You have learned the fish family — the X-Wing, Swordfish and their larger cousins — and now you are hunting one in a real grid. You find two rows where a digit is almost confined to two columns, the pattern practically glowing at you, except for a single stray candidate that spoils it. That stray candidate is the most common reason a textbook fish search comes up empty. It also has a name, a rule, and eliminations of its own. It is a fin, and the spoiled pattern is a finned fish.
This guide picks up exactly where the fish guide leaves off — that article defers the finned family as lying “beyond this site's ladder,” and this is the missing rung. Everything here is the same cover-set counting argument you already know, run with one extra candidate in play. The classifications and the fin rule below follow Bernhard Hobiger's HoDoKu, the reference solver whose taxonomy the community standardised on.
Why a spoiled fish can still work
Recall the engine of every fish. A digit's candidates in n base rows are confined to the same n cover columns; the n columns' copies of the digit must therefore come from those rows, and the digit is eliminated from those columns everywhere else. The whole argument rests on one word: confined. A single candidate outside the cover columns breaks it, because now a base row might place its digit out there instead, and the counting no longer closes.
The finned insight is to not throw the pattern away. Take a would-be fish with exactly one extra base candidate — the fin — sitting outside the cover columns. There are only two possibilities. Either the fin is false, in which case the base row is confined after all and you have an ordinary fish; or the fin is true. You do not know which. But if some cell would be eliminated in both cases, it can be eliminated regardless. That is the entire idea, and it is the same either/or reasoning behind chains and colouring.
The fin rule: eliminate only where the fin can see
Work through the two cases and the surviving eliminations fall out precisely. If the fin is false, the ordinary fish eliminates the digit from its cover columns in every non-base row. If the fin is true, the digit is placed at the fin cell, so it cannot appear anywhere else in the fin's box. A cell that would be killed by the ordinary fish and shares a unit with the fin is therefore dead in both cases.
That gives the rule in one sentence: in a finned fish you may eliminate the digit only from cells that a plain fish would eliminate and that also see the fin — that is, cells lying in a cover set, not part of the base sets, and sharing a row, column or box with the fin. In practice a single fin is almost always tucked inside a box, so “sees the fin” usually means “in the same box as the fin.” The plain fish's other eliminations, the ones that cannot see the fin, are forfeited — that is the price of the extra candidate.
A worked finned X-Wing
Fix the digit 7 and look only at where it can go (rows and columns are numbered 1–9 from the top-left). Suppose 7 is a candidate in row 1 only at columns 1 and 5, and in row 4 at columns 1, 5 and 6. Rows 1 and 4 are the base rows; columns 1 and 5 are the cover columns. The 7 in row 4, column 6 is the odd one out — the fin — and it sits in the centre box (rows 4–6, columns 4–6), the same box as the cover cell at row 4, column 5.
Now suppose the same box has candidate 7 at row 5, column 5 and row 6, column 5. Both can be eliminated:
- If the fin (row 4, column 6) is not the 7, rows 1 and 4 are a clean X-Wing on columns 1 and 5. The 7s of columns 1 and 5 are spoken for by rows 1 and 4, so 7 leaves column 5 in every other row — including row 5 and row 6.
- If the fin is the 7, then 7 is placed at row 4, column 6, and no other cell in the centre box can hold a 7 — including row 5, column 5 and row 6, column 5.
Either way those two cells cannot be 7, so the candidate is struck from both. Notice what does not happen: 7 is not removed from column 1 in other rows. A plain X-Wing would have cleared column 1 too, but those cells cannot see the fin, so the fin case leaves them untouched and the elimination is unsafe. The fin narrows the harvest to its own box. That restriction is the whole discipline of finned solving — it is exactly what an eager solver gets wrong.
Sashimi fish: a fin holding up a missing corner
Sometimes the fin is not a bonus candidate but the only thing keeping the pattern standing. Imagine that same finned X-Wing, but row 4 has lost its candidate at one of the two cover columns — say column 1 is now empty of 7 in row 4, leaving 7 in row 4 only at columns 5 and 6. Strike out the fin and the “fish” that remains is a single candidate in a single row: a degenerate, non-existent pattern. Yet the same either/or logic still holds, and the same box-sharing eliminations still follow.
That is a sashimi fish: a finned fish whose underlying pattern collapses, rather than merely shrinks, once you imagine the fin false. HoDoKu draws the line exactly there — “a finned fish becomes sashimi if the remaining fish is incomplete (or degenerate) when all fins are false.” The distinction is bookkeeping, not logic: you apply the identical fin rule to both. It matters only because a sashimi pattern is easier to miss, since the tidy fish skeleton you were scanning for was never fully there.
Franken and mutant fish, briefly
Two further generalisations complete the taxonomy, and they exist mostly for completeness. Ordinary fish use rows as base sets and columns as cover sets, or vice versa. A franken fish allows a box to serve as a base or cover set alongside the rows or columns; a mutant fish lets rows, columns and boxes mix freely on both sides. The cover-set counting argument is unchanged — it never cared whether a “unit” was a row, a column or a box — only the geometry gets stranger. Both can also carry fins.
Be honest with yourself about these: franken and mutant fish are the domain of solving software, not of a person with a pencil. They are genuinely valid, and worth recognising by name, but a human who reaches for one has almost always missed a simpler deduction elsewhere on the grid.
How to spot a fin while fish-hunting
The good news is that hunting finned fish costs almost nothing extra, because you find them with the same single-digit vision the plain fish requires. When you scan a digit for a fish and land on a base row that is one candidate away from qualifying, do not discard it — ask where that extra candidate lives.
- Find the near-miss. Two rows that would be an X-Wing but for one stray candidate, or three rows that would be a Swordfish but for one, are your finned candidates.
- Check the stray candidate's box. The fin only helps if it shares a box with one of the cover cells — that is the box whose cells its elimination can reach.
- Eliminate inside that box. Look in the fin's box, in the cover columns (or rows), for copies of the digit outside the base sets. Those, and only those, come off.
- Search both orientations. As with plain fish, a finned pattern that is invisible with rows as the base is often obvious with columns as the base.
Because a fin so often sits in the same box as a cover cell, many solvers find finned fish by scanning box-by-box for a digit rather than line-by-line — the fin and its target sit together, which the box view makes plain.
When to stop looking
Finned and sashimi fish are the last techniques in this family that reward a human solver. They turn up often enough — a spoiled X-Wing is a genuinely common sight — that learning the fin rule pays for itself. Beyond them, the returns collapse: franken and mutant fish are rare and awkward by hand, and if a puzzle truly needs one, it almost certainly also yields to a chain or a colouring pattern you would find faster. Master the single fin, keep your pencil marks honest so a stale candidate never fakes or hides one, and you have everything the fish family will ever ask of you.
The eye for this comes only from repetition. The walkthroughs show real fish with their eliminations drawn on the board, the technique picker will generate puzzles that demand the fish family, and once ten plain X-Wings feel automatic, the finned ones start announcing themselves.