The intuition
X-Wing works because two rows share the same two candidate columns, forcing a diagonal pattern. Swordfish is the same counting argument with one more line: three rows whose candidate cells for one digit all fall inside the same three columns force that digit to fill those three columns between them — using any three of the possible row/column combinations that satisfy every row and column exactly once. Either way, all three columns get fully booked by the three rows, so the digit can't appear in those columns anywhere else.
When you'll use it
Swordfish appears almost exclusively in Expert puzzles, usually after X-Wing has already been tried and failed to unlock the board. It's less common than X-Wing — most Expert boards use zero or one Swordfish — but it's the direct next step once X-Wing feels reliable.
How to spot a Swordfish
- Pick a candidate digit, e.g. 4.
- Find three rows where that digit is a candidate in two or three cells each.
- Check whether, across all three rows, the candidate cells use only three columns total (each column appearing in at least two of the three rows).
- If yes, eliminate the digit from those three columns in every other row.
- The same pattern works with rows and columns swapped.
Why the Swordfish logic works
Each of the three rows needs exactly one instance of the digit, and every candidate for that digit in those rows sits in one of only three columns. Whatever combination of positions the three rows end up using, between them they must occupy all three columns — there's no valid assignment that leaves a column unused, because each row's digit has to land somewhere and only those three columns are available. So all three columns have their supply of the digit fully accounted for by the three rows, and no other row can also place it in one of those columns.
A worked Swordfish example
Row 2 has digit 4 as a candidate only in C3 and C6. Row 5 has it only in C6 and C9. Row 8 has it only in C3 and C9. Together the three rows use only columns 3, 6 and 9 — a Swordfish. Digit 4 can now be eliminated from C3, C6 and C9 in every other row.
Walkthrough
Row 2 is filled everywhere except C3 and C6, and 4 is a candidate in both. Row 5 is filled everywhere except C6 and C9, with 4 a candidate in both. Row 8 is filled everywhere except C3 and C9, with 4 a candidate in both.
List the columns involved: row 2 uses {3, 6}, row 5 uses {6, 9}, row 8 uses {3, 9}. Combined, only three distinct columns appear — 3, 6 and 9 — and each one is used by exactly two of the three rows.
Try to place the three 4s without breaking any rule: whichever column row 2 picks, row 8 (which shares column 3 with row 2) is pushed toward the other option, and row 5 is pushed to fit the remaining slot. Every valid assignment ends up using columns 3, 6 and 9 exactly once each across the three rows.
Because those three columns are now guaranteed to be fully used up by rows 2, 5 and 8, no other row can place a 4 in column 3, 6 or 9. That's the elimination — eighteen cells (the other six rows across those three columns) lose 4 as a candidate in one move.
How to drill this technique
On an Expert puzzle, pencil-mark fully and, for each digit, write down which rows have exactly two or three remaining candidates for it, along with their columns. Look for any group of three rows whose columns overlap down to only three total. This is slow the first few times — budget twenty minutes — but it gets much faster once you've found three or four Swordfish patterns by hand.
Common mistakes
- Trying Swordfish before exhausting Hidden Singles, Naked Pairs and X-Wing — Swordfish patterns are much easier to spot once the candidate grid has already been thinned.
- Requiring exactly two candidates per row. Unlike X-Wing, a valid Swordfish row can have two OR three candidate cells, as long as all the cells across the three rows still collapse onto only three columns.
- Forgetting the column-to-row mirror version — three columns whose candidates collapse onto three rows work identically, eliminating down the rows instead of across the columns.
FAQ
Is Swordfish just a bigger X-Wing?
Yes. X-Wing is the 2×2 version of the 'fish' pattern; Swordfish is the 3×3 version; Jellyfish is 4×4. All of them rest on the same argument: N lines whose candidates for one digit collapse onto the same N cross-lines force the digit to fill those cross-lines, clearing it everywhere else on them.
Does every row in a Swordfish need exactly two candidates?
No — that's the main difference from X-Wing. A Swordfish row can have two or three candidate cells for the digit, as long as the full set of candidate cells across all three rows uses only three columns total.
How rare is Swordfish compared to X-Wing?
Noticeably rarer. X-Wing shows up in roughly a third of Expert puzzles; Swordfish is closer to one in ten. If you're stuck on an Expert board and X-Wing hasn't worked, Swordfish is the next thing to check before moving to chain-based techniques like XY-Wing.
Why is it called Swordfish?
It follows the same 'fish' naming convention as X-Wing, where the shape resembles a fish skeleton on the grid. Swordfish and Jellyfish just describe bigger fish — three and four lines respectively — for the same underlying pattern.
What should I learn after Swordfish?
XY-Wing. Where X-Wing and Swordfish reason about one digit across multiple lines, XY-Wing introduces chain logic — following an either-or relationship between three cells that share only two candidates each. It's a different family of reasoning that opens the door to Coloring and forcing chains.
What to learn next
Once Swordfish feels natural, move on to XY-Wing — it builds directly on the candidate-tracking habits you've just developed. Or revisit the full Sudoku techniques library to see the full progression from beginner to advanced.