empty | R9C3: given 22 | R9C4: given 55 | R9C5: given 88 | R9C6: given 33 | R9C7: given 66 | R9C8: empty | R9C9: given 77 |
Pattern cells: R3C1, R3C2, R3C5. Remove 4 from R3C3; Remove 4, 7 from R3C7; Remove 4 from R3C9.
- Pattern cells
- R3C1, R3C2, R3C5
- Pattern digits
- 2, 4, 7
- Reviewed unit
- Row 3
Exact candidate changes
- Remove 4 from R3C3Before: 3, 4 → After: 3
- Remove 4, 7 from R3C7Before: 1, 3, 4, 7, 9 → After: 1, 3, 9
- Remove 4 from R3C9Before: 1, 4, 8, 9 → After: 1, 8, 9
- Inspect one row, column, or box and compare groups of three empty cells.
- Confirm that every candidate in those cells belongs to the same three digits and that all three digits appear across the group.
- Reserve the three digits for the three pattern cells without guessing their order.
- Remove those digits only from the other cells in the same unit.
Fixed practice
Take the union of three candidate lists: it must contain exactly three digits, even when the individual lists differ.
Fixed practice · R4C9
R1C1: given 99 | R1C2: given 66 | R1C3: given 77 | R1C4: given 11 | R1C5: given 44 | R1C6: empty | R1C7: given 33 | R1C8: empty | R1C9: given 88 |
R2C1: given 11 | R2C2: given 33 | R2C3: empty | R2C4: empty | R2C5: empty | R2C6: empty | R2C7: empty | R2C8: given 66 | R2C9: empty |
R3C1: given 55 | R3C2: given 22 | R3C3: empty | R3C4: empty | R3C5: given 66 | R3C6: given 33 | R3C7: empty | R3C8: empty | R3C9: given 11 |
R4C1: empty | R4C2: given 44 | R4C3: given 99 | R4C4: empty | R4C5: empty | R4C6: given 66 | R4C7: empty; candidate deletion 5, 7; Before 1, 2, 5, 7, 8; After 1, 2, 8 | R4C8: empty; candidate deletion 5, 7; Before 1, 2, 3, 5, 7; After 1, 2, 3 | R4C9: empty; pattern cell; Before 5, 7 |
R5C1: empty | R5C2: given 11 | R5C3: given 55 | R5C4: empty | R5C5: empty | R5C6: empty | R5C7: empty; candidate deletion 4, 7; Before 2, 4, 7, 8; After 2, 8 | R5C8: given 99 | R5C9: given 66 |
R6C1: given 22 | R6C2: given 88 | R6C3: given 66 | R6C4: empty | R6C5: empty | R6C6: given 11 | R6C7: empty; pattern cell; Before 4, 5, 7 | R6C8: empty; candidate deletion 4, 5, 7; Before 3, 4, 5, 7; After 3 | R6C9: empty; pattern cell; Before 4, 5, 7 |
R7C1: given 44 | R7C2: given 77 | R7C3: given 22 | R7C4: given 55 | R7C5: given 11 | R7C6: given 99 | R7C7: given 66 | R7C8: given 88 | R7C9: given 33 |
R8C1: given 66 | R8C2: given 55 | R8C3: given 33 | R8C4: given 22 | R8C5: given 88 | R8C6: given 44 | R8C7: empty | R8C8: empty | R8C9: empty |
R9C1: given 88 | R9C2: given 99 | R9C3: given 11 | R9C4: given 66 | R9C5: given 33 | R9C6: given 77 | R9C7: empty | R9C8: empty | R9C9: given 22 |
Pattern cells: R4C9, R6C7, R6C9. Remove 5, 7 from R4C7; Remove 5, 7 from R4C8; Remove 4, 7 from R5C7; Remove 4, 5, 7 from R6C8.
- Pattern cells
- R4C9, R6C7, R6C9
- Pattern digits
- 4, 5, 7
- Reviewed unit
- Box 6
Exact candidate changes
- Remove 5, 7 from R4C7Before: 1, 2, 5, 7, 8 → After: 1, 2, 8
- Remove 5, 7 from R4C8Before: 1, 2, 3, 5, 7 → After: 1, 2, 3
- Remove 4, 7 from R5C7Before: 2, 4, 7, 8 → After: 2, 8
- Remove 4, 5, 7 from R6C8Before: 3, 4, 5, 7 → After: 3
Common mistakes
Common mistakes
Including a pattern cell with a fourth candidate, or deleting any of the three digits from the pattern cells themselves.
Review information
What is verified here
The independent verifier recomputes the canonical three cells, checks that their non-empty candidate subsets unite to the exact three digits, and verifies every deletion from the unit’s other cells.
- Fixture ID
- p3c-naked-triple-row-01 / p3c-naked-triple-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.