Fish with chains

Advanced methods and approaches for solving Sudoku puzzles

Fish with chains

Postby Wepwawet » Sat Apr 11, 2020 2:13 am

I previously posted this in the wrong section, so I have moved it to here. See below a Finned Jellyfish of the digit 2. Lilac cells indicates the regular jellyfish, the brown cell the fin, the purple cells indicate the digit 2 that would be eliminated if the fin was not a 2. There is a chain leading from the fin to r2c5 which means, whatever the value of the fin the 2 in r2c5 is always eliminated.

2 r9c9 - 2 - r8c7 = 2 = r2c7 > r2c5 <> 2

Finned Jellyfish with chain.png
Finned Jellyfish with chain.png (11.31 KiB) Viewed 255 times

So, would one of these be an acceptable notation;

[ Finned Jellyfish (2) r1469 c2459 fin r9c9 ] - 2 - r8c7 = 2 = r2c7 > r2c5 <> 2

or, as the digit 2 is already defined in the Jellyfish statement ...

[ Finned Jellyfish (2) r1469 c2459 fin r9c9 ] - r8c7 = 2 = r2c7 > r2c5 <> 2

or, something like;

[ Finned Jellyfish (2) r1469 c2459 fin r9c9 ]: r9c9 - 2 - r8c7 = 2 = r2c7 > r2c5 <> 2

I am just interested to know the correct notation, that will show the chain, leading to a definite conclusion. I am still hoping someone can answer, if there is a term for this type of hybrid fish/chain construct. Please note, I am not interested in other solutions, as you know, there are usually more than one way to skin a cat in sudoku. Thanks in advance.

... edited to make more readable, and correct typo as pointed out by Cenoman
Last edited by Wepwawet on Wed Apr 15, 2020 10:57 pm, edited 1 time in total.
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Re: Fish with chains

Postby Cenoman » Wed Apr 15, 2020 2:43 pm

Wepwawet wrote:I am just interested to know the correct notation, that will show the chain, leading to a definite conclusion.

A fin is a candidate "spoiling" a fish.
If the fish is not spoiled, you have in the eventual solution of the puzzle, one digit true per initial truth in the fish.
In your example: one 2 per each line 1,4,6,9. The fin 2r9c9 being True prevents 2r9c28 being True [i.e. it prevents (2r9c2 OR 2r9c8) being True]
Reciprocally, the fish being True prevents the fin being True
So you can infer: Whether JF(2)r1469\c2458 is true OR 2r9c9 is true
Thus you can write a strong link [JF(2)r1469\c2458] = r9c9, or [JF(2)r1469\c2458] = (2)r9c9 (if you search for more explicitness)
The complete chain for 2r2c5 elimination:

[JF(2)r1469\c2458] = r9c9 - r8c7 = (2)r2c7 -> r2c5 <> 2

The fin need not to be included within the brackets. You could write "Finned Jellyfish" as introductory words,

Note1: typo in your proposed chains: r2c5 <> 5 should read r2c5 <> 2

Note2: As the fin chain is also a chain of 2s, there must be a 5-fish type encompassing the additional truth 2r8c7=2r2c7.
Something like Starfish (or Squirmbag) (2)r1469c7\c2458b9 with a complex name that you can find in The Ultimate Fish Guide, aka UFG, here
I'm not a great fan of these complex fish names. A player, named SpAce, would have given it to you pretty soon !
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Re: Fish with chains

Postby Wepwawet » Wed Apr 15, 2020 11:18 pm

Many thanks Cenoman, for the notation and highlighting the typo.

I have never made any effort in looking for larger fish than a Jellyfish, e.g. Squirmbag, as I read somewhere that they always contain smaller fish. If there was no set name for this sort of hybrid fish/chain I had considered calling it a Catfish Type 4 - Cat being short for concatenate (to connect as a chain), Type 4, identifying it as a Jellyfish). Just a thought!
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Re: Fish with chains

Postby Cenoman » Thu Apr 16, 2020 1:22 pm

Some also use simply: 2-fish (X-wing), 3-fish (Swordfish), 4-fish, 5-fish, 6-fish...
It is fine to me, as well as names. The only important thing is clear logic.
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