## Swordfish

The final common advanced strategy is named Swordfish. Swordfish works like X-Wing, except that instead of looking for a candidate occurring only twice in two rows or columns, Swordfish is looking for a candidate that occurs two or three times in three columns, in the same three rows. Again, the idea is that wherever this candidate actually occurs in each of the three columns, it will set off a chain reaction that will force the candidate into a spot in each of the shared rows (Penny Publications 6). The strategy works not only for columns against rows, but also rows against columns. Figure 10 demonstrates this perfectly. First of all, note that in the second, sixth, and fifth rows the candidate 6 occurs twice. These occurrences have been highlighted. Because between the three rows, all of the candidate occurrences are limited to exactly three columns, Swordfish can be applied. Swordfish works because it is known that one of two cells in the rows in question will contain a 6, and the cell that gets the 6 will force a cell in another row but the same column not to be a 6, dictating a cell in that other row to have the value 6, in turn setting the location of the final 6 in the last final row. Because the chain of events, no matter which cell is initially determined to be 6, will lead to a 6 being a value in each column in one of the highlighted cells, other cells in those columns but not in the three rows containing 6 as a candidate can have that candidate removed, as indicated with red x-marks in the example. This is not a strategy for the faint of heart.

Fortunately, Swordfish is simpler to implement and utilize than it is to fully understand. Looping through all possible combinations of three rows or three columns and then all candidates 1-9, the algorithm will check to see that all three rowsâ€™ cells containing the given candidate number exactly two or three cells and are members of the same three columns. At this point, the candidate can be removed from each column in question in cells outside of the three rows. That is all it takes to program this final Sudoku strategy. But there is still a slight problem.

September 10th, 2010 at 8:14 pm #GREGORY

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