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Jellyfish

The Jellyfish is basically an old friend. The smallest version of this family is the X-Wing, followed by the Swordfish. And their bigger brother is in turn the Jellyfish. The logic is as simple as with the smaller siblings, but, with increasing complexity, the pattern is difficult to see. Which is why the Jellyfish is considered a very difficult higher method.

Just like its smaller siblings, the Jellyfish can be seen both from the row and the column perspectives. While the X-Wing and the Swordfish are special cases, the Jellyfish is the first "normal" member of this family.

Criteria, formulated for the row perspective:
We're looking for four rows in which the same candidate occurs exactly twice, and the occurences are distribute over a total of four columns. If this is the case, then the candidate can be eliminated in all fields in the columns that do not belong to the four lines of the Jellyfish.

There is no realistic example for this pattern because in 9x9 puzzles the Jellyfish is just as rarely the best option as the Quadruplet pattern.
Below are two sketches, but if you want to see a real Hexadoku that contains a Jellyfish, click here.

This sketch is intended to illustrate the pattern. The rows of the Jellyfish are pink, X represents the occurences of the candidates, and the fields where the candidate can be eliminated are yellow.

This distribution can only be solved in two ways: along the drawn lines.

Note that the occurences are regularly distributed over the columns. Each column contains exactly two occurences. This is an important detail, though it is not part of rules for the Jellyfish.

This regular distribution makes a big difference to the smaller brothers. In the Swordfish the distribution over the columns must be regular, otherwise it's not a Swordfish.

 

Sudoku example Jellyfish (schematic)

 

This sketch shows a Jellyfish with an irregular distribution over the columns.

Note two things: First, the right X is in both solution paths, and second, the green X will never be true.

In principle, this does not affect the Jellyfish, because the yellow fields are still elimination fields. But of course the green X would have been evident if you used the Blocked Blocks method, and the right X would have then become a Hidden One ... so you probably would have already found an other way to solve this puzzle.

That is what "the best option" means. Such patterns do sometimes emerge, but only rarely are they really needed to solve the puzzle.

A "proper" Jellyfish will always have a uniform distribution of occurences over the columns.

Sudoku example Jellyfish (schematic)

see also: Hexadoku with Jellyfish, Generalization: Multidimensional groups

 

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