Sudoku Swordfish
Sudoku Swordfish is a powerful technique used to solve some very hard Sudoku puzzles. Not every difficult Sudoku puzzle will have this pattern.
You will need to know this technique in order to solve the occasional Sudoku puzzle that has this pattern without (ugh!) guessing.
In this article, I will use one of my handcrafted Sudoku puzzles that has a known Swordfish pattern. Download this very hard Sudoku puzzle #2 if you wish to try to solve this puzzle yourself. You can print the puzzle from your Adobe® Reader.
You will need to partially solve the puzzle to reach the pattern as shown in the picture below. You will encounter naked and hidden singles, naked pairs, and locked candidates. You will also need to solve some cells using the colors technique.
Read my article “Solve Sudoku” for a step by step description on how to reach the place where you apply this technique.
Some of these terms (except locked candidates and color) are explained in my illustrative article Sudoku Tips.
Sudoku Swordfish Pattern
Sudoku Swordfish is a variation of the X-Wing pattern.
A Swordfish pattern occurs when three rows (or three columns) each contain 2 or 3 cells that hold a matching locked candidate.
This candidate must reside in each of the three rows and share the same three columns or vice versa.
In the example shown, a Sudoku Swordfish pattern occurs in rows 1, 8, and 9. The three columns are 1, 6, and 9. Each row has the number 1 in only two cells in this case.
In row 1 the cells are (R1,C1), (R1,C6), and (R1,C9). In row 8 the cells are (R8,C1), (R8,C6), and (R8,C9). In row 9 the cells are (R9,C1), (R9,C6) and (R9,C9). These cells are highlighted in grey.
It is not necessary that all nine cells contain the candidate number 1. In this case two cells (R1,C9) and (R9,C1) are already solved. The cell (R8,C6) doesn’t even have a 1.
The number 1 can only reside in three of the six highlighted cells.
Sudoku rules forbid any other combination. At this point we do not know which three cells the 1 will reside in.
We do know that it must reside in three of the six positions highlighted. (They are locked pairs.) Therefore it is safe to eliminate the 1s from all three columns (or rows) except for the six highlighted positions.
In this example, the two cells circled in red may have the number 1 removed from them safely. When you removed the 1s, you now expose a naked single 3 in (R3,C9).
Solve the naked single and the logjam is broken. You will be able to finish the puzzle quickly now.
Congratulations on solving a very difficult Sudoku puzzle. For more difficult puzzles see my collection of printable free Sudoku puzzles. They come in five levels of difficulty.
