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Generalization : Naked groups

If you have carefully read the descriptions of the solution procedures, you may have noticed that some of the methods are grouped together in families. It is Therefore, useful to describe their rules in an abstract, generalized form, so that they are universally applicable.

First, some definitions:
Dimension - the size of the puzzle. The dimension must always be a square number.
Character set - the symbol set used in the puzzle. It always contains a number of symbols equal to the dimension.
BSize - the size of each block. This refers to the length of the sides of the inside squares. It is always the root of the dimension.
Logical Unit - the general name for rows, columns and blocks. In other words, those logical units that must contain each symbol of the character set exactly once. Occasionally there are puzzles in which the diagonals are also considered logical units.
Order - the ordinal number of a group. 2nd order would be a Twin, 3rd order would be a Triplet, etc. In this context, the order is the number of rows or columns that are present in the pattern.

The general formulation of the criteria for Naked groups:
We're looking for order fields of a logical unit whose cumulative candidate list contains exactly order candidates. If this pattern is found, the candidates in the cumulative candidate list can be eliminated from all of the fields in the logical unit that do not belong to the group.
(Note: The fact that each field in the group contains at least two candidates of the group and no candidates which do not belong to the group is already implied by the accumulation and grouping of the fields and need not be mentioned separately.)

If we have already made the effort to abstract and generalize the methodology, it also seems necessary to briefly discuss how using them makes sense.
Technical analyses and logic suggest the following assessments:

  • Both basic methods are always needed to solve a puzzle. That includes the Naked One.
  • Searching for Naked groups of orders 2 to BSize is always useful.
  • Searching for Naked groups of orders (BSize + 1) to (½ * Dimension) is complex and rarely produces results. But if there is a lack of other options, it is justified.
  • Searching for Naked groups with orders greater than (½ * Dimension) is not useful , since such a group is usually complementary to a smaller Naked or Hidden group.

Special cases of the Naked group:

  • The Naked One is a special case because a One is not a group, and because it has a fill-in rule instead of a elimination rule.
  • Then there's the Naked Twin. It stands out because all fields of the group contain all candidates of the group.
  • Finally, the Naked Triplet is the first "normal" member of the family (as are all higher orders).

see also: Naked One, Naked Twins, Naked Triplets, Naked Quadruplets, Naked Quadruplets in Hexadoku

 

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