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Swordfish: the Sudoku technique explained

  • Master
  • Needed from Fiendish puzzles
  • 8 points in Duel

An X-Wing on three lines.

A Swordfish is an X-Wing stretched to three lines. When a digit's candidates in three rows all fall within the same three columns, the digit can be removed from every other cell of those columns.

How it works

Three rows each need one copy of the digit. If, in all three rows, the digit can only go in the same three columns, then those three copies will take one cell in each of the three columns. The columns are fully supplied by these rows, so no other cell in the three columns can hold the digit.

Each row does not need a candidate in all three columns. A row may have the digit in only two of them. What matters is that across the three rows the candidates cover three columns and no more. As with the X-Wing, it also works with rows and columns swapped.

  1. Choose a digit and list the rows where it has two or three candidate cells.
  2. Find three of those rows whose candidates, combined, sit in exactly three columns.
  3. Remove the digit from every other cell of those three columns.
  4. If rows give nothing, try columns.

A real example

11223344556677889957891524786147145783235678438378195678568378136781365347891467146782427169536896899135613563628146145673513568436972156956914789685367246378378296845367163453571283949
Swordfish. 6 in column 3, column 4 and column 7 is locked to row 3, row 5 and row 7, so 6 can be removed from the rest of those rows. That leaves a simple move: the cell at row 7, column 9 can only be 4: every other digit is already in its row, column or box.Blue: the pattern. Red: candidates that are removed. R3C7 means row 3, column 7.

The blue cells are the digit's candidates in the three base lines. They occupy just three crossing lines, so the red candidates elsewhere on those crossing lines are removed.

How to spot them

Work with one digit highlighted. Ignore rows where the digit is placed or has four or more candidates. Among the rest, look for three that agree on their columns. It helps to write down the column numbers for each row and look for three sets that fit inside the same three numbers.

How often you need one

Swordfish is the rarest technique Sudoku Clan uses, and it only appears in Fiendish puzzles, the top level. In Duel, a digit you place because of a Swordfish scores 8 points, the most a single digit can earn.

Questions

What is a Swordfish in Sudoku?

A pattern where a digit's candidates in three rows are confined to the same three columns. The digit is then removed from all other cells in those columns. It also works with columns as the base and rows as the cover.

What is the difference between an X-Wing and a Swordfish?

An X-Wing uses two rows and two columns. A Swordfish uses three rows and three columns. The reasoning is identical.

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