December 11, 2018

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December 11, 2018

Postby ArkieTech » Tue Dec 11, 2018 11:26 am

Code: Select all
 *-----------*
 |...|.1.|...|
 |43.|.72|.1.|
 |2.9|6.5|...|
 |---+---+---|
 |8..|...|2..|
 |.26|.9.|54.|
 |..4|...|..6|
 |---+---+---|
 |...|1.6|8.7|
 |.8.|74.|.53|
 |...|.2.|...|
 *-----------*


Play/Print this puzzle online
dan
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Re: December 11, 2018

Postby Cenoman » Tue Dec 11, 2018 3:20 pm

Code: Select all
 +----------------------+---------------------+--------------------+
 |  57     6     57     |  348   1     348    |  39    389    2    |
 |  4      3     8      |  9     7     2      |  6     1      5    |
 |  2      1     9      |  6     3-8   5      |  347   378   a48*  |
 +----------------------+---------------------+--------------------+
 |  8      579   1357   | F345   6     1347   |  2     379    19   |
 |  137    2     6      | e38    9     1378   |  5     4     a18*  |
 |  1357   579   4      |  2   Ga358* b1378   |  379  a3789*  6    |
 +----------------------+---------------------+--------------------+
 |  9      4     35     |  1     35    6      |  8     2      7    |
 |  6      8     2      |  7     4     9      |  1     5      3    |
 |  1357   57    1357   |Ed358   2    c38     |  49    6      49   |
 +----------------------+---------------------+--------------------+
                                                        (8=3)r5c4   -   (3)r6c5
                                                      /     e               G  \\
[kite(8)r6c5==r6c8-r5c9=r3c9] = (8)r6c6 - r9c6 = r9c4                           (8)r6c5 => -8 r3c5; ste
             a                     b       c      d   \                        //   G   
                                                       (5)r9c4 = r4c4 - (5)r6c5
                                                           E      F         G
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Re: December 11, 2018

Postby SteveG48 » Tue Dec 11, 2018 4:51 pm

Code: Select all
 *------------------------------------------------------------*
 | 57    6     57    | b348   1     348   | 39    389   2     |
 | 4     3     8     |  9     7     2     | 6     1     5     |
 | 2     1     9     |  6    c38    5     | 347   378  b48    |
 *-------------------+--------------------+-------------------|
 | 8     579   1357  |  345   6     1347  | 2     379   19    |
 | 137   2     6     |be38    9     1378  | 5     4    b18    |
 | 1357  579   4     |  2   de358   1378  | 379   3789  6     |
 *-------------------+--------------------+-------------------|
 | 9     4     35    |  1   de35    6     | 8     2     7     |
 | 6     8     2     |  7     4     9     | 1     5     3     |
 | 1357  57    1357  | a8-35  2     38    | 49    6     49    |
 *------------------------------------------------------------*


8r9c4 = [Skyscraper 8c49] - (8=3)r3c5 - 3r67c5 = (5r7c5)&(8r6c5)&(3r5c4) => -35 r9c4 ; stte
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Re: December 11, 2018

Postby SpAce » Tue Dec 11, 2018 6:16 pm

Code: Select all
.----------------.----------------------.--------------------.
| 57    6    57  |  348    1       348  | 39    389     2    |
| 4     3    8   |  9      7       2    | 6     1       5    |
| 2     1    9   |  6      3-8     5    | 347   378   dB4(8) |
:----------------+----------------------+--------------------:
| 8     579  357 |  345    6       1347 | 2     379     19   |
| 137   2    6   | A38     9       1378 | 5     4     dB18   |
| 1357  579  4   |  2   caA35(8)  c1378 | 379  c3789    6    |
:----------------+----------------------+--------------------:
| 9     4    35  |  1     a35      6    | 8     2       7    |
| 6     8    2   |  7      4       9    | 1     5       3    |
| 357   57   1   |  358    2      b38   | 49    6       49   |
'----------------'----------------------'--------------------'

Kraken Cell (358)r6c5


(38)b5p84 - 8r(5=3)c9                                [A-B]
||
(5*3)r67c5 - (3=8)r9c6 - 8r6c(*56=8) - 8r(5=3)c9     [a-d]
||
(8)r6c5

=> -8 r3c5; stte

The same decrypted: Show
(3)r6c5 - (3=8)r5c4 - r5c9 = (8)r3c9
||
(5*)r6c5 - (5=3)r7c5 - (3=8)r9c6 - r6c*56 = r6c8 - r5c9 = (8)r3c9
||
(8)r6c5
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: December 11, 2018

