Swordfish

Description

The Swordfish pattern is a 3x3 set of cells which have the same candidate in either 3 rows or 3 columns.

If the candidate is found 3 times in 3 rows, and they line up in the same 3 columns, it can be removed from all other cells in the 3 rows. Similarly, if the candidate is found 3 times in 3 columns and it lines up in the same 3 rows, than the candiate can be removed from all other cells in the 3 columns.

If one of the 9 cells contains a given or guess value, it can be considered as a valid cell with the candidate in it. Therefore not all 9 cells have to have the candidate in it.

Reasoning

Because the candidate appears exactly 3 times in each row and there are 3 rows, it means that the candidate must appear exactly three times in these 3 cells. Therefore it cannot apear anywhere else in the 3 rows. Similarly for the column based Swordfish.

A Swordfish pattern does not have to contain all 9 candidate cells, but there must be at least 2 candidates in each of the 3 row and column.

Examples

Row Example

9 forms a Swordfish in rows 1, 6 and 7.

That means that candidates 9 can be removed from all other cells in rows 1, 6, and 7, which are not in columns 1, 2, and 7, cells [1,4] and [1,5].

Column Example

7 forms a Swordfish in columns 1, 4 and 5.

That means that candidates 7 can be removed from all other cells in columns 1, 4 and 5, which are not in rows 1, 5, and 9, cell [2,5].

Algorithm

  1. Fill in all the pencil marks in the puzzle.
  2. For every available digit 1 to 9
    1. For every combination of 3 rows
      1. Find the if digit candidate is in the same exact 3 columns for all 3 rows. If a value is in a column, it's considered ok.
      2. If yes, then we can remove all the candidates from those rows which are not in our 3 columns.
    2. For every combination of 3 columns
      1. Find the if digit candidate is in the same exact 3 rows for all 3 columns. If a value is in a row, it's considered ok.
      2. If yes, then we can remove all the candidates from those columns which are not in our 3 rows.

Practice Puzzles

If you tap on the following links on an iOS device which has the Sudoku Tutor app installed, it will launch the app and open the practice puzzle. Tap hint once the puzzle is open to see the strategy in action.

Sample Puzzle 1
Sample Puzzle 2

Next Step

Back to Sudoku Solvers or continue to next algorithm Singles Chain