X-Wing

Summary

X-Wing is the fifth technique in Nyangjari, and the first that requires a fundamentally different kind of search. While Naked Pair and Naked Triple examine the union of regions, X-Wing focuses on a single color across the entire board. The pattern requires two conditions: first, a given color's candidates exist in exactly two rows; second, those two rows share the exact same set of candidate columns. When both conditions hold, the color's cat must land in one of those two columns, which means it cannot appear in those columns in any other row. All other candidate cells for that color in those two columns can be eliminated.

Connect the four corner cells of the 2×2 rectangle diagonally and you trace an X shape — hence the name. X-Wing marks the boundary for the "Very Hard" difficulty label in Nyangjari: any puzzle requiring X-Wing or stronger is considered very hard.

When to use

• Apply X-Wing only after Basic Elimination, Row/Column Lock, Naked Pair, and Naked Triple have all been exhausted with no further progress.
• For each color in turn, count how many rows still contain at least one candidate cell for that color. If the count is exactly two, check whether the column sets match.
• After checking row-based X-Wings for all colors, perform the symmetric check: find any color confined to exactly two columns whose row sets are identical.
• After each X-Wing elimination, re-run Basic Elimination before searching for the next X-Wing — new X marks can trigger cascades.
• Check every color independently. An X-Wing for one color does not prevent another color from having its own X-Wing.

Why it works

Suppose the red color's candidates appear in exactly two rows — row 2 and row 5 — and in both rows the candidate columns are {col 1, col 4}. The red cat must go to one of the four cells: (row 2, col 1), (row 2, col 4), (row 5, col 1), or (row 5, col 4). Regardless of which cell the cat ultimately occupies, it will land in either col 1 or col 4. Because Nyangjari places exactly one cat per column, the red cat consumes one slot in col 1 and the other slot becomes unused by red. But crucially, col 1 and col 4 are both fully claimed for red — no row outside row 2 and row 5 can contribute a red cat to either column. Every red candidate cell in col 1 or col 4 that is not in row 2 or row 5 can therefore be marked X.

The two strict conditions are: (1) the color's candidates span exactly two rows, and (2) those two rows share exactly the same column set. If the column sets differ even by one column, the rectangle is broken and no elimination follows.

Example

▲ Red region candidates: row 2 {cols 1·4}, row 5 {cols 1·4}. Column sets are identical → X-Wing. Red candidates in cols 1 and 4 outside rows 2 and 5 (rows 1, 3, 4) are marked ×.

1. Identify: Red's candidates appear only in rows 2 and 5 — exactly two rows.
2. Compare column sets: Row 2 candidate columns = {1, 4}; row 5 candidate columns = {1, 4}. Sets are identical → X-Wing confirmed.
3. Eliminate: In cols 1 and 4, mark all red candidates in rows other than 2 and 5 (rows 1, 3, 4) as ×.
4. Check column axis: Perform the symmetric check — look for any color confined to exactly two columns with identical row sets.
5. Re-apply Basic Elimination: With new X marks, check for any single-candidate regions, rows, or columns and confirm those cat placements.

Watch out for

• Exactly two rows required: If a color's candidates spread across three or more rows, X-Wing does not apply. Three rows is the domain of Swordfish.
• Column sets must be identical: Row 2 {cols 1, 4} and row 5 {cols 1, 4, 7} are different sets — X-Wing does not hold. Both sets must match exactly.
• Elimination targets other rows only: The two base rows (row 2 and row 5 in the example) are left unchanged. Only the cells in those two columns outside the base rows receive X marks.
• Check both axes: After row-based X-Wings, always run the symmetric column-based search. A board with no row-based X-Wings may still have a column-based X-Wing.
• Check every color independently: X-Wing applies per color. Failure to find an X-Wing for one color does not mean another color lacks one.
• Re-run Basic Elimination after every X-Wing: New X marks may trigger cascades. Never skip Basic Elimination after an X-Wing elimination.
• Very Hard threshold: If a puzzle requires X-Wing, it is rated Very Hard. Expect to apply this technique multiple times before the board resolves.