Swordfish Pattern

Swordfish is the three-row (or three-column) generalisation of the X-Wing pattern. It's one of the staple advanced techniques for Expert puzzles: when X-Wing doesn't quite fit, Swordfish often does. The good news is that once you understand X-Wing, Swordfish is a small conceptual step. The less-good news is that spotting one in a real puzzle takes a bit of practice.

The Rule

Consider a single digit, say 4. Scan three rows and note which columns still allow a 4 as a candidate. If those three rows share a common set of exactly three columns — meaning each row has its 4-candidates spread only among those three columns — you've found a Swordfish on 4.

Because each row must place a 4 inside its candidate columns, and the columns overlap across all three rows, the three 4s for those rows must occupy three of the cells inside the three-column frame. That means no other cell in those three columns can hold a 4. You can remove 4 as a candidate from every other cell in those columns.

A Concrete Example

Imagine the candidate positions of digit 4 in three rows look like this (columns shown as numbers 1–9; dots are non-candidates, X means "4 is still a candidate"):

Row 2:  . X . . X . . X .
Row 5:  . X . . X . . . .
Row 7:  . . . . X . . X .

Columns 2, 5, and 8 are the only columns where 4 appears as a candidate across these three rows. Each of the three rows needs exactly one 4, and every candidate cell falls in columns 2, 5, or 8. So three of the nine cells in the 3-row × 3-column rectangle will hold a 4 — one per row, one per column.

With those three 4s locked inside the frame, no other cell in columns 2, 5, or 8 can be a 4. That lets you remove 4 as a candidate from every other cell in those columns.

How to Spot a Swordfish

1. Choose a digit that still has several candidate cells scattered across the grid.
2. Look at each row. Note the columns where that digit can still appear.
3. Find three rows where the digit's candidates fit inside a shared set of three columns.
4. Verify. Each of the three rows must have at least two and at most three candidate cells, all inside those three columns. No row can have a candidate outside the three columns.
5. Apply the elimination. Remove the digit as a candidate from every other cell in those three columns.

The symmetric version — three columns whose candidates fit into three shared rows — works identically, with rows and columns swapped. The elimination then targets the other cells in those three rows.

Why This Works

The argument is a counting one. You have three rows that each need exactly one instance of the digit. Every possible placement sits inside a 3×3 skeleton formed by the three rows and three columns. The pigeonhole principle forces each of the three rows to place its copy of the digit in a different one of those three columns — one digit per row and one per column.

Once those three cells are used up, no other cell in those columns can hold the digit, because every such column already has its single permissible copy in one of the frame cells. That is what justifies the elimination.

Variations You May See

• Finned Swordfish: a near-Swordfish where one row has a "fin" — an extra candidate outside the three-column frame. The elimination is more restricted, only applying to cells that see both the fin and the frame.
• Jellyfish: the four-row or four-column extension. Four rows whose digit candidates all sit within a shared four-column frame produce the same kind of elimination. Jellyfish is rare and often doesn't give better results than Swordfish, because by the time one appears, other techniques usually have, too.

Common Mistakes

• Requiring three candidates per row. A row in a Swordfish can have two or three candidate cells — as long as all of them lie inside the shared three-column set.
• Mixing rows and columns. A Swordfish is "three rows confined to three columns" or "three columns confined to three rows" — not a mix of both.
• Forgetting the elimination direction. If your three rows are confined to three columns, you eliminate in the columns, not in the rows.
• Hunting too early. Swordfish rarely appears before locked candidates, hidden pairs, and X-Wing have all been applied. If a puzzle still has simpler eliminations available, those usually work first.

When to Look for Swordfish

In most Expert puzzles, Swordfish is a mid-to-late-game tool. Run through the cheaper techniques first: scanning, naked and hidden singles, naked and hidden pairs, locked candidates, and X-Wing. If the puzzle is still stuck and a specific digit appears often in the remaining candidate lists, Swordfish is the next thing to check.

Digits with lots of remaining candidates are the best targets. Look for digits where many rows still have exactly two or three possible positions — those are the ones most likely to form a frame.

Related Techniques

• X-Wing — the two-row equivalent. If you've never seen X-Wing before, read that first.
• Y-Wing — a different advanced pattern, based on a three-cell logical chain rather than a grid-spanning frame.
• Locked Candidates — cheaper elimination that often runs out just before Swordfish becomes useful.

Practice

• Today's Expert puzzle

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