Sashimi Swordfish Sudoku Technique

Updated

A Sashimi Swordfish is the three-line sashimi pattern: one of the three base lines is missing a candidate at one of the cover lines, but the fish still proves the same finned-style eliminations once the fin’s box is found.

When a Sashimi Swordfish applies

A Finned Swordfish keeps all three base lines close to a full Swordfish shape, with one stray candidate acting as a fin. A Sashimi Swordfish is thinner: one of the base lines has a candidate that would normally sit inside the three cover lines, but instead sits outside them, so that base line contributes only one cover-line cell rather than two or three. The line has been “cut”, in the same sense as the Sashimi X-Wing, and the displaced candidate becomes the fin.

The proof is unchanged from any other finned fish. Every cell that sits inside the three cover lines, outside the three base lines, and shares a unit with the fin, cannot hold the digit — because either the fin holds it, or the base lines settle back into a shape that covers the cell some other way. The sashimi cut only changes how thin the base lines are allowed to be, not the elimination rule itself.

As with the X-Wing’s sashimi variant, this pattern is stricter to confirm than a regular Finned Swordfish, since one base line is down to a single relevant candidate, but it still reaches real eliminations that a plain three-by-three Swordfish would miss.

Worked example

The digit 1 uses base columns 1, 5 and 7 over cover rows 4, 6 and 7. Column 5 keeps only r4c5 inside those rows, leaving r9c5 as a fin. The solver reports an elimination at r7c6.
c1c2c3c4c5c6c7c8c9
r1953168742
r2862734951
r341759592836
r47496891931425
r5281645397
r6349527191468
r7153859219674
r8574386219
r9629417583
Pattern cells
r7c1, r4c5, r4c7, r6c7, r9c5
Eliminations
1 from r7c6

Column 1 has one candidate for 1 in the cover rows: r7c1. Column 7 has two: r4c7 and r6c7. Column 5 also has two candidates for 1 overall, but only one of them, r4c5, falls inside rows 4, 6 and 7 — the other, r9c5, sits in row 9, outside the chosen cover rows. That leftover candidate is the fin, and column 5 supplying only one cover-row cell is the sashimi cut.

r9c5 sits in the bottom-middle box, the same box that holds r7c4, r7c5 and r7c6. r7c6 was carrying 1 and 9 before the deduction. Column 5 is already one of the fish’s own base columns, so it is excluded from the elimination search regardless; r7c6 sits in column 6, inside the box, and inside cover row 7. Whichever cell in the base lines actually holds 1, r7c6 cannot, because it shares the fin’s box and column 5 cannot itself be the source of that elimination. The solver removes the 1 and leaves 9 behind.

How to spot a Sashimi Swordfish

  1. Look for a thin base lineFind three lines where a digit’s candidates mostly line up across three cover lines, but one base line has only one candidate inside them.
  2. Find that base line’s leftover candidateConfirm the thin base line has exactly one more candidate for the digit, sitting outside the three cover lines. That is the fin.
  3. Check which cells share the fin’s boxLook at the cells inside the cover lines, outside the three base lines, and keep only the ones that also share a box with the fin.
  4. Eliminate the digit thereRemove the digit from that narrower set of cells, remembering that cells inside a base line itself are never eliminated.

Common mistakes

Sashimi Swordfish FAQ

How is this different from a Finned Swordfish?

A Finned Swordfish keeps all three base lines at their full corner count and adds one stray candidate. A Sashimi Swordfish instead lets one base line drop to a single cover-line candidate, with the fin taking the place of the missing one.

Can more than one base line be cut at once?

No. At least two of the three base lines need to keep enough cover-line coverage for the fish to still prove anything; cutting more than one line collapses the pattern.

Does the sashimi cut change where eliminations land?

No. Eliminations still land only on cells inside the cover lines that also share the fin’s box. The cut changes how thin the base lines are, not the elimination rule.

What comes after the fish family in difficulty?

The wing patterns — XY-Wing, XYZ-Wing and W-Wing — which reason about bivalue cells and strong links rather than rows and columns of the same digit.