Killer fish
Fish patterns adapted for killer Sudoku. The same X-wing or swordfish argument runs on candidate cells, with cage-sum constraints sometimes tightening the elimination set.
Killer fish are the standard fish techniques — X-wing, swordfish, jellyfish — applied to killer Sudoku grids. The fish argument doesn't change: a digit confined to N rows, with all candidates falling in the same N columns, must occupy exactly one cell per row and one cell per column inside that grid; the digit can be eliminated from those columns elsewhere. What does change is the constraint stack. Killer cages add a sum constraint that often interacts with the fish pattern in useful ways.
How cages can sharpen the fish
A standard X-wing on digit 4 in rows 2 and 7 across columns 3 and 8 places 4 at two of the four corners. In killer, those corners might fall inside cages whose sums and remaining cells further constrain which digits land there. If the cage at one corner has a sum that excludes 4 from that cell — for example, a cage of 2 cells with sum 14 where the other cell is already a 7 — the X-wing's "either diagonal" claim collapses to a specific diagonal, and the placement becomes determinate before the fish's standard eliminations even fire.
The fish technique's eliminations don't change with cages — they apply to the same columns outside the four corners. What cages add is additional eliminations through the cage-sum constraint, which can sometimes resolve the fish to a placement directly.
Cage-aware fish in their own right
Beyond the standard fish, killer Sudoku admits fish-shaped patterns that use cage sums rather than candidate cells. Consider a cage spanning multiple rows and columns whose sum forces a particular digit to appear at most N times within its cells. If those forced occurrences are confined to exactly N columns across N rows, a cage-aware fish argument applies — the digit's placements within the cage must follow the fish's diagonal rule, and the digit can be eliminated from columns outside the cage but in the same rows.
These cage-aware variants are rare in practice and not always cataloged separately. Most killer solvers find them by searching for standard fish first, then applying cage-sum constraints as a sharpening step.
When you'll see it
Killer fish appear on expert and master killer puzzles. The signature is the same as in classic Sudoku — a digit that's been stuck across two or three rows where the candidate columns repeat — combined with a cage layout that hasn't yet resolved the digit through simpler arithmetic. Reach for the fish scan after unique combinations and cage splitting have run; if a fish is alive, the cages will often turn the elimination into an immediate placement.
See also
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Swordfish— The X-wing's three-row counterpart. When a digit's possible cells across three rows fall in the same three columns, that digit can be eliminated from those columns elsewhere.
- Cage— In Killer Sudoku, a contiguous group of cells outlined by a dotted line, with a printed sum the digits inside must add up to. Replaces the classic Sudoku given.
- The 45 rule— In Killer Sudoku, the fact that every row, column, and 3×3 box must sum to 45 — because 1+2+…+9 = 45. The foundational arithmetic identity behind most killer techniques.
- Jellyfish— The four-row, four-column generalisation of swordfish. A digit confined to the same four columns across four rows lets you eliminate it elsewhere in those columns.
Read more
- Meet Killer Sudoku
An introduction to Killer Sudoku for someone who knows the classic version — what changes, how the experience differs, and where to start.