The New Sudoku Players' Forum

[ArkieTech]

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 *-----------*
 |..2|..8|.76|
 |...|...|18.|
 |8..|29.|...|
 |---+---+---|
 |..6|97.|.5.|
 |..3|...|4..|
 |.8.|.64|7..|
 |---+---+---|
 |...|.49|..7|
 |.45|...|...|
 |63.|8..|2..|
 *-----------*


Play/Print this puzzle online

[SCLT]

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+-------------------+----------------+--------------+
| b13     5    2    |  4   c13  8    |  9  7   6    |
|  379    679  4    |  57   35  567  |  1  8   2    |
|  8      67  a1-7  |  2    9   167  |  3  4   5    |
+-------------------+----------------+--------------+
|  4      12   6    |  9    7   123  |  8  5   13   |
|  12579  79   3    |  15   8   125  |  4  6   19   |
|  159    8    19   |  135  6   4    |  7  2   139  |
+-------------------+----------------+--------------+
|  12     12   8    |  6    4   9    |  5  3   7    |
|  79     4    5    |  137  2   137  |  6  19  8    |
|  6      3   f79   |  8   d15  157  |  2 e19  4    |
+-------------------+----------------+--------------+


1r3c3 = r1c1 - r1c5 = r9c5 - (1=9)r9c8 - (9=7)r9c3 => -7r3c3; stte

[Cenoman]

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 +---------------------+-------------------+------------------+
 |  13      5     2    |  4     13   8     |  9    7    6     |
 |  379     679   4    |  57    35   567   |  1    8    2     |
 |  8       67   d17   |  2     9    67-1  |  3    4    5     |
 +---------------------+-------------------+------------------+
 |  4       12    6    |  9     7   a123*  |  8    5    13    |
 |  12579   79    3    | a15*   8   a125*  |  4    6    19    |
 |  159     8     19   | a135*  6    4     |  7    2    139   |
 +---------------------+-------------------+------------------+
 |  12      12    8    |  6     4    9     |  5    3    7     |
 |  79      4     5    | a137*  2   a137*  |  6   b19   8     |
 |  6       3    c79   |  8     15   157   |  2   c19   4     |
 +---------------------+-------------------+------------------+

Almost X-chain (grouped turbot-fish ?)
[(1)r8c6*=r8c4-r56c4=r45c6] = (1)r8c8-(1=97)r9c38-(7=1)r3c3 => -1 r3c6; ste

[SCLT]

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 +---------------------+-------------------+------------------+
 |  13      5     2    |  4     13   8     |  9    7    6     |
 |  379     679   4    |  57    35   567   |  1    8    2     |
 |  8       67   d17   |  2     9    67-1  |  3    4    5     |
 +---------------------+-------------------+------------------+
 |  4       12    6    |  9     7   a123*  |  8    5    13    |
 |  12579   79    3    | a15*   8   a125*  |  4    6    19    |
 |  159     8     19   | a135*  6    4     |  7    2    139   |
 +---------------------+-------------------+------------------+
 |  12      12    8    |  6     4    9     |  5    3    7     |
 |  79      4     5    | a137*  2   a137*  |  6   b19   8     |
 |  6       3    c79   |  8     15   157   |  2   c19   4     |
 +---------------------+-------------------+------------------+

Almost X-chain (grouped turbot-fish ?)
[(1)r8c6*=r8c4-r56c4=r45c6] = (1)r8c8-(1=97)r9c38-(7=1)r3c3 => -1 r3c6; ste

Seems strange to call that a Grouped Turbot Fish, since if the chain were true, it would be degenerate! There would be claiming in block 8, followed by a single 1 in c5. Given that, you can rewrite your chain as:

1r1c5 = r9c5 - (1=97)r9c38 - (7=1)r3c3 => -1r3c6 ; stte

At which point the similarities to my chain become obvious

[SpAce]

