Rooted: Created page with "The '''Grouped Turbot Fish''' solving technique extends the definition of a regular Turbot Fish, by allowing nodes in the loop which are '''groups''' of cand..."

2020-06-04T03:35:00Z

Created page with "The '''Grouped Turbot Fish''' solving technique extends the definition of a regular Turbot Fish, by allowing nodes in the loop which are '''groups''' of cand..."

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The '''Grouped Turbot Fish''' [[solving technique]] extends the definition of a regular [[Turbot Fish]], by allowing [[node]]s in the [[loop]] which are '''groups''' of [[candidate]]s instead of single candidates.

In fact, the Grouped Turbot Fish only covers a small area of [[Grouped Coloring]], since it is limited to [[discontinuous]] loops with 5 nodes. The [[Empty Rectangle]] is a pattern which often appears in a Grouped Turbot Fish.

== How it works ==

When all members of a group of candidates can [[see]] all members of another group, these groups are [[link]]ed. The only way this can happen is when all candidates in both groups belong to a single [[house]]. The groups have a [[strong link]] if no other candidates exist in that house, otherwise they have a [[weak link]]. To be useful in a Turbot Fish, each group must be linked at both ends. This limits the number of places where groups can be found. They must be located in an [[intersection]] to be able to interact with 2 houses.

The following diagram shows a '''Grouped Turbot Fish''':

[[Image:Grouped turbot.png]]

The Turbot Fish has two weakly linked groups ('''r46c5''' and '''r5c46'''). The cell '''r5c5''' cannot hold candidate X otherwise there is no weak link between r46c5 and r5c46. Any of the cells in r46c5 or r5c46 may miss the candidate X. It can be described with the following [[loop]]:
(X): r2c2-r2c5=r46c5-r5c46=r5c2-r2c2 => r2c2<>X

A more common variant is better known as [[Empty Rectangle]]. Here is a diagram:

[[Image:Empty rectangle.png]]

This Turbot Fish has two strongly linked groups ('''r46c5''' and '''r5c46'''). The cell '''r5c5''' may also hold candidate X, since this still establish a strong link between r456c5 and r5c456. Any of the cells in r46c5 or r5c46 may miss the candidate X. Here is the loop notation:
(X): r5c2-r2c2=r2c5-r46c5=r5c46-r5c2 => r5c2<>X

== Grouped Turbot Chain ==

Larger Turbot Fish are also known as [[Turbot Chain]]. This implies that there must also be a Grouped Turbot Chain. These do exist, but they are more difficult to recognize as a pattern.

Here is an example:

[[Image:grouped turbot cycle1.png]]

5 groups and 2 standalone candidates are included in this pattern. Here is the written chain:
(X): r13c46-r2c456=r2c8-r8c8=r8c46-r79c5=r123c5-r13c46 => r13c46<>X
Notice that groups may overlap when it does not disrupt the loop. r2c456 and r123c5 can safely overlap, but the groups in box 8 cannot.

[[Category:Solving Techniques]]

Grouped Turbot Fish - Revision history

Rooted: Created page with "The '''Grouped Turbot Fish''' solving technique extends the definition of a regular Turbot Fish, by allowing nodes in the loop which are '''groups''' of cand..."