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. Take an X-Wing whose corner is simply missing: one base row holds the digit in only one of the two cover columns, plus a stray candidate somewhere else. Strike out the stray and what remains is not a smaller fish but no fish at all — a lone candidate in that row, which is a single, not an X-Wing. Yet the same either/or logic still holds, and the eliminations that both cases agree on 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.
A worked Sashimi X-Wing
Stay with the digit 7. This time row 1 has 7 only at columns 1 and 5, as before, but row 4 has 7 only at column 5 and column 2. Rows 1 and 4 are the base rows and columns 1 and 5 the cover columns, exactly as in the finned example — except that the corner at row 4, column 1 is gone. The 7 at row 4, column 2 is the fin. It sits in the middle-left box (rows 4–6, columns 1–3), which is the box that holds the missing corner.
Suppose 7 is also a candidate at row 5, column 1 and row 6, column 1 — cover-column cells in the fin's box, outside the base rows. Both can be eliminated:
- If the fin (row 4, column 2) is not the 7, row 4's only remaining 7 is at column 5, so it goes there. That takes column 5 away from row 1, whose 7 is forced into column 1. Column 1's 7 is then at row 1, and it leaves every other cell of column 1 — including rows 5 and 6.
- If the fin is the 7, then 7 is placed at row 4, column 2, and no other cell in the middle-left box can hold a 7 — including row 5, column 1 and row 6, column 1.
Both branches clear the same two cells, so the 7 comes off them. With the fin removed, the “X-Wing” is just two singles in a row, so this fish is sashimi, but the elimination is as solid as the finned one. The rule is the one HoDoKu gives for every fin: only cover candidates that “see all the fins (and are of course not base candidates)” may go.
Where the fin sits is what makes this pattern worth knowing. Had the stray 7 been in the centre box instead, next to the surviving corner at row 4, column 5, every 7 in row 4 would lie inside one box, and an ordinary box/line reduction would clear that box without any fish reasoning. A sashimi X-Wing earns its keep when the fin shares a box with the missing corner. That leaves the base row spread across two boxes, and nothing simpler sees the elimination.
If you already know the Skyscraper, you have seen this pattern before under another name. Row 1 has exactly two 7s, at columns 1 and 5, and so does row 4, at columns 5 and 2. Each row is a strong link, and the two links share column 5, so at most one of their column-5 ends can be the 7. That forces a 7 into at least one of the free ends, row 1, column 1 or row 4, column 2. HoDoKu's Skyscraper rule is that “all candidates that can see both cells can be eliminated,” and the same page notes that a Skyscraper “can be seen as two Sashimi X-Wings.” Four cells see both free ends. Two are rows 5 and 6 of column 1, the eliminations above. The other two are rows 2 and 3 of column 2, in the top-left box, and the fish view misses them because neither lies in a cover column. So when you find a sashimi X-Wing, read it as a Skyscraper too and check the box beside the other free end.
Sashimi Swordfish
Nothing in the argument depends on there being two base rows, so the same thing happens with three. A Swordfish needs three base rows whose candidates for the digit lie within three cover columns. Each row may use two or three of those columns, as long as all three columns are used between them. A finned Swordfish allows extra base candidates outside the cover columns, and they all have to sit in one box. It becomes a sashimi Swordfish when the pattern is incomplete once the fins are struck out. Usually that means one base row is left with a single cover candidate, which would just be a placement.
The elimination rule does not change. Look for cells that lie in a cover column, sit outside the three base rows, and see every fin. In practice those are the cover-column cells inside the fin's box. A missing corner can be any cell where a base row meets a cover column. As with the X-Wing, a useful fin shares its box with a cover column, because otherwise no cell satisfies both conditions and nothing can be eliminated. The case split is the same too: fin false gives you the fish (degenerate in the sashimi case, but its forced placements clear the cover columns just the same), and fin true clears the fin's box. A Swordfish just has more cells to check.
Finned vs sashimi at a glance
| Finned fish | Sashimi fish | |
|---|---|---|
| Imagine the fin false | A complete, ordinary fish remains | The fish is incomplete — a corner is missing and a single appears instead |
| Where eliminations happen | Cover-column cells outside the base rows that see every fin | Exactly the same |
| Typical fin position | In the box of a cover cell of its own base row | In the box of the missing corner |
| Why it gets missed | The fish looks spoiled by one extra candidate | There is never a full fish to spot in the first place |
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.
Frequently asked questions
What is a sashimi X-Wing?
An X-Wing in which one of the four corners is missing and a fin stands in for it. One base row has the digit in both cover columns, the other has it in only one cover column plus a candidate outside them. You may remove the digit from cover-column cells outside the base rows that also see the fin, which usually means the two cells of the fin's box in the cover column. The worked example above walks through both cases.
Is a sashimi fish the same as a finned fish?
It is a special case of one, and the elimination rule is identical. The only difference is what you have left when you imagine the fins false: a finned fish leaves a complete ordinary fish, while a sashimi fish leaves an incomplete one. The name is about recognising the pattern, not about a different logic.
Can a Swordfish be sashimi?
Yes. Any fish size can be. A sashimi Swordfish has three base rows and three cover columns, and once its fins are removed at least one base row has too few cover candidates left to form the pattern. The eliminations are the cover-column cells outside the base rows that see every fin.
Do I need sashimi fish to solve hard puzzles?
No. They are a convenient way to name an elimination, but not the only route to it. Each sashimi fish is a two-case argument (fin true, fin false), and chains and colouring make the same eliminations through the same kind of reasoning. Learn them if you enjoy fish hunting. Skipping them won't leave a puzzle unsolvable.