Wednesday, February 07, 2007

Fishy-SwordFish

Sword-Fish Strategy With X-Wing we looked at a rectangle formed by four numbers at the corners. This allowed us to exclude other occurrences of that number in either the row or column. We can extend this pattern to nine cells connected by locked pairs. In the example below (concentrating on the number 5) we have three sets of locked pairs at AB, CD and EF. They are all horizontal pairs but they also lock each vertically in a staircase fashion (I guess this inspired the name).

The vertical pairing is between AF, BD and CE. Now, in this example we can clearly see that the green horizontal lines connect pairs of 5. Because 5 is also locked vertically the red lines represent columns where if a 5 is not on our grid of nice nodes it can be excluded. There is one such 5 on cell X (E2).
Another way of looking at it is to consider any 5 on the Sword-Fish grid. Pretending for a moment its a real 5 the others in the row and column are repressed. What we're left with is an X-Wing

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