Calling the shape an X-Wing when either base line has a third position for the digit or the two pairs use different cover lines.
Sudoku technique · Candidate elimination
X-Wing
An X-Wing appears when one digit has candidates in exactly two cells in each of two base rows or columns, and those four cells lie on the same two crossing columns or rows.
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 44 | R1C2: empty | R1C3: empty | R1C4: empty | R1C5: empty | R1C6: given 55 | R1C7: empty; candidate deletion 8; Before 1, 2, 8; After 1, 2 | R1C8: empty | R1C9: empty |
R2C1: empty | R2C2: given 88 | R2C3: empty | R2C4: empty | R2C5: given 22 | R2C6: empty | R2C7: given 77 | R2C8: given 66 | R2C9: given 44 |
R3C1: given 22 | R3C2: empty | R3C3: empty | R3C4: empty | R3C5: given 44 | R3C6: empty; Base/cover candidate; Before 1, 7, 8 | R3C7: empty; Base/cover candidate; Before 1, 8 | R3C8: given 55 | R3C9: given 99 |
R4C1: given 77 | R4C2: empty | R4C3: empty | R4C4: given 44 | R4C5: given 33 | R4C6: empty | R4C7: given 55 | R4C8: given 88 | R4C9: given 11 |
R5C1: empty | R5C2: empty | R5C3: empty | R5C4: given 88 | R5C5: empty | R5C6: given 66 | R5C7: given 44 | R5C8: empty | R5C9: empty |
R6C1: given 88 | R6C2: empty | R6C3: empty | R6C4: empty | R6C5: empty | R6C6: empty | R6C7: given 33 | R6C8: empty | R6C9: given 66 |
R7C1: given 66 | R7C2: empty | R7C3: given 88 | R7C4: empty | R7C5: given 11 | R7C6: given 44 | R7C7: empty | R7C8: empty | R7C9: empty |
R8C1: given 33 | R8C2: empty | R8C3: empty | R8C4: given 22 | R8C5: given 66 | R8C6: empty; Base/cover candidate; Before 8, 9 | R8C7: empty; Base/cover candidate; Before 8, 9 | R8C8: given 11 | R8C9: given 55 |
R9C1: given 11 | R9C2: given 99 | R9C3: empty | R9C4: empty | R9C5: empty | R9C6: given 33 | R9C7: given 66 | R9C8: given 44 | R9C9: empty |
- Base/cover candidate: 8
Pattern cells: R3C6, R3C7, R8C6, R8C7. Remove 8 from R1C7.
- Pattern cells
- R3C6, R3C7, R8C6, R8C7
- Pattern digits
- 8
- Orientation
- Row-based
- Base lines
- Row 3, Row 8
- Cover lines
- Column 6, Column 7
Exact candidate changes
- Remove 8 from R1C7Before: 1, 2, 8 → After: 1, 2
- Choose one digit and compare the complete candidate positions in pairs of rows, then pairs of columns.
- Find two base lines where the digit appears in exactly two cells and both pairs use the same two cover lines.
- Keep all four pattern candidates because the digit can occupy either diagonal of the rectangle.
- Remove only that digit from the cover lines outside the two base lines.
Fixed practice
Track one digit at a time and write down every position in each possible base line before comparing the two cover lines.
Fixed practice · R1C5
R1C1: given 44 | R1C2: given 11 | R1C3: given 66 | R1C4: given 99 | R1C5: empty; Base/cover candidate; Before 3, 7 | R1C6: given 55 | R1C7: given 22 | R1C8: empty | R1C9: empty; Base/cover candidate; Before 7, 8 |
R2C1: given 99 | R2C2: given 88 | R2C3: given 55 | R2C4: empty | R2C5: given 22 | R2C6: given 11 | R2C7: empty | R2C8: given 66 | R2C9: given 44 |
R3C1: empty | R3C2: empty | R3C3: empty | R3C4: given 66 | R3C5: given 44 | R3C6: given 88 | R3C7: given 11 | R3C8: given 55 | R3C9: given 99 |
R4C1: empty | R4C2: empty | R4C3: empty | R4C4: given 44 | R4C5: empty | R4C6: given 22 | R4C7: given 55 | R4C8: empty | R4C9: empty |
R5C1: given 55 | R5C2: empty | R5C3: empty | R5C4: empty | R5C5: empty | R5C6: given 66 | R5C7: given 44 | R5C8: given 77 | R5C9: empty |
R6C1: empty | R6C2: empty | R6C3: given 44 | R6C4: empty | R6C5: empty | R6C6: given 77 | R6C7: empty | R6C8: empty | R6C9: given 66 |
R7C1: empty | R7C2: empty | R7C3: empty | R7C4: empty | R7C5: given 11 | R7C6: given 44 | R7C7: given 99 | R7C8: empty | R7C9: given 33 |
R8C1: given 33 | R8C2: given 44 | R8C3: empty | R8C4: given 22 | R8C5: given 66 | R8C6: given 99 | R8C7: empty | R8C8: empty | R8C9: given 55 |
R9C1: empty; candidate deletion 7; Before 1, 2, 7, 8; After 1, 2, 8 | R9C2: empty; candidate deletion 7; Before 2, 5, 7, 9; After 2, 5, 9 | R9C3: empty; candidate deletion 7; Before 1, 2, 7, 8, 9; After 1, 2, 8, 9 | R9C4: empty; candidate deletion 7; Before 5, 7, 8; After 5, 8 | R9C5: empty; Base/cover candidate; Before 5, 7, 8 | R9C6: given 33 | R9C7: given 66 | R9C8: given 44 | R9C9: empty; Base/cover candidate; Before 1, 2, 7, 8 |
- Base/cover candidate: 7
Pattern cells: R1C5, R1C9, R9C5, R9C9. Remove 7 from R9C1; Remove 7 from R9C2; Remove 7 from R9C3; Remove 7 from R9C4.
- Pattern cells
- R1C5, R1C9, R9C5, R9C9
- Pattern digits
- 7
- Orientation
- Column-based
- Base lines
- Column 5, Column 9
- Cover lines
- Row 1, Row 9
Exact candidate changes
- Remove 7 from R9C1Before: 1, 2, 7, 8 → After: 1, 2, 8
- Remove 7 from R9C2Before: 2, 5, 7, 9 → After: 2, 5, 9
- Remove 7 from R9C3Before: 1, 2, 7, 8, 9 → After: 1, 2, 8, 9
- Remove 7 from R9C4Before: 5, 7, 8 → After: 5, 8
Common mistakes
Common mistakes
Removing the digit from a pattern cell, from outside the two cover lines, or from a cell on one of the base lines.
Review information
What is verified here
The independent verifier recomputes the chosen digit’s exact positions, the row-based or column-based orientation, both base and cover lines, and the complete ordered deletion list.
- Fixture ID
- p3d-x-wing-row-01 / p3d-x-wing-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.