a new (?) view of fish (naked or hidden)

Advanced methods and approaches for solving Sudoku puzzles

An Arcilla Logical

Postby Sudtyro2 » Sat Sep 21, 2013 1:14 am

Thx, DPB and blue, for your feedback. Let me work on this issue a bit.

The key point here is that FJF(c1257) is a composite entity, whereas the XW(c16) is the "definned" X-Wing and must be treated with the Fish=Fin strong-link rule.
On the other hand, for the JFJ, because its single fin sees PE r1c9 directly, it doesn't matter whether the fin is true or the definned fish is true. One of them has to be true, so the composite entity is true, and therefore the exclusion of the PE at r1c9 applies. There is no need to use the Fish=Fin rule separately, as was done on the X-Wing.

Does this make any sense?
[Edit to add: IOW, ...=r6c6-[r6c6 peers] => 4-Fish c1257\r1279 + fr3c7 => r1c9<>7. There's no "chain" here, so how does one include the r1c9 exclusion in the original implication stream?]
Last edited by Sudtyro2 on Sat Sep 21, 2013 4:32 am, edited 1 time in total.
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Re: a new (?) view of fish (naked or hidden)

Postby daj95376 » Sat Sep 21, 2013 3:02 am

I would have been more impressed if your approach had found something like:

Code: Select all
(7): [XW(c16\r29) = fr6c6] - [XW(c27\r67) = fr1c2,r23c7] - [fr1c9 = Kite(r1c1)]  =>  r9c5<>7

Which I'm fairly sure is bidirectional when you read ...

Code: Select all
l-to-r:   = fr1c2,r23c7     as meaning at least one is true

r-to-l:     fr1c2,r23c7 -   as meaning none are true
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Re: An Arcilla Logical

Postby blue » Sat Sep 21, 2013 5:33 am

Sudtyro2 wrote:On the other hand, for the JFJ, because its single fin sees PE r1c9 directly, it doesn't matter whether the fin is true or the definned fish is true. One of them has to be true, so the composite entity is true, and therefore the exclusion of the PE at r1c9 applies.

My mistake. You're right of course. I had been trying to mimic the chain in XSudo, and with r1 appearing as both a cover sector for the FJF and a base sector forthe kite, I missed the fact that r1c9 was a PE.
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Re: a new (?) view of fish (naked or hidden)

Postby David P Bird » Sat Sep 21, 2013 9:18 am

Right, I think I've found the mirage in that inference chain.

Code: Select all
2Fish:c16\r29 = r6c6 - r4c5,r6c257 = 4Fish:c1257\r1279
      False     True       False       True?

The 4 fish is true when it must hold 4 truths, but that needs r3c7 to be false as well. As that hasn't been shown to follow from the previous step, whether the 4Fish is true or false is uncertain, the inference is unsound, and the chain can't be continued.

DPB
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Re: An Arcilla Logical

Postby Sudtyro2 » Sat Sep 21, 2013 12:46 pm

David P Bird wrote:... the inference is unsound, and the chain can't be continued.

Fully agree...am working on the fix now.
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Re: An Arcilla Logical

Postby Sudtyro2 » Sat Sep 21, 2013 1:26 pm

Thx, DPB and blue, for your feedback. I'm working new ground here with an old brain, so some confusion abounds...

First, just to be clear (mostly to myself), my “chain” is not an AIC, but rather a unidirectional (left-to-right) implication stream as defined by Jeff in the head post of the Forcing Chains topic. By itself, then, my “hybrid” stream is not a chain at all. One needs a second implication stream to form the desired end result of a valid Forcing Chain.

And secondly, implication streams are often presented in abbreviated form in which the “=>” are implied and not shown explicitly. I think my mistake was trying to use a strong-inference in [r6c6 peers]=FJF(c1257) to connect the two nodes. The [r6c6 peers] node does, in fact, imply the finned Jellyfish, but the strong-inference link is not proper. However, the FJF does imply that PE r1c9<>7, since the fin sees the PE directly. We can therefore easily fix the implication stream(s) as follows:
Code: Select all
XW(c16)=r6c6-[r6c6 peers] => FJF(c1257)-r1c9=Kite(r1c1) => r9c5<>7
XW(c16)-r6c6                                            => r9c5<>7

And finally, a (true) Fin at r6c6 does see the target PE (r9c5) remotely via the following network diagram:
Code: Select all
                r9c1                     => r9c5<>7
                 ||
                 ||    -------------r1c2                 
r6c6-r6c2=r45c3-r7c3  /              ||
   \             ||  /               ||                 
    \            || /                ||
     \          r7c2-r1c2=r2c1-r2c7  ||
      \            \            ||   ||
       \            -----------r7c7  ||
        \                       ||   ||
         ----------------------r6c7  ||
                                ||   ||
                               r3c7-r1c9
                                     ||
                                    r1c5  => r9c5<>7

