Finned/Sashimi Fish
Finned/Sashimi X-Wing
A Finned X-Wing is a regular X-Wing where one or more base candidates are not covered by a cover set. Only cover candidates that see all the fins (and are not base candidates) can be eliminated. A Finned Fish becomes Sashimi if the remaining fish is incomplete (or degenerate), when all fins are false.
Left example: X-Wing in r24/c35. The fin is an additional base candidate in r2c1 (not in cover sets c35). If the fin is false, a regular X-Wing eliminates 9 from r35c3 and r5c5. If the fin is true, it eliminates 9 from r1c1, r2c35, and r3c3. The elimination is the intersection of both sets — only r3c3 is in both, so r3c3 is eliminated.
Right example: c36/r37 with two fins at r89c3. If the fins are false, an X-Wing remains, but it's degenerate (could be replaced by singles in r3c3 and r7c6). This degeneracy makes it Sashimi. The elimination is r7c1 — the only cover candidate that can see both fins.
Finned/Sashimi Swordfish
This works exactly like Finned/Sashimi X-Wing, only with three base/cover sets instead of two.
Left example: Swordfish c159/r357. The fin is r1c9 (leftover base cell). Possible eliminations without the fin are r3c7, r5c3, r7c6. Only r3c7 sees the fin (same box), so r3c7 is eliminated.
Right example: Swordfish in rows r269/c258. The fin is r6c4. Cover cells seeing the fin are r45c5, so two eliminations: r45c5. Without the fin, a single in r6c2 remains, therefore it's Sashimi.
Finned/Sashimi Jellyfish
Adding another base/cover set combination beyond Swordfish yields a Finned/Sashimi Jellyfish.
Left example: Jellyfish r2479/c1348. The fin is r4c9. Cover cells seeing the fin are r56c8. If the fin is false, it degenerates into a Swordfish (r479/c134), eliminating 9 from r26c3. This could also be called Sashimi due to the degeneracy.
Right example: Jellyfish r1469/c1289. The fin is r9c3. Eliminations are r7c12 and r8c12. Without the fin, a single in r9c9 remains, therefore it's Sashimi.
Larger Finned/Sashimi Fish
For larger Finned/Sashimi Fish a complementary fish will exist for the same eliminations. Searching for larger fish sizes beyond Jellyfish is therefore unnecessary.
Key Elimination Logic
The core reasoning across all sizes follows the same two-case logic: If the fin is false, standard fish eliminations apply. If the fin is true, it eliminates candidates in its row/column/box. The actionable eliminations are the intersection — candidates that would be eliminated in both scenarios, meaning they must see all the fins and be cover candidates (not base candidates).
Content based on HoDoKu by Bernhard Hobiger, licensed under GNU FDLv1.3.