The Swordfish Pattern: Sudoku's Most Satisfying Technique

If the X-Wing is the gateway to advanced Sudoku, Swordfish is the room behind the gate. It's the technique solvers talk about when they describe cracking a puzzle they thought was impossible — the moment that transforms a completely stalled grid into a cascade of forced placements. Swordfish sounds intimidating by name, and it takes a little longer to spot than an X-Wing, but the underlying logic is identical. Once you understand X-Wing, Swordfish is simply the next step up.

The Setup: Three Rows, Three Columns

Swordfish extends the X-Wing principle from two rows to three. The conditions are: choose a candidate digit, find three rows where that digit appears as a candidate in exactly two or three cells each, and all of those cells must fall within the same three columns. That's the full setup — three rows, up to three candidate cells per row, confined to the same three columns.

Notice that not every row needs candidates in all three columns — as long as every candidate in each of the three rows falls within the three designated columns, the pattern holds. A row with candidates in only two of the three columns still participates fully in the Swordfish.

Why the Logic Works

The reasoning follows directly from X-Wing. In each of the three rows, the digit must be placed somewhere — and its only options are the designated columns. Across all three rows, the digit will be placed exactly three times: once per row. Those three placements must land in the three designated columns. Therefore, the three columns are fully accounted for by the Swordfish rows — the digit cannot appear anywhere else in those columns.

The elegance of the argument is that it doesn't matter which specific cells within the pattern end up being correct. No matter how the three rows distribute the digit across the three columns, each column receives exactly one instance of the digit from within the Swordfish. Any other candidate in those columns is impossible.

How to Hunt for Swordfish

The practical scanning method is the same as for X-Wing, extended by one step. For a given digit, scan each row and note which rows have two or three candidates. Group those rows by which columns their candidates occupy. You're looking for three rows whose candidates collectively fall within a set of exactly three columns.

This sounds like a lot of cross-referencing, but with full candidate notation the scan becomes surprisingly quick. Mark every row where the digit has two or three candidates. Then look at the column sets: do any three of those rows share the same three columns? When you find the match, you have your Swordfish.

Some solvers find it helpful to write the column numbers next to each qualifying row as they scan — so row 1 gets labelled "2,5,8", row 4 gets "2,8", row 7 gets "5,8" — and then look for three rows whose combined column labels use only three distinct numbers. The label system makes the visual matching much faster than holding it all in your head.

Swordfish on Columns

As with X-Wing, the pattern works identically in the column direction. Find three columns where a digit is confined to two or three cells each, all within the same three rows. Eliminate the digit from all other cells in those three rows. Both orientations appear with roughly equal frequency, so always check both when hunting.

What Swordfish Feels Like to Find

There's a reason experienced solvers describe finding a Swordfish as one of the most satisfying moments in puzzle solving. You've been staring at a grid that refuses to move. Every simpler technique has been exhausted. Then you spot the three rows, confirm the column alignment, and a wave of eliminations cascades through the grid — often triggering Singles and Pairs that carry the puzzle most of the way to completion in minutes.

That experience is worth working toward. Learn X-Wing first, let it become automatic, then add Swordfish to your toolkit. The puzzles that defeat most solvers will start yielding to you instead.