Swordfish technique

Strategy #14 for solving Sudoku: Swordfish

The Swordfish technique is a crucial method for eliminating unnecessary candidates from cells. What's interesting is that nobody knows why this technique is called Swordfish. Its pattern bears no resemblance to a swordfish. Nevertheless, this term has become deeply rooted, and everyone is accustomed to using it daily to solve complex Sudoku puzzles.

This strategy is a derivative of the previous X-Wing strategy. However, in Swordfish, three rows and three columns are involved, which is the main difference. To successfully solve Sudoku puzzles, you need to master both of these strategies.

Sudoku Swordfish Pattern

Finding the Swordfish pattern on the game board is the most challenging task.

The basic Swordfish pattern consists of three candidate cells of the digit "X" in one row, with the remaining candidates in the row ("/") being any other candidate except "X." There should be only three such rows, arranged one below the other. Considering that the digit X must be in one of the three cells in the row, according to Sudoku rules, if the current digit X is in the intersection of the row and column in a cell, then this digit cannot appear anywhere else in that column. These cells are marked with a red asterisk "*."

In the image above, you can see the Swordfish pattern in the rows, where the current candidate can be placed in the position of X. The result of our strategy will be the removal of all X candidates from the "*" cells.

The diagram above shows the basic Swordfish pattern in the columns. Here, a strong relationship between the candidates in the columns is visible. Accordingly, these candidates cannot repeat in the rows where the cells are marked with a red asterisk "*."

Swordfish Sudoku Examples

Let's proceed to Sudoku Swordfish practice:

Above, we see a classic Sudoku game board. For ease of understanding, we have hidden unnecessary numbers and left only assumptions for the number 3. It is important to note that this scheme is taken from a real Sudoku puzzle.

The turquoise color marks the Swordfish pattern with a relationship in the rows. Often, near the first Swordfish figure, you can find the second one. In our case, the yellow cells are marked, which belong to the second Swordfish pattern but with a relationship in the columns. The red cells indicate the cells from which the candidate 3 needs to be removed. Interestingly, these three cells, which "bother" us, contradict two Swordfish figures that we found. Because if we place a larger digit 3 in at least one of these red cells, we immediately violate Sudoku rules, which state that there can only be one digit 3 in a row and column.

On the left side of the image, we already have an example from a real Sudoku puzzle. Here you can see 2 Swordfish patterns for the digit 5. The first Swordfish is perfect, consisting of 3 rows, and the candidates are circled in blue. Since there is only one digit 5 in each of these 3 rows, there cannot be more digit 5s in the columns intersecting with these rows, and they need to be removed from the candidates. The second Swordfish has an almost perfect shape, lacking only one element at the intersection of the fifth row and the eighth column. The figure itself consists of 3 columns, and the candidates are circled in green.

The next step is to clean up unnecessary candidates, and we get the result as shown on the game board on the right. Interestingly, applying this technique allowed us to place a larger digit 5 in the ninth block (circled in yellow).

In the image above, you see the second "live example" of solving Sudoku. In this example, we see one Swordfish construction for the digit 1 (circled in green). It has an irregular shape with rigid connections in the columns. Therefore, we need to remove unnecessary digit 1 candidates in the rows where these columns intersect. The unnecessary digit 1 candidates are marked with a red cross. On the right, we see the result of our strategy.

Conclusions:

This is a very powerful and popular Sudoku-solving strategy for professionals. For those who have read this far, here's a life hack for Swordfish on the game board: look for the Swordfish pattern for digits that have three, two, or one large numbers, but they are located in 3x3 blocks in different rows and columns. Apply this technique only to complex Sudokus, preferably at the third stage, when all basic techniques have already stopped working.

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