X-Wing
Perfect symmetry.
The X-Wing is the first of the advanced fish techniques, and the puzzle's first admission that basic scanning alone won't finish the grid. It occurs when a digit appears as a candidate in exactly two cells in each of two different rows, and those four cells line up in exactly the same two columns — forming a rectangle of candidates.
Because the digit must appear somewhere in each of those two rows, and its only legal cells in both rows fall on the same two columns, one of those columns receives the digit from one row and the other column receives it from the other row, regardless of which arrangement plays out. That guarantee lets you eliminate the digit from every other cell in those two columns, cells the X-Wing's two rows have no other connection to. The same pattern works with rows and columns reversed. Finding an X-Wing often cascades into follow-on eliminations that expose hidden pairs or obvious pairs nearby.
How It Works
An X-Wing exists when a digit appears as a candidate in exactly two cells in each of two different rows, and those cells lie in the same two columns.
Say digit D appears in rows R1 and R2:
- In row R1, D is possible only in columns C1 and C2.
- In row R2, D is possible only in columns C1 and C2.
Because D must appear in each row, it occupies one of the two cells in each row. Regardless of which arrangement occurs, one of the two columns gets D from R1 and the other gets D from R2. This means D cannot appear in any other cell in those two columns.
- Find a digit D that appears in exactly two positions in two different rows — and those positions share the same two columns.
- Eliminate D from all other cells in those two columns.
The same logic works with rows and columns swapped: find two columns where D appears in exactly two rows each — the same two rows — and eliminate D from those rows.
Example
Below board presents an example of an X-Wing pattern on digit 4, locked into columns 2 and 5 across rows 2 and 6.
Digit 4 appears only in columns 2 and 5 within both row 2 and row 6 — the two blue corners in each row. It must occupy one of those two cells in each row, so column 2 and column 5 each receive a 4 from either row 2 or row 6. Every other 4 in those columns, shown in red, can be eliminated.
On Evil Boards
The X-Wing rewards the solver who looks at the structure of the entire grid. It eliminates candidates from cells that simpler techniques cannot touch. The eliminations often cascade through hidden pairs and naked pairs until placements finally appear. When two rows aren't enough, the same logic extends to three in the swordfish technique. If you see a partial x-wing, try looking for a y-wing instead.