Techniques / Basic fish

Basic fish: X-Wing, Swordfish and Jellyfish

One digit, N rows, N columns, and nowhere else to go.

7 techniques in this family, introduced at tier 3, 7 with a worked example from a real board. How to read a sudoku grid explains the notation used below.

What these have in common

Every fish is one digit considered alone. You ignore the other eight entirely, look at where this one digit can still go, and find that its options in some rows are confined to the same few columns.

Why the logic holds

Pick a digit and two rows. If in both rows that digit can only sit in the same two columns, then those two rows will use both of those columns between them. A column holds the digit once. So both columns are now spoken for, and the digit cannot sit anywhere else in either one. That is an X-Wing. Three rows held to three columns is a Swordfish. Four and four is a Jellyfish. The argument is the same each time.

When to reach for it

After subsets and locked candidates. Fish are a one digit at a time scan, so the practical method is to pick a digit that is nearly placed everywhere, mark its remaining options, and look at the shape.

How the members differ

Only in size, and the names past four are mostly trivia. Squirmbag, Whale and Leviathan are five, six and seven. They are curios rather than tools. A fish of size N in a nine by nine grid has a twin fish of size nine minus N holding the same news, so anything a Leviathan finds a two row X-Wing finds sooner. The base and cover form is the general statement that covers every size, and it is the bridge to the complex fish family.

The mistake to avoid

Confusing rows and columns halfway through the scan. Fix the direction before you start: either you are looking at rows and eliminating in columns, or the reverse, and swapping midway produces a pattern that looks right and is not.

Every technique in this family

• Basic Fish (base and cover formulation)Pick some rows where a digit has only a few spots left.
• JellyfishThe X-Wing idea stretched to four rows and four columns.
• LeviathanA seven by seven version.
• SquirmbagA five by five version of the same idea.
• SwordfishThe same idea as an X-Wing but with three rows and three columns.
• WhaleA six by six version.
• X-WingA digit is stuck in the same two columns in two different rows, making a rectangle.