The New Sudoku Players' Forum

[Sudtyro2]

Using Obi-Wahn's transformations, this then simplifies to r3457b3\c135899b49 (5 base and 8 cover sectors) but the k-rank stays the same, and still there are no eliminations.
I'm therefore coming to believe that, unless anyone can do any better, this puzzle may serve as a counter-example to show that NxM fish can't replicate all net eliminations.

Interesting thought...
Allan Barker also started off with a 5-Fish, c124b36\r25689c89b7, of raw rank 3. However, he somehow reduced the rank to 1 and got the elimination, but I could never understand how the linkset-triplet logic was able to do that. Fortunately, tho, I can understand a Kraken 1-Fish solution.

[blue]

On a more serious note, and getting back to the question that you posed: if the original puzzle had an X-Wing, for example, where all of the eliminations had been done ... then the X-Wing candidates couldn't have remote weak links to the target.

On second thought, this is probably incorrect. An initial "box-type" weak link, might do the trick.

Using Obi-Wahn's transformations, this then simplifies to r3457b3\c135899b49 (5 base and 8 cover sectors) but the k-rank stays the same, and still there are no eliminations.
I'm therefore coming to believe that, unless anyone can do any better, this puzzle may serve as a counter-example to show that NxM fish can't replicate all net eliminations.

Interesting thought...
Allan Barker also started off with a 5-Fish, c124b36\r25689c89b7, of raw rank 3. However, he somehow reduced the rank to 1 and got the elimination, but I could never understand how the linkset-triplet logic was able to do that. Fortunately, tho, I can understand a Kraken 1-Fish solution.

I have a piece of code that's telling me that the minimum rank for an Obi-Wahn fish for the r8c9 exclusion, is 4, and that the minimum number of base sectors for such a fish, is 7. (It also says that 7 is the minimum number of base sectors for an Obi-Wahn fish of any rank).
The two "r8c9" diagrams that I showed, were twists on two such fish: r33c2477b4\r56689c399b199 and r34c247b33\r2689c38999b59.

[daj95376]

Is this just one big whale of a fluke (or vv, maybe )?

Your approach reminds me of manually simulating the Templates technique when there's a single elimination -- no starting point other than the elimination cell will contain the elimination cell. That said, your approach may not be a fluke, but I'm pretty sure that it falls into the category of T&E.

Templates Results: every combination contains at least one cell that sees r8c9 -- any starting point must lead to r8c9<>8

Code: Select all

.....8..........8...8..........8....8..............8..........8.8..........8.....
.....8....8...............8.......8....8.......8............8......8....8........
.....8....8...............8.......8....8.......8......8............8..........8..
.....8....8...............8....8....8..............8....8.............8....8.....
.....8....8...............8..8.........8...........8.........8.....8....8........
.....8....8...............8..8.........8...........8......8...........8.8........
.....8...8................8.......8....8.......8............8......8.....8.......
.....8...8................8.......8....8.......8..........8.....8.............8..
.....8...8................8.......8....8......8.........8..........8..........8..
.....8...8................8....8...........8...8............8...8..........8.....
.....8...8................8..8.............8.....8..........8...8..........8.....
.....8...8................8..8.........8...........8.........8.....8.....8.......
.....8...8................8..8.........8...........8......8...........8..8.......
                                                                     ^
                                                                     |----------- r8c9 void


[daj95376]

I have a piece of code that's telling me that the minimum rank for an Obi-Wahn fish for the r8c9 exclusion, is 4, and that the minimum number of base sectors for such a fish, is 7. (It also says that 7 is the minimum number of base sectors for an Obi-Wahn fish of any rank).

The two "r8c9" diagrams that I showed, were twists on two such fish: r33c2477b4\r56689c399b199 and r34c247b33\r2689c38999b59.

Impressive! An NxM fish for an elimination that isn't found by traditional fish patterns.

[Sudtyro2]

Is this just one big whale of a fluke (or vv, maybe )?

Your approach reminds me of manually simulating the Templates technique when there's a single elimination -- no starting point other than the elimination cell will contain the elimination cell. That said, your approach may not be a fluke...

