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Strategies for Popular Number Puzzles

# Y-Wing Chains

This strategy has been deprecated. It is a clear subset of other chaining strategies and does not need to be identified uniquely

The Y-Wing strategy can be extended into chains. Remember, the Y-Wing consists of a pivot cell and two pincers. We keep the principle of the pincers exactly the same. The difference is that the pivot can be replaced by locked pairs.

Our pivot chain for a Y-Wing must proceed at odd numbered cells (or even number of links). A Y-Wing is simply a chain with length = 1.

In Figure 1 we have a Y-Wing Chain marked out in green cells. The 5/7 pivot consists of three pairs of 5/7. The first 5/7 (in which ever order) is connected to the last 5/7 by a third 5/7 in the middle, and by definition this is a locked pair. If the first 5/7 is a 5 then the third one must be a 5 as well. Same goes for number 7.

Our pincer is based on the two green cells marked with a red border - the pairs 7/9 and 5/9. The principle of the Y-Wing says that any cells that both those can see we can eliminate the common number - in this case 9. The two cells marked with a red circle can be 'seen' by both and the 9 removed.
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## ... by: Trevor Bainbridge

In the Y-Wing Chain example there is an opportunity to exploit a special case of three cells looking like a Remote Pairs chain against the rule that it must consist of an odd number of links. If F9=5 then H8=5 and 5 can be erased from F8. But if F9=7 then H8=7 and 7 can be erased from F8. Thus F8=1. This suggests that such a pattern looking like a Remote Pairs chain but with only three cells should have a place in the list of available techniques. But what would it be called? And in what strategy would it belong?

## ... by: Trevor Bainbridge

In this example there is an opportunity to exploit a special case of three cells looking like a Remote Pairs chain against the rule that it must consist of an odd number of links. If F9=5 then H8=5 and 5 can be erased from F8. But if F9=7 then H8=7 and 7 can be erased from F8. Thus F8=1. This suggests that such a pattern looking like a Remote Pairs chain but with only three cells should have a place in the list of available techniques. But what would it be called? And in what strategy would it belong?

## ... by: Donald

This had been one of the most difficult strategies for me to apply or find. I had resolved to using other chaining methods instead. This clears up a big question I have had for a while.
Thanks
Article created on 11-April-2008. Views: 141880