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.

Works Classic Sudoku Completes the finned-fish family for the hardest Classic grids, where finned fish outnumber clean ones. → Limited Killer Sudoku Essentially never reached in Killer. → Limited Sudoku X Diagonals crack the grid long before an order-4 fish forms. → Limited Samurai Sudoku Overkill for Samurai. →

Where to practise this

This technique starts paying off at Evil, which is where puzzles first stop yielding to anything simpler. Reading about a pattern and spotting it on a live grid are different skills - the second one only comes from playing.

Play Evil Sudoku About Evil Sudoku

Related techniques

Jellyfish - the Order-4 Sudoku Fish One digit confined to the same four columns across four rows (or vice versa) - eliminate it from the rest of those columns. Finned Swordfish - Sudoku Fish Variation An almost-Swordfish with one extra candidate; the digit is eliminated only from cover cells that also see the fin. BUG+1 - Bi-Value Universal Grave Technique When all cells but one are bi-value, the extra candidate in that one cell must be the solution, or the puzzle would have two answers. Sue de Coq - Advanced Sudoku Technique Cells at a box-and-line intersection, plus almost-locked sets in the box and line, force eliminations in both.