X-Wing (2-Fish)

Show the last hint page first

Loading demo...

An X-Wing is a size-2 basic fish.

How to spot it

• For each candidate x from 1 to 9, find two rows (or columns), each containing exactly two occurrences of x.
• Check all occurrences of x in those two rows (or columns): together, they must be confined to exactly two columns (or rows). The selected rows (or columns) form the base set, and those columns (or rows) form the cover set.
• Eliminate candidate x from all cells in the two cover columns (or rows) outside the base set.

How it works

Each of the two base rows (or columns) must eventually contain one placed digit x, for a total of 2 placements. All of them lie in the two cover columns (or rows). Since a column (or row) cannot contain two xs, these placements must occupy different columns (or rows), with exactly one in each.

Therefore, no cell in the cover set outside the base set can contain x, so candidate x can be eliminated from those cells.

Examples

On the board above, for candidate 2, rows {4, 7} form the base set, and columns {2, 5} form the cover set. All occurrences of 2 in the base set lie within the cover set.

Candidate 2 can be eliminated from R5C2, R5C5, and R9C5, since these cells lie in the cover set outside the base set.

---

On the board above, for candidate 6, columns {2, 5} form the base set, and rows {5, 7} form the cover set. All occurrences of 6 in the base set lie within the cover set.

Candidate 6 can be eliminated from R5C3, R5C4, R7C1, R7C3, and R7C8, since these cells lie in the cover set outside the base set.