This network avoids using both the finned Swordfish and the Kite, but a network like this one is a real bear to find and even worse to type up! I much prefer the arcilla fish and the “hybrid” implication streams, assuming, of course, that those streams are actually valid! Hopefully, DPB and blue can now feel better about the more proper Forcing Chain. Meanwhile, DAJ appears to have cooked up a real, bidirectional AIC!
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Re: a new (?) view of fish (naked or hidden)

Postby David P Bird » Sat Sep 21, 2013 2:29 pm

SudTryo2, Here is a chain that proves the elimination which may be of help:

r2467c5,r9c468 =[Oddogon:r1c25,r29c2,r9c5]= r1c9 - r1c2,r23c7 = #2:r2c1,r6c7 - r2c6,r6c6 = r9c6 => r9c5 = false

My notation conventions:
=[Pattern]= : a strong link provided by the pattern
#n : the number of truths, if >1, required for the node to be true

If you aren't familiar with Oddogons, they are Deadly Patterns consisting of unsolvable loops of an odd number of cells. At least one of the external cells in a containing house (called Guardians) must therefore be true to prevent the DP. Here the oddogon is your kite with extra candidates. Two of the containing houses, c1 and b1 don't contain guardians, so either a guardian must be true in r9 or c5 (in sight of r9c5) or in r1 at r1c9.

DPB
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Re: a new (?) view of fish (naked or hidden)

Postby daj95376 » Sat Sep 21, 2013 4:27 pm

_

I'm sorry, but I don't see that much wrong with Sudtyro2's original AIC.

XW(c16)=r6c6-[r6c6 peers]=FJF(c1257)-r1c9=Kite(r1c1) => r9c5<>7

Starting with the original candidate grid, I can identify this fish pattern.

Code: Select all
 4-Fish c1257\r1279 + fr3c7 + fer4c5,r6c257
 +-----------------------------------+
 |  . *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 only thing I would do is reword his AIC slightly.

XW(c16)=r6c6 - [fer4c5,r6c257]=FJF(c1257) - r1c9=Kite(r1c1) => r9c5<>7

All that remains is to clarify the definition of FJF. I say that it's (4-Fish c1257\r1279 + fr3c7) sans [fer4c5,r6c257].

It now appears to me that [fer4c5,r6c257]=FJF(c1257) is bidirectional, and an AIC exists.
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Re: a new (?) view of fish (naked or hidden)

Postby blue » Sat Sep 21, 2013 5:13 pm

daj95376 wrote:I'm sorry, but I don't see that much wrong with Sudtyro2's original AIC.

I agree (FWIW).
Apologies to everyone, if my earlier post caused some confusion.

Blue.
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Re: a new (?) view of fish (naked or hidden)

Postby Sudtyro2 » Sat Sep 21, 2013 6:57 pm

daj95376 wrote:It now appears to me that [fer4c5,r6c257]=FJF(c1257) is bidirectional, and an AIC exists.

Well, color me impressed! And a real AIC, to boot, it seems! I never thought to look at it in terms of just those remote fins. I was stuck on the modified grid, and couldn't quite see how to make the link to the finned 4-Fish. Sure learning a lot on this one...and thx to all for the enlightening inputs!

I think even "Mikey Likes It!"

EDIT: My original post has been edited to acknowledge the flawed AIC and to note DAJ's resolution.

EDIT: Just for the record, I've added a grid (in DAJ's notation) and corrected AIC for the alternate CPR-based 4-Fish mentioned in the original post. Note that this 4-Fish is a bit simpler in having only one remote fin cell.
RPC: (29)(167)(457)(3589)(124679)(269)(2367)(45689)(13568)
CPR: (259)(1567)(479)(358)(3489)(256789)(2357)(489)(14568)
Code: Select all
4-Fish r3458\c3489 + fr3c7 + fer4c5
  . 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  .

XW(c16)=r6c6-r4c5=FJF(r3458)-r1c9=Kite(r1c1) => r9c5<>7,
where FJF(r3458)is defined as 4-Fish r3458\c3489 + fr3c7.
Last edited by Sudtyro2 on Tue Sep 24, 2013 6:53 pm, edited 2 times in total.
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Re: a new (?) view of fish (naked or hidden)

Postby David P Bird » Sat Sep 21, 2013 11:31 pm

Yes, I concur. When I jotted down the original chain I omitted the finned specification of the 4Fish. I also agree with DAJ that in this case it would be best to identify the surviving fin node(s) along with the fish in the notation.

Playing with the grid, it turns out that the available body (or vertex) cells for the 4Fish are a deadly pattern which simple colouring shows can never contain 4 truths, so either one of the fin cells seen by r6c6 or r3c7 must be true. That suggests another line of exploration perhaps.

DPB
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