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Naked Quadruplet

The Naked Quadruplet is of course the logical continuation of the Naked Triplet. While the Triplet is still considered moderately difficult, the Quadruplet is considered a very difficult higher method. So it is more difficult than the Kite or Skyscraper method.
This assessment is quite plausible, because the pattern has very many possible manifestations. This makes it difficult to see in practice.

We're looking for four fields of a logical unit whose cumulative list of candidates includes exactly four candidates. At the same time each field in the group must contain at least two candidates of the group and must (logically) not contain any candidates which do not belong to the group. This is logical because additional candidates are automatically included in the cumulation.
Since it is certain in this scenario that ultimately each of the four fields will be filled in with one of the four candidates, these candidates can be deleted from all other fields of the logical unit.

Does this sound familiar? It should, because basically this principle of thought started with the basic method Naked One.

As is often the case, the logic of the pattern is immediately apparent, but it is hard to see because the fields of the direct Quadruplet can contain very different candidates. Suppose, for instance, that the Quadruplet includes the candidates 2,3,6,8. Then the fields could, for example, contain the following list of candidates; (38) (26) (368) (23).
Even if you know that this is a Naked Quadruplet, it is still hard to see.

There isn't a realistic example for this method, because in 9x9 puzzles it is extremely rare that a situation arises in which all easier methods fail and a Naked Quadruplet is suddenly the best option for further progress.

If you want to see an example, there is one in the Hexadoku section. The larger the dimensions of the puzzle, the higher the probability of complex patterns.

see also: Generalization: Naked groups



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