Swordfish Sudoku - The 3-Row Extension of the X-Wing Pattern

Swordfish is a pattern where the following holds for a specific digit (e.g., 5). Three rows are selected, and in each row, candidates for 5 are limited to 2-3 cells. Furthermore, the columns containing those candidate cells collectively fit within 3 columns. In this situation, exactly 3 of the 5s in the puzzle must occupy positions within the 3-row × 3-column intersection grid. Therefore, 5 can be eliminated from all other rows in those 3 columns. While X-Wing is a 2-row × 2-column rectangle pattern, Swordfish extends this to 3 rows × 3 columns as the second tier of fish-family (Fish) techniques.

Following the logic strictly: each of the 3 rows contains exactly one 5 (Sudoku rules forbid duplicates in a row). Each row's 5 must be located in one of the 3 chosen columns. So the 3 rows together contribute 3 fives distributed across 3 columns. By the pigeonhole principle, exactly one 5 lands in each column. This means all 5s in the chosen 3 columns are accounted for by the chosen 3 rows. There's no room left for 5 in any other row of those columns, so 5 can be eliminated from those cells. This is the same principle as X-Wing extended to a third dimension.

Swordfish exists in two variants: row-based and column-based. Row Swordfish, as described above, starts from 3 rows and eliminates from 3 columns. Column Swordfish is the reverse: starting from 3 columns where 5 is limited to 2-3 cells per column, those candidates collectively fit within 3 rows, and 5 can be eliminated from other columns in those rows. The logic is symmetric, but in actual puzzles, one direction is often easier to spot than the other depending on the board state. Habitually scanning both directions reduces oversight. Note that candidates need not be exactly 2 cells per row (column); 3 is fine. The key point is that 'the 3 rows (columns) collectively fit within exactly 3 columns (rows).'

Swordfish scanning follows these steps. Step 1: Examine each digit from 1 to 9 in order. Step 2: Prioritize digits with 3-5 placements (not too many, not too few). Step 3: Record the column positions of that digit's candidates in each row. Example: Row 2 has {3, 7}, Row 5 has {3, 5}, Row 8 has {5, 7}. Step 4: Find combinations of 3 rows whose candidate columns collectively fit within 3 columns. In the example, rows 2, 5, 8 have candidate columns summing to {3, 5, 7} - exactly 3 columns. Step 5: Eliminate the target digit from rows other than the 3 chosen (rows 1, 3, 4, 6, 7, 9) in those 3 columns. With practice, you can pattern-recognize candidate distributions visually.

Swordfish sits in the middle of the fish-technique hierarchy. The smallest is X-Wing (2 rows × 2 columns), then Swordfish (3 rows × 3 columns), then Jellyfish (4 rows × 4 columns). Jellyfish and beyond are practically rare, but the logical structure is identical. Generally, 'N-Fish' has N rows × N columns, with each row's candidate positions fitting within N columns. The larger N is, the harder it becomes to spot. In Master/Extreme puzzles, Swordfish often serves as the decisive breakthrough. Because it can be searched more systematically than <a href="/en/articles/sudoku-coloring-technique/">Coloring</a> or <a href="/en/articles/xy-wing-technique/">XY-Wing</a>, it's the next priority technique to master after stable Expert solving.

Swordfish is a technique within easy reach if you understand the X-Wing. If the X-Wing is a structure closed within two rows and two columns, Swordfish is merely that extended to three rows and three columns. The logical core is the same - the pigeonhole principle that if a number appears in limited rows and its columns fit within a fixed count, you can erase candidates from the leftover places. The only difference is that the rows and columns handled increase by one. Therefore, once you can find X-Wings stably, the next thing to acquire naturally becomes Swordfish. Even though it looks complex, viewing it as merely widening the X-Wing idea by one step lowers the psychological barrier.

Actually finding a Swordfish is hard in your head alone. A device of writing out, as column numbers, which columns the target number's candidates lie in for each row is effective. For example, list the candidate columns of each row for a number, and look for a combination of three rows whose candidate columns total exactly three columns. This work presupposes accurate marks. A missed candidate makes you overlook a valid Swordfish, and an un-erased one makes you misread an invalid one. Making a habit of checking both row-based and column-based directions alternately greatly reduces what you miss.