Swordfish in Sudoku

Specialist S5 Fish

Work on one digit. Find three rows with two or three possible cells each for it, all within the same three columns. Those columns must contain the digit in the selected rows, so remove it from their other cells. The same pattern works with rows and columns reversed.

A candidate is a digit that can still go in an empty cell. Cells see each other when they share a row, column or 3×3 box. A strong link means a digit has exactly two possible cells in one such group: exactly one must contain it.

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. Each selected column must be reached by at least two of the rows; otherwise a smaller pattern is involved.
  • You can also start with three columns and look for the same restriction to three rows.

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 a candidate to cross it out; click it again to restore it. Remove the 6 candidates ruled out by this technique, then press Check. This exercise leaves your game unchanged.

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 covers plain Swordfish in both orientations, with two or three possible cells per selected line. Patterns that reduce to an X-Wing are handled as the smaller technique.

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 follows one digit through a network of strong links. Colour linked cells alternately: either every cell of colour A holds the digit and none of B does, or the reverse. Those two possibilities can rule out candidates.
  • Y-Wing A Y-Wing uses three cells with two candidates each. One cell, the pivot, sees both wings. Whichever digit fills the pivot, one wing must hold the digit shared by the wings, so any cell seeing both wings loses that candidate.

All Sudoku techniques