Expert 7 min read
Four lines, and the point where counting stops paying
The logic is unchanged from X-Wing and Swordfish. What changes is the cost of finding it — and whether that cost is worth paying.
The short version
A Jellyfish is the four-line member of the fish family: four base lines, each with at most four homes for a digit, all contained within the same four perpendicular lines.
Four lines each need the digit, four cover lines supply it, so the cover lines are full and can be cleared outside the intersections.
The logic is identical to X-Wing and Swordfish. Everything that changes is the cost of finding it.
The shape
- Base: four parallel lines, each with at most four homes for the digit.
- Cover: the four perpendicular lines containing all those homes.
- Eliminate: in the cover lines, outside the base lines.
By now the pattern should look familiar, because it is the same sentence with a different number. Two lines is X-Wing, three is Swordfish, four is Jellyfish. The structure does not change; only the width does.
Why it works
Four base lines each need exactly one copy of the digit. All their homes lie in four cover lines. No cover line can hold two copies, so the four placements must be distributed one per cover line.
Four lines, four slots, one each. The cover lines are fully supplied, and the digit cannot appear in them anywhere outside the base.
The pigeonhole argument is the same at every size. If you understood why X-Wing works, you understand why Jellyfish works — the extra lines add bookkeeping, not reasoning.
A real board
Digit 7, and again the base is on columns rather than rows:
- Column 4: 7 can only go in R8C4 or R9C4.
- Column 7: 7 can only go in R3C7, R4C7, R8C7 or R9C7.
- Column 8: 7 can only go in R3C8, R4C8, R8C8 or R9C8.
- Column 9: 7 can only go in R4C9, R8C9 or R9C9.
Every home in all four columns falls inside rows 3, 4, 8 and 9. Four columns, four rows, one placement each.
The rows are therefore supplied. Clearing them outside the base columns leaves exactly one elimination on this board: R4C1 loses its 7.
One candidate, from a pattern that took four line-counts to find. That ratio is the honest summary of Jellyfish.
How to scan for one
Do not scan for Jellyfish directly. Scan for the conditions that make one possible, and check the cheap patterns first.
- Finish the cheaper scans. X-Wing and Swordfish first, on every digit. A Jellyfish is almost never the only available move, and the cheaper patterns are far faster to verify.
- Look for digits with many homes. A digit with four to six homes spread across four lines is the raw material. A digit with three homes is a Swordfish or a wing, not a Jellyfish.
- Count homes per line. Four lines, each with at most four, all inside the same four perpendicular lines. The "at most four" is the condition that matters.
- Check for a fifth home. One base line with a home outside the four cover lines invalidates everything.
- Sweep the cover lines. Then repeat with rows and columns swapped.
In practice, step 1 eliminates most candidates for a Jellyfish search, which is why the honest advice is to learn the principle and rarely perform the search.
The traps
Treating rarity as difficulty. Jellyfish are not logically harder than X-Wing. They are harder to find. Solvers who assume they are conceptually deeper end up overcomplicating a simple counting argument.
Scanning for it too early. If you are hunting a Jellyfish while a hidden single sits unswept, the problem is your order of operations, not the puzzle. Work the ladder in order.
A fifth home. Same failure as every fish, and it is the only condition that can invalidate the pattern. One stray candidate outside the four cover lines and the whole thing is nothing.
Direction confusion. Eliminations go into the cover lines. Four lines of base, four of cover, and only one of those sets gets cleared. Reversing them produces invalid deletions.
Where to use it
The honest answer is: rarely. Jellyfish appear in expert puzzles and in puzzles designed to demonstrate the technique, and almost never as the only path to a solution.
What is worth knowing is the family. Once you see that X-Wing, Swordfish and Jellyfish are one idea at three widths, the whole fish category stops being a list of tricks to memorise. You learn one argument and three sizes of it.
The realistic stopping point for most solvers is Swordfish. Beyond that, chains tend to resolve the board faster than hunting for a wider fish.
Questions people actually ask
What is a Jellyfish in sudoku?
Four parallel lines where a digit has at most four homes each, all confined to the same four perpendicular lines. Each base line places the digit, so the four cover lines are supplied and can be cleared.
How often does a Jellyfish appear?
Rarely in human-made puzzles, and almost never as the only way forward. Most published puzzles are solvable with techniques up to Swordfish.
Is Jellyfish harder than Swordfish?
Harder to find, yes. The logic is identical, but you are now tracking four lines and up to sixteen intersections, and the shape is invisible without systematic counting.
Should I learn Jellyfish at all?
Learn the principle, not the search. Knowing the fish family generalises keeps you from treating each size as a separate trick. Actually hunting for Jellyfish is rarely worth the time.