X-Wing
An X-Wing is a pattern of one digit and four cells at the corners of a rectangle. If the digit has exactly two candidate cells in each of two rows, and those cells lie in the same two columns, then the digit must occupy two opposite corners of the rectangle. It can therefore be removed from every other cell of those two columns. The same works with rows and columns swapped. It is the first Expert technique in Bare Sudoku.
When to use it
When singles, locked candidates and subsets are exhausted. X-Wings are the most common Expert pattern and often appear when a digit has few candidates left, typically with four to six copies already placed. They need complete notes for the digit you examine.
How to spot it
Choose a digit and look for rows in which it has exactly two candidate cells. If two such rows share the same two columns, check those columns for other candidates of the digit: those are the eliminations. Then repeat with columns as the base. In the game, tap the digit key: every candidate for it is highlighted, and a rectangle of four highlighted notes is easy to see.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 38 | 68 | 368 | 9 | 1 | 2 | 4 | 7 | 5 |
| r2 | 1 | 4 | 9 | 7 | 5 | 8 | 2 | 6 | 3 |
| r3 | 2 | 5 | 7 | 346 | 346 | 46 | 1 | 8 | 9 |
| r4 | 4 | 2678 | 168 | 12346 | 346 | 9 | 37 | 5 | 14 |
| r5 | 9 | 28 | 5 | 1234 | 7 | 14 | 6 | 134 | 148 |
| r6 | 47 | 3 | 16 | 8 | 46 | 5 | 9 | 2 | 147 |
| r7 | 6 | 78 | 38 | 14 | 9 | 147 | 5 | 134 | 2 |
| r8 | 57 | 1 | 4 | 56 | 2 | 3 | 8 | 9 | 67 |
| r9 | 35 | 9 | 2 | 1456 | 8 | 1467 | 37 | 134 | 146 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- Digit 7 has exactly two candidate cells in row 6 and exactly two in row 8, and they line up in the same two columns, 1 and 9: r6c1, r6c9, r8c1, r8c9.
- Row 6 puts its 7 in column 1 or 9, and row 8 puts its 7 in the other one. Either way, columns 1 and 9 each receive a 7 from these two rows.
- So 7 cannot appear anywhere else in columns 1 and 9. Remove 7 from r4c1, r4c9, r9c1, r9c9.
Common mistakes
- Using a row that has three candidate cells for the digit. Each base row must have exactly two, and both must be in the two shared columns.
- Removing the digit from the rows instead of the columns. With rows as the base, the eliminations are in the columns, and vice versa.
- Forgetting the swapped version. An X-Wing built on columns eliminates in rows.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: X-Wing
Frequently asked questions
What is an X-Wing in Sudoku?
A digit that has exactly two candidate cells in each of two rows, in the same two columns. The digit occupies two opposite corners of that rectangle, so it is removed from the rest of the two columns. Rows and columns can be swapped.
Why does an X-Wing work?
Each of the two rows must place the digit in one of the two columns, and the two rows cannot use the same column. So the two columns each receive their copy of the digit from these rows, and every other candidate in those columns is impossible.
Is an X-Wing a fish?
Yes. The X-Wing is the fish of size two; Swordfish is the fish of size three. Bare Sudoku finds both.
Which level has X-Wings?
Expert. A puzzle that needs an X-Wing, Y-Wing, Swordfish or XYZ-Wing is rated Expert.
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