Requiring all three digits to have identical position lists; only their combined union must be the same three cells.
Sudoku technique · Candidate elimination
Hidden Triple
A Hidden Triple appears when three digits each have at least one candidate position in a row, column, or box and the union of all their positions is exactly the same three cells.
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: empty | R1C3: given 99 | R1C4: given 77 | R1C5: empty | R1C6: given 11 | R1C7: empty | R1C8: empty | R1C9: empty |
R2C1: empty | R2C2: empty | R2C3: empty | R2C4: given 99 | R2C5: empty | R2C6: given 44 | R2C7: empty | R2C8: given 55 | R2C9: empty |
R3C1: given 88 | R3C2: empty; pattern cell; candidate deletion 2, 6; Before 1, 2, 4, 6, 7; After 1, 4, 7 | R3C3: empty | R3C4: empty | R3C5: empty | R3C6: empty | R3C7: given 99 | R3C8: empty; pattern cell; candidate deletion 2, 3, 6; Before 1, 2, 3, 6, 7; After 1, 7 | R3C9: empty; pattern cell; candidate deletion 2, 3; Before 1, 2, 3, 4, 7; After 1, 4, 7 |
R4C1: given 44 | R4C2: given 33 | R4C3: empty | R4C4: empty | R4C5: empty | R4C6: given 99 | R4C7: empty | R4C8: empty | R4C9: empty |
R5C1: empty | R5C2: empty | R5C3: empty | R5C4: empty | R5C5: empty | R5C6: empty | R5C7: given 66 | R5C8: empty | R5C9: given 99 |
R6C1: empty | R6C2: empty | R6C3: given 11 | R6C4: given 88 | R6C5: given 77 | R6C6: empty | R6C7: empty | R6C8: empty | R6C9: empty |
R7C1: empty | R7C2: empty | R7C3: given 55 | R7C4: empty | R7C5: empty | R7C6: empty | R7C7: empty | R7C8: given 44 | R7C9: empty |
R8C1: given 33 | R8C2: empty | R8C3: given 77 | R8C4: empty | R8C5: empty | R8C6: given 22 | R8C7: empty | R8C8: empty | R8C9: given 55 |
R9C1: empty | R9C2: empty | R9C3: given 44 | R9C4: empty | R9C5: given 55 | R9C6: empty | R9C7: given 22 | R9C8: empty | R9C9: given 66 |
Pattern cells: R3C2, R3C8, R3C9. Remove 2, 6 from R3C2; Remove 2, 3, 6 from R3C8; Remove 2, 3 from R3C9.
- Pattern cells
- R3C2, R3C8, R3C9
- Pattern digits
- 1, 4, 7
- Reviewed unit
- Row 3
Exact candidate changes
- Remove 2, 6 from R3C2Before: 1, 2, 4, 6, 7 → After: 1, 4, 7
- Remove 2, 3, 6 from R3C8Before: 1, 2, 3, 6, 7 → After: 1, 7
- Remove 2, 3 from R3C9Before: 1, 2, 3, 4, 7 → After: 1, 4, 7
- Choose one unit and map the candidate positions of each missing digit.
- Find three digits whose combined candidate positions occupy exactly three cells.
- Reserve those cells for the three digits without deciding which digit goes where.
- Remove only the non-triple candidates from those three pattern cells.
Fixed practice
Count positions by digit, then combine three position lists and check that their union is exactly three cells.
Fixed practice · R2C7
R1C1: given 33 | R1C2: given 88 | R1C3: given 55 | R1C4: given 66 | R1C5: empty | R1C6: given 11 | R1C7: empty | R1C8: empty | R1C9: empty |
R2C1: given 11 | R2C2: empty | R2C3: given 99 | R2C4: given 55 | R2C5: empty | R2C6: empty | R2C7: empty; pattern cell; candidate deletion 2, 4, 7; Before 2, 3, 4, 6, 7, 8; After 3, 6, 8 | R2C8: empty | R2C9: empty; pattern cell; candidate deletion 4, 7; Before 3, 4, 6, 7, 8; After 3, 6, 8 |
R3C1: empty | R3C2: given 22 | R3C3: empty | R3C4: empty | R3C5: given 33 | R3C6: empty | R3C7: given 55 | R3C8: given 11 | R3C9: empty; pattern cell; candidate deletion 4, 7, 9; Before 4, 6, 7, 8, 9; After 6, 8 |
R4C1: empty | R4C2: empty | R4C3: empty | R4C4: empty | R4C5: empty | R4C6: given 55 | R4C7: empty | R4C8: empty | R4C9: empty |
R5C1: empty | R5C2: given 33 | R5C3: empty | R5C4: empty | R5C5: given 11 | R5C6: empty | R5C7: empty | R5C8: given 66 | R5C9: empty |
R6C1: empty | R6C2: empty | R6C3: empty | R6C4: given 44 | R6C5: empty | R6C6: empty | R6C7: empty | R6C8: empty | R6C9: empty |
R7C1: empty | R7C2: given 11 | R7C3: given 77 | R7C4: empty | R7C5: given 55 | R7C6: empty | R7C7: empty | R7C8: given 88 | R7C9: empty |
R8C1: empty | R8C2: empty | R8C3: given 33 | R8C4: given 11 | R8C5: empty | R8C6: empty | R8C7: given 99 | R8C8: empty | R8C9: empty |
R9C1: empty | R9C2: empty | R9C3: empty | R9C4: empty | R9C5: empty | R9C6: given 77 | R9C7: given 11 | R9C8: given 33 | R9C9: given 22 |
Pattern cells: R2C7, R2C9, R3C9. Remove 2, 4, 7 from R2C7; Remove 4, 7 from R2C9; Remove 4, 7, 9 from R3C9.
- Pattern cells
- R2C7, R2C9, R3C9
- Pattern digits
- 3, 6, 8
- Reviewed unit
- Box 3
Exact candidate changes
- Remove 2, 4, 7 from R2C7Before: 2, 3, 4, 6, 7, 8 → After: 3, 6, 8
- Remove 4, 7 from R2C9Before: 3, 4, 6, 7, 8 → After: 3, 6, 8
- Remove 4, 7, 9 from R3C9Before: 4, 6, 7, 8, 9 → After: 6, 8
Common mistakes
Common mistakes
Removing the triple digits from other cells instead of removing extra candidates only from the pattern cells.
Review information
What is verified here
The independent verifier recomputes each digit’s non-empty position set, confirms that their union is the exact three pattern cells, and checks every extra candidate removed only from those cells.
- Fixture ID
- p3c-hidden-triple-row-01 / p3c-hidden-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.