Lesson:X-Wing
An X-Wing happens when a candidate appears exactly twice in two rows, and they align in the same two columns.
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💾 Saved locallyAbout This Lesson
X-Wing is the simplest and most well-known of the "fish" family of Sudoku techniques. Named for the X-shaped pattern of cells it uses, X-Wing enables powerful candidate eliminations across an entire row or column by exploiting the alignment of a single candidate digit in exactly two rows and two columns.
The core idea: if a candidate digit appears in exactly two cells in each of two different rows, and those pairs of cells align in the same two columns, then regardless of which cells ultimately receive the digit (there are two possible arrangements), the digit must appear in those two columns. This means the digit cannot appear anywhere else in those two columns. Every other candidate occurrence of that digit in those columns can be eliminated.
X-Wing is typically the first advanced technique that intermediate solvers learn, and it opens the door to the broader world of fish patterns (Swordfish, Jellyfish) and chain-based reasoning (Coloring, AICs).
How It Works — Step by Step
Step 1 — Find rows where the digit appears in exactly two columns
Scan all rows for a chosen digit. Identify every row where the digit appears in exactly two cells. Note which two columns those cells occupy.
Step 2 — Find a matching pair of rows
Look for two rows where the digit appears in the same two columns. For example, digit 6 appears in columns 3 and 7 in both Row 2 and Row 8. These two rows and two columns form the X-Wing.
Step 3 — Eliminate from the two columns
In the two identified columns (3 and 7 in the example), eliminate the digit from every cell that is NOT in one of the two base rows (2 and 8). The digit in those columns must land in the base row cells.
Step 4 — Check for column-based X-Wings
X-Wing can also be found column-first: if a digit appears in exactly two cells in each of two columns, and those cells align in the same two rows, eliminate the digit from those two rows (excluding the four X-Wing cells).
When to Use This Technique
After Naked and Hidden Singles, Pointing Pairs, Box-Line Reduction, and Naked/Hidden Pairs. X-Wing is most productive when a digit has many candidates spread across the board but its row-based or column-based distribution shows the two-in-two-columns pattern.
Worked Examples
Digit 9 appears only in Column 1 and Column 6 in Row 3. It also appears only in Column 1 and Column 6 in Row 7. X-Wing! In Column 1, eliminate 9 from every row except 3 and 7. In Column 6, eliminate 9 from every row except 3 and 7. This may immediately reveal Hidden Singles in those columns.
Frequently Asked Questions
What if the digit appears in three columns in one of the rows?
A three-column row cannot participate in an X-Wing — the digit must appear in exactly two columns in each base row. However, it could participate in a Swordfish (three rows, three columns).
Is X-Wing a special case of Coloring?
Yes. An X-Wing can be fully explained by Coloring — the four X-Wing cells form two conjugate pairs (one per row), and the alternating color deduction proves the eliminations. X-Wing notation is simply more concise for this specific pattern.
Related Lessons
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