The Templates would certainly seem to verify that, at least for this one grid. Thx for making the run...first time I've ever even seen a full set printed out...very interesting!

...but I'm pretty sure that it falls into the category of T&E.

No argument there...it was a real trial to generate those 20 network diagrams without a single error.

BTW, I'm not quite done with 25 new network diagrams, but it appears that the "Fluke Conjecture" also applies to your 7s grid, which has been discussed recently in the UFG thread. That would now make it two single-elimination grids down...only about a billion more to go.

[JasonLion-Admin]

A side conversation about the NoFish list has been moved to here.

[Pat]

[ exclude at r8c9 — an Obi-Wahn beast of order 7\11 ]


• r33c2477b4\r56689c399b199
  
  
• r34c247b33\r2689c38999b59

Impressive! An NxM fish for an elimination that isn't found by traditional fish patterns.

depends how you define "traditional"

finned bluefish of order 7

r334c2477\r689c3b156
with fins r3c9 + r79c7

[Sudtyro2]

finned bluefish of order 7

r334c2477\r689c3b156
with fins r3c9 + r79c7[/list]

Seems like yet another awesome catch, Pat! And maybe a first for duplicate sectors in an NxN Fish? Is this for real?

[Pat]

for real?
you tell me — did i miss something?
(sorry, no software, just tried to activate my human brain)

same house twice in cover — bizzare
same house twice in base — beyond bizzare, i never considered it until i saw blue's 7\11

[ronk]

finned bluefish of order 7

r334c2477\r689c3b156
with fins r3c9 + r79c7[/list]

Seems like yet another awesome catch, Pat! And maybe a first for duplicate sectors in an NxN Fish? Is this for real?

We end up with "non-traditional fish" like this because we don't know how to deal with the "link triplets", formerly "linkset triplets", of Allan Barker's XSUDO.

In this example, the link triplets occur at r3c3 and r6c7, the first due to intersection of covers c3 and b1 and the second due to covers r6 and b6. I think a link triplet works like a fin, either exo-fin or endo-fin, except the candidate is taken to be false instead of true. I expect this is the underlying reason for the double appearances of r3 and c7 in Pat's notation.

r3c3<>8 => r3c9=8 => r8c9<>8
r6c7<>8 => r79c7=8 => r8c9<>8

Code: Select all

 .  .  . |  .  .  . |  .  .  .
 8 *8  . |  .  .  . |  .  8  .
 .  . &8 |  .  .  . |  .  . #8
---------+----------+---------
 .  . *8 |  . *8  . |  . *8  .
 8  .  . | *8  .  . |  .  8  .
 . *8  8 |  .  8  . | &8  .  .
---------+----------+---------
 8  .  8 |  .  8  . | #8  8  8
 . *8  . |  .  8  . |  .  8 -8
 8 *8  . | *8  .  . | #8  .  .

Note the two linkset triplets are necessarily remote. However, many many examples are unfortunately not this simple.

[daj95376]

[Withdrawn: possibly an impractical example.]

[ronk]

In my Templates list above, only one entry contains r2c8/r3c2=8, and each of these cells form a strong link with r3c9. So, if we assume r3c9<>8, then this template must follow as true. Any candidate, that sees r3c9 and any assignment in this template, can be eliminated.
...
Apparently this can't be replicated easily as a Fish.

Even if difficult to replicate, what "fish" would that be?

[daj95376]

Even if difficult to replicate, what "fish" would that be?

A poor choice of words on my part ... and an example that may be impractical.

[Sudtyro2]

I think a link triplet works like a fin, either exo-fin or endo-fin, except the candidate is taken to be false instead of true.

That statement brings back some painful memories of trying to understand Allan's triplet logic. His original 5-Fish was c124b36\r25689c89b7 of raw rank 3. There were no set triplets, but there were five linkset-triplets (sorry for the old terminology). Two of those (r2c8 and r9c2) were used to lower the rank to 1 and thereby effect the elimination at r8c9.
I think there was one brief period back then (2009) during which I could actually fathom the triplet-processing logic, but it always made my head hurt. Nevertheless, I've included as hidden text a PM correspondence from aran regarding linkset triplets that confirms your statement. It's a nice explanation for anyone that might still be interested in the logic.

