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X-Wing Family
 
     
 
X-Wing Family

X-Wings are the start of a family of strategies with such evocative names as Sword-Fish, Jelly-Fish, Squirm-Bag and Burma.   They are often considered an advanced strategy but they all operate on a single number so I believe they are mid way and relatively easy to spot.  Only X-Wings are common but we’ll discuss the whole family to be thorough and logical and you’ll soon see the pattern.

X-Wings got their name from the X pattern they make but the original person also had the Star Wars fighter in mind as well (although he confused it with the Tie Fighter which has an X wing shape). 

Naked Pairs
Fig. 12.1

Let’s clear the clutter from an example and see the principle.  On this board with just the 1’s left (candidates – not solutions), we have two columns with just two 1’s left as possibilities.  Now, they are aligned on the same two rows. I’ve marked these special 1’s as 1A, 1B and 1C and 1D. Our logic goes – if A is 1 then B and C will not be and this forces D to be 1.  But if A is not 1 then B and C must be 1’s.  Whatever way round it is any 1 trapped between A and C or B and D, along those rows, can be eliminated.

This introduces us to the idea of Locked Pairs.   The 1’s in A and B lock C and D into being the opposite.  We won’t know which way round the actual solution is until much later after we’ve cracked more of the Sudoku.  But a lot of information is carried in the idea that AB and CD influence each other.  To re-cap:  What ever A and B are they force C and D to be the opposite if you start imagining them having a solution. But either way, there is no room for any other candidates along the alignment of these two sets of pairs.

Going back to our example, let’s fill in the board with all the numbers and overlay the X-Wing.

Naked Pairs
Fig. 12.2

This example is in the opposite direction and we’re looking at number 6.  Quite a few 6’s can be removed in columns 2 and 5. 

Naked Pairs
Fig. 12.3

We can make a rule for X-Wings:

When there are

  • only two possible cells for a value in each of two 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.

However, there is a logical extension of X-Wings to boxes which is counter-intuitive.  Before that, let’s glance over the rest of the X-Wing family which keeps us involved with columns and rows.

 

 
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