Swordfish

Summary

Swordfish is X-Wing's 3×3 sibling and the most advanced technique in Nyangjari. Where X-Wing requires a single color confined to exactly two rows with identical column sets, Swordfish relaxes the identical-column requirement and scales up to three rows. The two conditions are: a given color's candidates exist in exactly three rows, and the union of candidate columns across those three rows spans exactly three columns. When both hold, that color's cat is locked into the 3×3 grid of intersections, meaning no other row can contribute that color to any of those three columns. All other candidate cells for that color in those three columns can be eliminated.

The technique family scales as X-Wing (2×2), Swordfish (3×3), Jellyfish (4×4). Nyangjari supports up to Swordfish. A puzzle requiring Swordfish is rated at the highest difficulty — the last technique before guessing would be required.

When to use

• Apply Swordfish only after all five preceding techniques — Basic Elimination, Row/Column Lock, Naked Pair, Naked Triple, and X-Wing — have been fully exhausted with no further progress.
• For each color in turn, count how many rows still contain at least one candidate cell. If the count is exactly three, proceed to check the column union.
• Compute the union of candidate columns across the three rows. If the union contains exactly three columns, Swordfish applies.
• After each Swordfish elimination, re-run Basic Elimination before searching for the next Swordfish or X-Wing.
• After checking all row-based Swordfish patterns, perform the symmetric column-based search.

Why it works

Suppose the red color's candidates appear in exactly three rows — rows 1, 3, and 5. Collect the candidate columns from each row: row 1 uses {col 1, col 3}, row 3 uses {col 1, col 5}, row 5 uses {col 3, col 5}. The union is {col 1, col 3} ∪ {col 1, col 5} ∪ {col 3, col 5} = {col 1, col 3, col 5} — exactly three columns. The red cat must go to one of the nine intersections of these three rows and three columns. Whichever cell it occupies, it will land in exactly one of cols 1, 3, or 5. Because Nyangjari places exactly one cat per column, col 1, col 3, and col 5 are all fully claimed for red by these three rows. No other row can contribute a red cat to any of those columns. Every red candidate in cols 1, 3, or 5 outside rows 1, 3, and 5 is therefore impossible and receives an X mark.

Note the key difference from X-Wing: Swordfish does not require each row to have the same column set. Row 1 {cols 1, 3}, row 3 {cols 1, 5}, and row 5 {cols 3, 5} all differ — yet the union equals exactly three columns, which is sufficient. The single requirement is that the union spans exactly three columns.

Example

Red color's candidates are distributed as follows after all previous techniques have been applied:

• Row 1 candidate columns: {col 1, col 3}
• Row 3 candidate columns: {col 1, col 5}
• Row 5 candidate columns: {col 3, col 5}

Regions R·G·U candidate column union = {1, 3, 5}. Any other region's candidates in columns 1, 3, or 5 of rows 2 and 4 can be eliminated.

Union = {col 1, col 3} ∪ {col 1, col 5} ∪ {col 3, col 5} = {col 1, col 3, col 5}. The union spans exactly three columns — Swordfish is confirmed.

Elimination result: In cols 1, 3, and 5, mark all red candidate cells in rows other than rows 1, 3, and 5 (for example rows 2 and 4) as X. After these new X marks, run Basic Elimination to check whether any region, row, or column has been reduced to a single candidate.

1. Identify: Red's candidates appear only in rows 1, 3, and 5 — exactly three rows.
2. Compute union: {col 1, col 3} ∪ {col 1, col 5} ∪ {col 3, col 5} = {col 1, col 3, col 5}. Union spans exactly 3 columns → Swordfish confirmed.
3. Eliminate: In cols 1, 3, and 5, mark all red candidates outside rows 1, 3, and 5 as ×.
4. Check column axis: Perform the symmetric search — look for any color confined to exactly three columns whose row union also spans exactly three rows.
5. Re-apply Basic Elimination: With new X marks in place, check for single-candidate regions, rows, or columns and confirm those cat placements.

Watch out for

• Exactly three rows required: Two rows is X-Wing territory; four or more rows means Swordfish does not apply. The row count must be exactly three.
• Union must span exactly three columns: If the union of candidate columns across the three rows spans four or more columns, Swordfish does not hold for that color.
• Per-row column sets need not be identical: Unlike X-Wing, Swordfish allows each row to have a different subset of the three columns. Only the union matters.
• Elimination targets other rows only: The three base rows are left unchanged. Only the cells in those three columns outside the base rows receive X marks.
• Check both axes: After row-based Swordfish, always run the symmetric column-based search.
• Check every color independently: Swordfish applies per color. Scan all colors before concluding the board is unsolvable by standard techniques.
• Re-run Basic Elimination after every Swordfish: New X marks may trigger cascades. Never skip Basic Elimination after a Swordfish elimination.

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