X-Wing in Sudoku: verify the four-corner pattern
Follow one digit across two rows. Do not stop at a rectangle shape: each starting row must have exactly two possible cells, and the two rows must use the same columns.
Definition
An X-Wing occurs when two rows restrict one digit to the same two columns, or two columns restrict it to the same two rows; that digit can be removed elsewhere in the crossing lines.
When to use it and what to verify
When to look for it
Choose one digit and find rows with exactly two candidate positions. Then look for a second row using the same two columns.
Required condition
The two base rows must each restrict the digit to the same two cover columns. The column-based form reverses rows and columns.
Common near miss
A rectangle is not enough. If either base row has a third position for the digit, the basic X-Wing proof does not hold.
Rows 2 and 8 restrict candidate 7 to columns 3 and 9.
- 1. Verify the first two-place rowRow 2 can place 7 only at R2C3 or R2C9.
- 2. Match the second rowRow 8 also places 7 only in columns 3 and 9. The rows must use opposite corners.
- 3. Clear the crossing columnsEach shared column receives one 7 from the pattern, so remove candidate 7 elsewhere in columns 3 and 9. Keep all four corners.
Rows 2 and 8 each place one 7 in columns 3 or 9. The placements occupy opposite corners, so every other candidate 7 in columns 3 and 9 is impossible.
A reference verified by Doku.su
Doku.su checks every placement or elimination in this example with its deterministic Sudoku engine. Illustrative candidates are labelled when they do not represent a complete puzzle state.
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