Swordfish

What Is It?

A Swordfish is the natural extension of the X-Wing pattern from two rows and two columns to three rows and three columns. Pick a digit: if it appears as a candidate in at most three cells in each of three rows, and all those cells fall within the same three columns, the digit is locked into those nine intersections. It can be eliminated from all other cells in those three columns.

Unlike an X-Wing where each row has exactly two candidate cells, a Swordfish allows rows to have two or three cells. The key requirement is that the union of all column positions across the three rows uses at most three columns.

Swordfish is the second member of the "fish" family. It's rarer than X-Wing but follows the same logic. Understanding X-Wing makes Swordfish straightforward, it's the same reasoning applied to a larger pattern.

How It Works

Scan for a digit and find three rows where that digit appears in 2-3 cells each. Check whether all candidate cells fall within three columns. If so, the digit is locked: it must appear once in each of those three columns, using these three rows.

Apply the elimination: remove the digit from all other cells in those three columns that are not in the three defining rows.

The same logic works transposed: three columns with 2-3 candidate cells each, all within three rows, eliminating from other cells in those rows.

Worked Example

Step 1: Scanning digit 3, we find three rows with limited positions. In row 3, digit 3 appears in R3C4 and R3C6. In row 6, it appears in R6C1, R6C4, and R6C6. In row 7, it appears in R7C1 and R7C6. All positions fall within columns 1, 4, and 6.

Step 2: This is a Swordfish. Digit 3 must occupy exactly one cell from each defining row within columns 1, 4, and 6. Therefore, 3 can be eliminated from all other cells in columns 1, 4, and 6.

Step 3: Eliminate 3 from R5C1, R8C1, R8C4, and R8C6. The Swordfish locks digit 3 into the three defining rows.

Key Points

• A Swordfish uses three rows (or columns) where a digit appears in 2-3 cells each, all within three columns (or rows).
• Not every row needs three candidate cells. Rows with two cells are valid, the pattern just needs at most three columns total.
• Row-based Swordfish eliminates from columns; column-based Swordfish eliminates from rows.
• If you understand X-Wing, Swordfish is the same logic with one more row and one more column.

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