Swordfish: the three-row version of X-Wing

Once you can see an X-Wing, Swordfish is the same idea with one more row and one more column. It is harder to spot, because the three rows do not each need to use all three columns. Yet it is still a fixed pattern that you can check step by step. You will need it when the simpler techniques stop working on an Expert puzzle.

What is a Swordfish?

A Swordfish is a fish pattern for one digit across three rows. In those three rows, the digit’s candidates fall into only three columns, and each row holds it in two or three of those columns. The digit can then be removed from the same three columns in every other row. In plain words, the three rows use exactly three columns for that digit, so those columns are taken care of.

How it works

Cells are written as r#c#, row first and then column. So r5c4 is row 5, column 4.

The logic is simple once you see it. Each row must contain the digit somewhere, and each column can hold it only once. The three rows therefore place the digit in three different columns. If all their candidates lie in three columns, then those three columns hold the digit in the three rows and nowhere else. Any other row loses the digit in those columns.

The method has three steps:

1. Find three rows with the digit. Each of the three rows should have two or three candidate cells for the digit.
2. Check the columns. The candidate cells of all three rows must fall in the same three columns.
3. Remove the digit from those columns. Every other row loses the digit in those three columns.

The first diagram shows candidate 5 in rows 2, 5 and 8. Row 2 has 5 in columns 1 and 7. Row 5 has 5 in columns 1, 4 and 7. Row 8 has 5 in columns 4 and 7. The three columns are 1, 4 and 7. The cells marked x are the pattern. The cells marked - are r1c1, r3c4 and r6c7, where 5 is removed. Rows 2 and 8 each hold only two of the three columns, which is allowed.

The column-based version

The same pattern works with rows and columns swapped. In the next diagram, candidate 8 sits in columns 2, 5 and 9, and every 8 in those columns falls in rows 1, 4 or 7. The cells marked x are the pattern, and the cells marked - are r1c8, r4c3 and r7c6.

How to spot it

• Start with a digit that appears in few cells per row. Rows with two or three candidate cells for the digit are the building blocks of a Swordfish.
• Collect the candidate columns. Write down the columns of all candidates in each of the three rows. If they fit inside three columns, you have a Swordfish.
• Accept a row with only two columns. A row does not need all three columns. Two is enough, and that is the case that most people miss.
• Check for a stray candidate. A candidate of the digit outside the three columns, in any of the three rows, breaks the pattern.
• Search both directions. Swordfish appears in rows and in columns. Check both before you decide that a puzzle has no Swordfish.

A worked example

Take the column-based diagram and follow candidate 8. Columns 2, 5 and 9 are the defining columns.

• Column 2 has 8 in r1c2 {3,8} and r4c2 {2,8}.
• Column 5 has 8 in r1c5 {5,8}, r4c5 {1,8} and r7c5 {6,8}.
• Column 9 has 8 in r4c9 {4,8} and r7c9 {2,8}.

All of these candidates fall in rows 1, 4 and 7. Each of those columns must hold an 8, and the three 8s must sit in three different rows: 1, 4 and 7. So no cell in rows 1, 4 or 7 outside columns 2, 5 and 9 can be 8.

That removes 8 from three cells:

• r1c8 {1,8,9} loses the 8 and becomes {1,9}.
• r4c3 {3,6,8} loses the 8 and becomes {3,6}.
• r7c6 {6,8,9} loses the 8 and becomes {6,9}.

A rarer extension: Jellyfish

The Swordfish has a larger relative called the Jellyfish. It uses four rows and four columns, and the same logic applies: one digit is confined to four columns across four rows, so it can be removed from those four columns elsewhere. Jellyfish is much rarer, and few players will meet it in practice. Hush’s Expert level is built on Swordfish, XY-Wing and XYZ-Wing, so you can treat Jellyfish as a curiosity rather than a requirement.

Common mistakes

• Expecting all three columns in every row. Each row must have two or three candidates in the columns, not necessarily all three.
• Removing from the pattern rows. The rows that make up the Swordfish keep the digit. Only the other rows lose it in the three columns.
• Missing one candidate. A single stray candidate outside the three columns breaks the pattern.
• Looking only at rows. Columns can hold the same pattern. Check both orientations.
• Confusing it with X-Wing. An X-Wing needs two rows and two columns. A Swordfish needs three of each, and a row may use just two of the columns.

Practice Swordfish in Hush

Hush rates Swordfish as an Expert technique. Expert puzzles in Hush need at least one of Swordfish, XY-Wing or XYZ-Wing, and the first 10 solved Hard or Expert puzzles are free. Hush Plus, a one-time purchase at $4.99, unlocks unlimited Hard and Expert puzzles. Highlights for row, column, box and matching numbers help you see every place a digit still appears, which is what a Swordfish search needs. Notes clean themselves up when you place a number, so the candidate lists stay accurate. Hush also works fully offline, so you can practice anywhere; see offline sudoku.

Before you tackle Swordfish, make sure you are comfortable with X-Wing, the two-row version of the same idea. Once Swordfish is familiar, the next technique is XY-Wing. If you are comparing apps, the Good Sudoku alternative page explains how Hush and Good Sudoku differ. For the complete path through the levels, visit the technique guides or read about Expert sudoku.