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 Sword-Fish
Sword-Fish

X-Wing operates on two rows (or columns) aligned with two columns (or rows).   Can it be extended to three rows and columns?  Logically yes, and we’re taking about a grid of nine cells here, not four, but interestingly not everyone of the nine cells needs to have the number under consideration.

Let’s look at the Sword-Fish ‘grid’ and see what’s going on. Here we are looking at all the 5 candidates in this Sudoku, everything else removed.

Fig. 13.1

Three rows all have three number 5’s on them: rows B, F and G.  It so happens that all the fives are aligned vertically on the same columns (2, 5 and 8).  The intersection of these three rows and columns occurs at nine points (circled) but only three of these cells can be a 5 and still confirm to Sudoku rules.   We don’t know which three of the nine (apart from B5 which has been eliminated earlier).  But they are all locked and mutually exclusive.   Because of this there can be no 5’s along the lines of this grid.   All 5’s in the grey columns in this example can be removed.

If we reveal the actual Sudoku you’ll agree it’s pretty hard to see and it will be a diabolical grade if this strategy is necessary.

Fig. 13.2

Where does the Sword-Fish name come from?   Well, the first time this was spotted the grid was stepped jaggedly – not every nodes needs the number under consideration.  As long as there are at least two numbers in each of the three lines, the logic holds.  Some possible configurations are in Figure 14.3. To show this, pretend any of these nodes has the solution and how that forces the others in the triple to contain that number or not.

The Rule for Sword-Fish can be expressed as follows:

When there are

• only three possible cells for a value in each of three different rows,
• and these candidates lie also in the same columns,

then all other candidates for this value in the columns can be eliminated.  The reverse is true for columns instead of rows.

Fig. 13.3

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