Almost X-chain (grouped turbot-fish ?)
[(1)r8c6*=r8c4-r56c4=r45c6] = (1)r8c8-(1=97)r9c38-(7=1)r3c3 => -1 r3c6; ste

Seems strange to call that a Grouped Turbot Fish, since if the chain were true, it would be degenerate! There would be claiming in block 8, followed by a single 1 in c5. Given that, you can rewrite your chain as:

1r1c5 = r9c5 - (1=97)r9c38 - (7=1)r3c3 => -1r3c6 ; stte

Indeed. It's an unnecessary complication, but a valid one (though I'd prefer Turbot Crane for obvious reasons To me Turbot Fish is the parent type, and I've always hated it that there's no distinct name for one of the children -- so I invented one). Anyway, if one wants to complicate things, I'd rather see it as a Kraken Franken X-Wing:

(1)B58\c46 = (197)r9c583 - (7=1)r3c3 => -1 r3c6; stte

[Sudtyro2]

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+----------------+--------------+--------------+
| 3-1   5   2    | 4  e13  8    | 9   7   6    |
| 379   679 4    | 57  35  567  | 1   8   2    |
| 8     67  17   | 2   9   67-1 | 3   4   5    |
+----------------+--------------+--------------+
| 4     12  6    | 9   7   123  | 8   5   13   |
| 12579 79  3    | 15  8   125  | 4   6   19   |
| 159   8  a19   | 135 6   4    | 7   2   139  |
+----------------+--------------+--------------+
| 12    12  8    | 6   4   9    | 5   3   7    |
| 79    4   5    | 137 2   137  | 6   19  8    |
| 6     3  b79   | 8  d15  157  | 2  c19  4    |
+----------------+--------------+--------------+

Speaking of fish...how 'bout three 1-Fish caught with the same worm (remote-fin chain).

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Sashimi Kraken (1)C3\r1 + rfr6c3 + fr3c3 => -1 r1c1; stte
Kraken Franken (1)C3\b1 + rfr6c3         => -1 r1c1; stte
        Kraken (1)C3\r3 + rfr6c3         => -1 r3c6; stte
The worm: (1-9)r6c3 = r9c3 - (9=1)r9c8 - r9c5 = r1c5 - 1r1c1|r3c6

SteveC

[SteveG48]

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 *--------------------------------------------------------------------*
 | 3-1    5      2      | 4     a13     8      | 9      7      6      |
 | 379    679    4      | 57     35     567    | 1      8      2      |
 | 8      67    d17     | 2      9      67-1   | 3      4      5      |
 *----------------------+----------------------+----------------------|
 | 4      12     6      | 9      7      123    | 8      5      13     |
 | 12579  79     3      | 15     8      125    | 4      6      19     |
 | 159    8      19     | 135    6      4      | 7      2      139    |
 *----------------------+----------------------+----------------------|
 | 12     12     8      | 6      4      9      | 5      3      7      |
 |c79     4      5      |b137    2     b137    | 6      19     8      |
 | 6      3     d79     | 8     b15     157    | 2      19     4      |
 *--------------------------------------------------------------------*


1r1c5 = (137)b8p468 - 7r8c1 = (71)r39c3 => -1 r1c1,r3c6 ; stte

[SpAce]

Hi SteveC!

Speaking of fish...how 'bout three 1-Fish caught with the same worm (remote-fin chain).

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Sashimi Kraken (1)C3\r1 + rfr6c3 + fr3c3 => -1 r1c1; stte

I have no problem with the others, but this one seems to be headless (a cover sector without any base candidates), so it's not really a fish as per current standards. As previously discussed, it would make more sense as a DP since the finless fish body can never be true (C3 would be empty):

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Illegal fish (1)C3\r1 with two guardians:

(1)r3c3 == (1-9)r6c3 ...

(Never mind the fact that the guardians are also natively linked.)

