Swordfish in Sudoku

Specialist S5 Fish

A Swordfish is the same idea as an X-Wing with three lines instead of two. One candidate has only two or three possible cells in each of three rows, and together those cells touch exactly three columns. The candidate is then confined to those three columns and can be removed from every other cell in them.

How to spot it

  • Pick one candidate and follow only that digit, exactly as with an X-Wing.
  • Find rows where the candidate has two or three possible cells. Three is allowed here - that is the difference from an X-Wing.
  • Take three such rows at a time and see which columns they collectively touch.
  • Exactly three columns means you have a Swordfish. Four or more and the pattern does not hold.
  • It does not need nine cells. Anything from six to nine works, as long as they spread across three rows and three columns.

Why it works

The three base rows must each contain the candidate exactly once - three times in total.

Every possible position lies within three columns. So three occurrences have to be distributed across three columns, and no two can share a column, because a column also holds the candidate only once.

Each of the three columns therefore takes exactly one. The candidate is fully accounted for in all three, so it can be cleared from the remaining cells.

A real example from Sudokuno

The board below is a real Sudokuno puzzle, shown exactly as it stands just before Swordfish applies. Everything up to this point was solved with ordinary techniques.

3 2
5 4
9
1
1
9
2
4
6 4
9 3 1
3
8
1 2
2 1 5
3
1 6
9
7 8
1 8 6
9
3
7
6 1
2 6
1 9

Click away the candidates the technique removes - 6 of them - then press Check. Nothing is saved, and your own game is untouched.

Sudoku: SNC-00577 — Sudokuno

  • Candidate 4
  • Houses: column 3, column 6, column 8, row 4, row 5 and row 9
  • Pattern: R4C3, R4C6, R5C6, R5C8, R9C3 and R9C8
  • Removes 4 from R4C1, R4C9, R5C1, R5C9, R9C4 and R9C9
  • Step 18 of 59 in the solve

Key: pattern cells target cells

How the hint helps you

Sudokuno's hint reveals the structure in three steps, without giving away the digit straight away.

  1. Hint 1 The next technique is Swordfish. The name, but no digit and no cells.
  2. Hint 2 One candidate appears in only three columns across these three rows. The six lines are highlighted; the digit is held back.
  3. Hint 3 The three rows confine the candidate to these three columns, so it can be removed from the highlighted cells in those columns.

If the pattern is column-based instead, the hint says the same thing with rows and columns swapped. The digit is never named at any stage.

Ready to try it yourself?

You will get a real Sudokuno puzzle at Specialist level S5, where Swordfish is needed to finish it.

Practise Swordfish

What Sudokuno covers

Sudokuno finds plain, finless Swordfish in both orientations. Finned variants, Jellyfish and larger fish, and Franken and Mutant variants are not implemented. Patterns that are really a hidden X-Wing are rejected, so the technique is always a genuine Swordfish.

Where to go next

  • X-Wing An X-Wing appears when one candidate has exactly two possible cells in each of two different rows, and both pairs sit in the same two columns. The four cells form a rectangle. The candidate must then occupy two opposite corners, one per row, so it can be removed from every other cell in those two columns.
  • Simple Colouring Simple Colouring looks at one digit at a time. When a row, column or box has exactly two places left for that digit, the two cells are strongly linked: exactly one of them holds it. Join such pairs together and you get a network that can be coloured alternately in two colours, and then exactly one of the colours is the true one. That is enough to remove candidates, even though you do not know which colour is which.
  • Y-Wing A Y-Wing is three cells that each have exactly two candidates. The pivot sees both wing cells. It shares one candidate with each wing, and the two wings have a third candidate in common. That third candidate has to land in one of the wings, so it can be removed from any cell that sees both of them.

All Sudoku techniques