Mirrored from Sudopedia, the Free Sudoku Reference Guide

# Fish

The term fish is now accepted by most players as a name for all single-digit solving techniques which eliminate candidates by comparing sets of rows and columns.

Aliases are seafood and sealife.

Not all sizes of fish were discovered at the same time. Size 2 was already familiar to many players before they realized that the same trick could also be performed with more than 2 rows and columns. Here is a list of names given to fish of different sizes. They are often seen as different solving techniques. The term Swordfish has also been in use for all types of fish with more than 2 rows or columns.

## Introducing Boxes

It became clear in the big fish discussion that fish did not need to be restricted to rows and columns alone. It is also possible to include boxes in the pattern. Nowadays, any single-digit pattern that compares 2 partially overlapping constraint sets of equal size is called a fish. In standard Sudoku, the sets can contain rows, columns, and boxes. In Sudoku Variations with additional constraints, any combination is possible. This viewpoint allows us to redefine a Law of Leftovers move as a fish pattern. In Killer Sudoku, constraint sets can also include cages, as long as each cage involved is known to contain the digit on which the Fish pattern is based.

## Constraint Sets

In each fish, we consider 2 sets of constraints. Both sets must partially overlap. The sets are called the defining set and the secondary set.

These are the rules to select these sets:

• Houses may overlap within a set, but in the defining set, the overlapping cells may not contain any candidates. It is imperative that each candidate can only satisfy a single constraint within this set.
• Each house in the defining set must overlap at least one house in the secondary set.
• Each house in the secondary set must overlap at least one house in the defining set.
• All candidates in the defining set must also belong to a house in the secondary set. Each of the overlapping candidates must belong to a single house in the secondary set.
• The secondary set must have candidates which do not belong to the defining set. These surplus candidates are the ones to be eliminated. The surplus candidates may belong to more than one house in the secondary set.

## Fins

A fin is a candidate or group of candidates in the defining set, which does not belong to the secondary set. It is a surplus to the underlying fish pattern. For each finned version of a fish pattern, we can only eliminate in cells in that we could eliminate with respect to the fish pattern and that can see all fins.

## Species

Basic Fish
Rows vs. columns or columns vs. rows.
X-Wing (2) | Swordfish (3) | Jellyfish (4) | Squirmbag (5)
Finned Fish
Basic Fish with additional candidates in a single box.
Finned X-Wing | Finned Swordfish | Finned Jellyfish
Sashimi Fish
Finned Fish without candidates for the basic pattern in the box containing the fin.
Sashimi X-Wing | Sashimi Swordfish | Sashimi Jellyfish
Franken Fish
Boxes are allowed in either the defining set or the secondary set.
Franken Swordfish | Franken Jellyfish
Mutant Fish
Any type of fish which does not fit in one of the other categories.
Mutant Swordfish | Mutant Jellyfish
Kraken Fish
A fish pattern with indirect connections to a candidate which can be eliminated.

Some people use the term N-Fish to refer to a (basic) fish of N rows or columns. That is:

## Fish and Subsets

Fish and Subsets are complementary to each other. One can transform a problem of finding a fish into a problem of finding a subset, and vice versa. See Fish and Subsets for more.