[Sudtyro2]

Hi SpAce,

I'm late today getting back to you and need some time to review your concerns about the Sashimi Kraken 1-Fish. In the meantime, what I recall in initially learning about this type of 1-Fish started with Pat here and continued with a key post from DAJ. The idea from DAJ was that an intersection at a Fish digit was not needed between the base and cover sectors. In the above case of the Sashimi Kraken 1-Fish, there's no such intersection, but there is both a direct and remote fin that see the elimination cell at r1c1. DAJ seemed to feel this was OK.

SteveC

[SpAce]

Hi Steve,

I'm late today getting back to you and need some time to review your concerns about the Sashimi Kraken 1-Fish. In the meantime, what I recall in initially learning about this type of 1-Fish started with Pat here and continued with a key post from DAJ. The idea from DAJ was that an intersection at a Fish digit was not needed between the base and cover sectors. In the above case of the Sashimi Kraken 1-Fish, there's no such intersection, but there is both a direct and remote fin that see the elimination cell at r1c1. DAJ seemed to feel this was OK.

As discussed previously, the fish logic seemingly works even with an invalid fish body because its falseness forces at least one of the fins to be true. That doesn't mean it makes any sense from a base\cover point of view, and it has since been agreed that such a construct (where a cover sector has no base candidates) is not a UFG fish. XSudo doesn't allow such constructs either. That's why I don't think such things should be presented as valid fishes, and our resident UFG master tarek agreed here. In fact, I wouldn't mind him chiming in on this topic!

I think tarek would also remind that the term Sashimi refers to a valid fish that would degenerate into a smaller valid fish if all fins were removed (or non-existent). It can't be used with an invalid fish body which disallows removing all the fins. In that case the proper term is Headless, not Sashimi, and a fish can't be alive without a head. Thus it's a dead(ly) fish, i.e. a DP.

[Sudtyro2]

Hi Space,

Thx again for your constructive feedback AND for also playing the watchdog role!

I do recall our recent discussions about "false Fish" and the effect on the Fish=Fin(s) strong-link rule. However, regarding DAJ's 1-Fish example cited in the previous link, I did not realize (along with DAJ?) that a cover sector with no base-sector cells was considered a non-fish entity. I also picked up the Sashimi designation from that same posting and had been using the term in 12-odd 1-Fish postings of my own since 2016.

But, it's also curious that, at least for all those "Sashimi" 1-Fish postings, the UFG Rx does seem to provide both the correct fin designations and the eventual elimination. I.e., the (1)C3\r1 cover sector contains no base cells, so the two cover cells are both then "potential eliminations." Similarly, the C3 sector contains no covered base cells, so those two cells then become fins, one direct and one Kraken remote, leading to the proper "eventual elimination" of (1)r1c1.

So, my only question is this. Would it suffice to simply relabel my false 1-Fish as, say: Headless Kraken (1)C3\r1 + rfr6c3 + fr3c3 => -1 r1c1; stte
Hoping for a yes...

SteveC

[tarek]

Thanks to all and SpAce for reminding about the discussion regarding the headless creature.

In the link provided by SpAce I did mention the main reasons why this is not a fish

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1. I demonstrated the logic behind the Headless creature eliminations. They based on the fact that the Fish body is false therefore forcing the fin(s) to be true which then forces the elimination that you would see in the basic finned fish setup. The logic is not "Either the fish is true or the fin(s) are true" anymore like in our UFG fish. That is one point against calling it a UFG fish.

2. I also demonstrated how in this headless creature the fins(s) truthfulness cascades to eliminate all PEs in the cover rows that have vertices (which is what a franken fish does). It is therefore a UFG Franken fish in disguise & not an equivalent. That is another point against calling it a UFG fish.

[SpAce]

Thx again for your constructive feedback AND for also playing the watchdog role!

