### ... by: Pieter, Newtown, Oz

Hi Andrew

I found an interesting Jelly-Fish (my first ever, actually) in the local paper [Load Puzzle].

It's interesting cuz there are 2 simultaneous Jelly-Fish on 4's! The Solver finds CDFG2357 (a 3-4-2-3 J/F), but there is also one at ABEJ1469 (a 3-4-4-3), and also interestingly, the same 7 eliminations are made by both.

BTW - Since I use Letters & Numbers to define cells, I found the rYcX notation totally confused me at first! "JF=r3467c2357"???
Andrew Stuart writes:

This is an interesting example. To see the second Jelly Fish, use the [<<] back button and then rotate once 90 degress (either way). Hit take step a few times.

### ... by: John Francis

John White observes:

You can extend all of these in the following ways:

A. You are not restricted to rows and colums.

B. As with X-Wing and Swordfish, you can 'Fin' Jellyfish.

C. Why stop at 4......

The reason for stopping at 4 is because of the symmetry between possible candidates in a cell and potential sites for a given digit.

It's best explained by considering Naked and Hidden n-tuples.

Consider a Naked heptuple. This is a set of seven cells in one set (row, col or box) which between them only have seven different candidates. This means that these seven cells will contain those seven values in some order.

Now describe that situation it another way. The cells *not* in the n-tuple are the only ones which can include numbers not in those n candidates.

This is the description of a hidden (9-n)-tuple (hidden pair, in this case).

This means there's no need to go beyond 4 in describing a strategy; Naked quints are the same as hidden quads, and so on. For a strategy described using numbers greater than four there is an equivalent description using smaller numbers (and interchanging the roles of candidates in a cell and positions for a digit).

### ... by: Philipp Huebner

Shouldn't John White's main sentence be: "If the overlap of these two groups contains all the possible candidates for any given number in one of the groups then you can remove all the candidates in the other group that are not in the overlapping area." (I added: "... in one of the groups ...")

### ... by: John White

Jelly fish is a sub category of a more general system:

Take any group of N disjoint (not overlapping) sets(row,column or box) and compare them to any other group of N disjoint sets. If the overlap of these two groups contains all the possible candidates for any given number then you can remove all the candidates in the other group that are not in the overlapping area.

If N=2 you get X-Wing

If N=3 you get Swordfish

If N=4 you get Jellyfish

What this means is that you can extend all of these in the following ways:

A. You are not restricted to rows and colums.

B. As with X-Wing and Swordfish, you can 'Fin' Jellyfish.

C. Why stop at 4......

(Finning: if all candidates from one of the groups that are not contained in the overlap can be contained by one more set (row, colum or box) (the set must not be in the original 2 groups!), then the candidates contained in overlap of this extra set and the second group can be removed.