Hidden Text: Show

Triplets are essentially (and maybe only) about overlapping sets.
Example
suppose a base of 7 sets ie exactly 7 truths (as you know well).
suppose a cover for those truths which itself consists of a maximum of 8 truths with an overlap (ie to be clear: either 7 truths or 8 truths).
Then you look at the overlap and reason like this:

if the overlap candidate is true: it removes from consideration 1 base set and 2 cover sets (think about that if not clear) thus reducing the structure to 6 sets 6 covers and hence rank 0 with all that follows.

if the overlap is false, then see if there is some resulting chain arising which produces any identical elimination(s): if so, such eliminations is/are definitively established.

[Sudtyro2]

As mentioned previously, a Fluke check on DAJ's 7s grid confirmed that all 25 potential remote fins can see the CEC at r9c5. The 25 network diagrams are not listed here (more typing yet to do), but one remote cell (r4c3) was of particular interest because it was very difficult for me to develop its network diagram. DAJ's grid follows, with (-) marking the CEC.

Code: Select all

 .  7  . |  .  7  . |  .  .  7
 7  .  . |  .  7  7 |  7  .  .
 .  .  . |  7  .  . |  7  .  7
---------+----------+---------
 .  .  7 |  .  7  . |  .  7  .
 .  .  7 |  7  .  . |  .  7  7
 .  7  . |  .  7  7 |  7  7  7
---------+----------+---------
 .  7  7 |  .  7  . |  7  .  .
 .  .  . |  7  .  . |  .  7  7
 7  .  . |  7 -7  7 |  .  7  .

The final network diagram for the remote cell (r4c3):

Code: Select all

     r5c4-----------          r1c5               => r9c5<>7
      ||            \          ||
r4c3-r5c3     r8c4-r3c4=r3c79-r1c9         
      ||       ||            / ||
     r5c8-----r8c8          / r1c2-r2c1=r9c1     => r9c5<>7
      ||       ||          /
      ||      r8c9---------
      ||                 /
     r5c9---------------

The problem initially was that I kept building implication streams that led to contradictions. JC Van Hay then offered up the following clever and very compact “hybrid” stream:
r4c3-r5c3=FSF(r358)-r1c9=Kite(r1c1)-r9c5.

FSF(r358) is a finned Swordfish:
3-Fish r358\c489 + fr3c7 => r1c9<>7.

The Kite then completes the CEC elimination as a bidirectional AIC:
r1c5=r1c2-r2c1=r9c1 => r9c5<>7.

I would certainly not have known to look for that finned 3-Fish, but I always find it interesting how arcilla's lists can spot Fish patterns right off. Numbers shown below are the CPR list's columns per row-position. R4c3 appears as the “3” in r4's (358), and r4c3's five peers are shown bolded:
CPR: (259)(1567)(479)(358)(3489)(256789)(2357)(489)(14568)

After removing the five peer candidates (since r4c3 will be assigned as true), the list becomes:
(259)(1567)(479)(3)(489)(56789)(257)(489)(14568)

One can now easily recognize that the underlined column-elements form the arcilla-equivalent of an ALS, where (7) is the spoiler, and the (489) triple is the LS. This immediately translates to:
3-Fish r358\c489 + fr3c7, which then eliminates r1c9.

The 3-Fish was used to generate the network diagram shown above. Everything to the right of “r4c3” and up through “r1c9” is actually the 3-Fish and its elimination. The strong-inference sets (SIS) plus the one strong-inference link define the base sectors, while the weak-inference links define the cover sectors. The fin is included in the r3c79 node.

OK, bottom line after reviewing all the evidence:
It's pretty obvious that JC's hybrid stream makes my network diagram look like a bunch of big SISsies! But, you gotta ask how JC found that 3-Fish!