No problem! Glad to know there's at least one person who doesn't hate it

I do recall our recent discussions about "false Fish" and the effect on the Fish=Fin(s) strong-link rule. However, regarding DAJ's 1-Fish example cited in the previous link, I did not realize (along with DAJ?) that a cover sector with no base-sector cells was considered a non-fish entity.

I guess it wasn't back then. I think "headless" or "skinny" fishes were originally considered fishes in their own right, and the baseless cover sector wasn't seen as a problem. As we've seen, the fish logic does work with them in practice, so it's not like that POV would produce incorrect eliminations. It's just wrong from a more general set logic POV, where a cover set without any base candidates doesn't make sense.

I also picked up the Sashimi designation from that same posting and had been using the term in 12-odd 1-Fish postings of my own since 2016.

Few people (and no software solvers that I know of) use the term exactly as it's defined, so it doesn't seem like a huge sin! However, I do like tarek's precise definition, even if it means writing "Finned Sashimi" instead of just "Sashimi" in the usual case.

So, my only question is this. Would it suffice to simply relabel my false 1-Fish as, say: Headless Kraken (1)C3\r1 + rfr6c3 + fr3c3 => -1 r1c1

At least it's better. However, I think tarek should give a more definite answer. Here's what he said originally:

In balance IMO it shouldn't be a UFG fish. With the presence of many non-UFG creatures I can't see why you shouldn't use it if it is easier to spot though. This discussion (which can be referenced if needed) would explain why it is a valid elimination despite not being a UFG fish. It also can be used (pending examples to say otherwise) to catch a more complex UFG fish which would have been difficult to spot otherwise.

Personally I think it would be better to avoid presenting a headless fish as a solution step, because it's no longer considered a UFG fish and the above notation looks too much like one. If there's a headless fish around, there's always a valid UFG fish too, so I'd rather use the headless one as a spotting aid to find that valid fish.

Here's my original ponderings about the pros and cons of using the headless concept, written before tarek's final judgment. I still think that my point 4 is valid, so there's nothing wrong in using the concept to spot such a creature and the corresponding eliminations (and tarek seems to agree above). Whether it should be notated as such is another question. Apparently there's always a valid Franken Fish that provides the same eliminations (and maybe more), so why not present that instead? It would avoid any controversy.

[SpAce]

Hi tarek, and thanks for participating in this discussion!

Just one minor point about this:

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The logic is not "Either the fish is true or the fin(s) are true" anymore like in our UFG fish.

In our previous discussions with Steve, I thought about that statement a bit more. I don't think it's exactly accurate. The usual "fish=fins" strong link still works, even if the fish body is invalid (i.e. a known false). It just reduces to "false=fins" which reduces to "fins". In general, "false OR something" => "something".

It's similar to what I did here:

UR(68)b14 = (4)r5c3 - r5c4|r6c3 =UL(68)b12345= (2|3)r6c5 => -68 r6c5; stte

The first node is obviously false in a valid puzzle, which means that all the right sides of the strong links must be true, including the last node. One can similarly use any contradiction in a strong link (or a SIS) -- it's just a constant false meaning that a truth must be found in at least one of the other ORed nodes. In other words, using contradictions in a chain doesn't break the logic. They just can't have meaningful weak links (that I can think of).

[tarek]

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The logic is not "Either the fish is true or the fin(s) are true" anymore like in our UFG fish.

In our previous discussions with Steve, I thought about that statement a bit more. I don't think it's exactly accurate. The usual "fish=fins" strong link still works, even if the fish body is invalid (i.e. a known false). It just reduces to "false=fins" which reduces to "fins". In general, "false OR something" => "something".

The eliminations will be valid under some form of logic. I also agree that it will be helpful as a spotting technique too.
For a UFG fish with the ideals it carries, it was always assumed that the eventual eliminations can be eliminated if the fish body were to be true … This ideal has been challenged by this creature and is possibly the main reason behind the rejection.

The fish body was always fundamental in the ideals of the UFG logic. Logic however remains logic no matter what idealists like me say.

Tarek