Basic Fish (base and cover formulation)

Also called Fish, Rank-zero fish, Basic Fish pattern, N-Fish.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Pick some rows where a digit has only a few spots left. If all those spots line up in the same number of columns, the digit uses up every one of those columns. So it cannot appear anywhere else in them. It works with rows and columns swapped too.

The exact rule, for stronger players

The rule, stated exactly: For digit d, choose n base sets, all lines of one orientation, and n cover sets, all lines of the other. If every candidate of d in the base sets lies in some cover set, then d may be eliminated from any cover-set cell not in a base set.

What it removes: Remove d from cover cells not covered by a base set.

Why it works: Each base line places d exactly once, giving n placements. All lie in the n cover lines, and each cover line admits d at most once, so the covers hold exactly n placements with no room left. Any candidate in a cover outside the bases is therefore impossible. The count n bases to n covers is what makes the rank zero.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Basic Fish (base and cover formulation). In r1, r7 every 6 lies in c7, c9. Each of those rows needs a 6, and between them they use up c7, c9 entirely, so no other cell in those columns can be 6. — In r1, r7 every 6 lies in c7, c9. Each of those rows needs a 6, and between them they use up c7, c9 entirely, so no other cell in those columns can be 6.

Sudoku grid showing Basic Fish (base and cover formulation). In r2, r6 every 8 lies in c5, c6. Each of those rows needs a 8, and between them they use up c5, c6 entirely, so no other cell in those columns can be 8. — In r2, r6 every 8 lies in c5, c6. Each of those rows needs a 8, and between them they use up c5, c6 entirely, so no other cell in those columns can be 8.

Learn these first

Locked Candidates (general form)Sometimes all the spots for a digit inside one group also sit inside a second group.
Hidden PairTwo digits in one group can only go in the same two squares.

Related basic fish

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.

How often does it come up?

Our rough estimate: umbrella page. Teaching the base and cover formulation once makes finned, Franken, and Mutant fish comprehensible later, which is why this page exists rather than six separate size-specific explanations.

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