X-Wing Technique in Sudoku: Multi-Line Elimination Guide
What is an X-Wing?
An X-Wing is a powerful multi-line candidate pattern that spans across two parallel rows and two intersecting columns (or vice versa).
When a specific candidate digit appears in exactly two cells in Row A, and in the exact same two columns in Row B:
- Because each row must contain that digit, one row will take the left column while the other row takes the right column (or vice versa).
- These two diagonal possibilities form an “X” shape.
- Either way, both columns are guaranteed to have their digit placed in one of those two rows.
- Therefore, that digit cannot appear anywhere else in those two columns!
Worked Example: X-Wing on Digit 4 Eliminates 4 from Cell R6C3
Observe digit 4 across Row 5 and Row 8 on the board below:
- Row 5: Candidate 4 can only be placed in two columns: Column 3 (R5C3) and Column 7 (R5C7).
- Row 8: Candidate 4 can also only be placed in the exact same two columns: Column 3 (R8C3) and Column 7 (R8C7).
- The Rectangular Lock: If Row 5 places 4 at R5C3, then Row 8 must place 4 at R8C7. If Row 5 places 4 at R5C7, then Row 8 must place 4 at R8C3. In both outcomes, Column 3 and Column 7 have their 4s locked into Row 5 and Row 8!
- Target Elimination at R6C3: Follow Column 3 down to cell Row 6, Column 3 (R6C3). This cell has candidates
{2, 4}. Because the X-Wing claims Column 3's 4, candidate 4 is eliminated from R6C3, leaving 2 as a Naked Single!
⚠️ The Tempting Wrong Move: Placing 4 in R6C3
A player searching for a place to put 4 in Column 3 might guess 4 in R6C3 because the cell only has two candidates {2, 4}.
Why this fails: Placing 4 in R6C3 eliminates 4 from both R5C3 and R8C3 along Column 3. This forces Row 5 to place 4 at R5C7, and Row 8 to place 4 at R8C7. That puts two 4s directly in Column 7, causing an immediate, fatal contradiction!
💡 Solving Tip: The Fish Pattern Finder
X-Wing is the smallest member of the “Fish” family (where N parallel lines hold a candidate in the same N perpendicular lines). When you hit an advanced deadlock, pick one digit at a time and highlight all rows that have exactly two candidate cells for that digit. If two rows share the same two columns, you have found an X-Wing!
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