Finned Jellyfish
A Finned Jellyfish is the order-4 member of the finned fish family. A clean jellyfish confines one digit to four columns across four rows; a finned jellyfish is the same shape spoiled by one or two extra candidates — the fin — that sit outside the tidy pattern. The fin does not destroy the fish; it simply narrows where you may eliminate.
The idea
In a clean jellyfish, the digit can be struck from every other cell of the four cover columns. When a fin is present, that promise weakens: the elimination is guaranteed only for cover cells that also see the fin. The reasoning is a case split. Either the fin is false — and then a perfect jellyfish remains, so all its normal eliminations hold — or the fin is true, in which case any cell seeing the fin loses the digit directly. A cover cell that sees the fin loses the digit either way, so it is safe to remove.
A worked example
Take the digit 5. Across rows 1, 3, 6 and 8 it is confined to columns 2, 4, 7 and 9 — almost a jellyfish — except row 8 carries one extra 5 in column 5, the fin. The clean part would clear 5 from the rest of columns 2, 4, 7 and 9. With the fin in play, only the cover cells that also see r8c5 keep that guarantee. One such cell is r7c4: it lies in cover column 4 and shares box 8 with the fin, so it loses its 5 either way — if the fin is false the clean jellyfish clears it, and if the fin is true its box-mate r7c4 cannot also be 5. Cells far from the fin must wait, but this removal near it often breaks the grid open.
Digit 5 nearly forms a jellyfish on rows 1/3/6/8 × columns 2/4/7/9 (blue). The orange 5 in r8c5 is the fin. Only r7c4 — a cover cell sharing box 8 with the fin — is safe to clear.
Step by step
- Look for a near-jellyfish — a digit almost confined to four columns across four rows (or the transpose).
- Spot the fin — the stray candidate that stops it being clean.
- Restrict the eliminations to cover cells that also see the fin.
- Remove the digit from those cells only.
Common mistakes
- Eliminating everywhere. With a fin, only cells seeing the fin are safe — the full jellyfish sweep no longer applies.
- Too many fins. One small fin (ideally within a single box) keeps the logic clean; scattered extras usually mean there is no fish at all.
- Reaching for it early. Order-4 fish are rare — exhaust singles, pairs and smaller fish first.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.