Postby blue » Tue Dec 11, 2018 7:35 pm

Code: Select all
+-----------------+-------------------+------------------+
| 57    6    57   | a348  1     a348  | 39   389     2   |
| 4     3    8    | 9     7     2     | 6    1       5   |
| 2     1    9    | 6     a3-8  5     | 347  378     e48 |
+-----------------+-------------------+------------------+
| 8     579  1357 | 345   6     1347  | 2    379     19  |
| 137   2    6    | d38   9     1378  | 5    4       e18 |
| 1357  579  4    | 2     c358  c1378 | 379  c3789   6   |
+-----------------+-------------------+------------------+
| 9     4    35   | 1     35    6     | 8    2       7   |
| 6     8    2    | 7     4     9     | 1    5       3   |
| 1357  57   1357 | 358   2     b38   | 49   6       49  |
+-----------------+-------------------+------------------+

Code: Select all
Kraken Duo  => -8r3c5; stte

  a       b           c
3r1c6 - (3=8)r9c6 - 8r6c6
  ||                  ||
  ||                8r6c5 ---------------
  ||                  ||          e       \
  ||                8r6c8 - 8r5c9 = 8r3c9 - 8r3c5
  ||      d               /               /
3r1c4 - (3=8)r5c4 -------                /
  ||                                    /
3r3c5 ---------------------------------

(machine generated)
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Re: December 11, 2018

Postby eleven » Tue Dec 11, 2018 11:36 pm

Code: Select all
 *-----------------------------------------------------------------*
 |  57     6     57     | c3+48  1     348    |  39    389    2    |
 |  4      3     8      |  9     7     2      |  6     1      5    |
 |  2      1     9      |  6    a38    5      |  347   378   #48   |
 |----------------------+---------------------+--------------------|
 |  8      579   1357   | c3+45  6     1347   |  2     379    19   |
 |  137    2     6      | b38    9     1378   |  5     4     #18   |
 |  1357   579   4      |  2    c3+58  1378   |  379   3789   6    |
 |----------------------+---------------------+--------------------|
 |  9      4     35     |  1     35    6      |  8     2      7    |
 |  6      8     2      |  7     4     9      |  1     5      3    |
 |  1357   57    1357   |  358   2     38     |  49    6      49   |
 *-----------------------------------------------------------------*

w-wing 38r3c5,r5c4, SL 8r3c59 -> 3r3c5=r5c4
xy-wing 84-45-58 r14c4,r6c5 -> -8r3c5
In one step: 3r3c5 =w-wing= 3r5c4 - 3r14c4,r6c5 = xy-wing => -8r3c5, stte
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Re: December 11, 2018

Postby Sudtyro2 » Thu Dec 13, 2018 12:54 pm

Code: Select all
+----------------+-------------------+-----------------+
| 57   6   57    | 348*  1     348#  | 39   389*   2   |
| 4    3   8     | 9     7     2     | 6    1      5   |
| 2    1   9     | 6     3-8*  5     | 347  378#   48  |
+----------------+-------------------+-----------------+
| 8    579 1357  | 345   6     1347  | 2    379    19  |
| 137  2   6     | 38    9     1378  | 5    4      18  |
| 1357 579 4     | 2     358*  1378# | 379  3789*  6   |
+----------------+-------------------+-----------------+
| 9    4   35    | 1     35    6     | 8    2      7   |
| 6    8   2     | 7     4     9     | 1    5      3   |
| 1357 57  1357  | 358   2     3-8   | 49   6      49  |
+----------------+-------------------+-----------------+

In 8s, a simple 5-link oddagon(*) having three guardians(#).
Guardians 8r1c6,r3c8 directly see 8r3c5, while guardian 8r6c6 needs a network to remotely see 8r3c5. But, guardian 8r6c6 does directly see 8r9c6. Since at least one guardian must be true, let's write the following kraken column:
Code: Select all
8r1c6,r3c8 => -8r3c5; stte
  ||
8r6c6      => -8r9c6; stte
We've avoided the long network solution, but is the logic valid? My old brain wants to say yes, but SpaCe pointed out for a similar situation here that this is probably not the case. There does exist a derived weak inference between the two stte digits, so at least one must be false, but we have not shown a "common outcome" that would definitively eliminate one of the two digits. Do the Forum rules for stte eliminations specifically require that common outcome? Comments would be most welcome!

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Re: December 11, 2018

Postby Cenoman » Thu Dec 13, 2018 9:29 pm

Sudtyro2 wrote:My old brain wants to say yes, but SpaCe pointed out for a similar situation here that this is probably not the case. There does exist a derived weak inference between the two stte digits, so at least one must be false, but we have not shown a "common outcome" that would definitely eliminate one of the two digits. Do the Forum rules for stte eliminations specifically require that common outcome? Comments would be most welcome!

Hi Steve,
I noticed SpAce's doubt at the time and thought I had to dig it. Your question is a good opportunity. The situation is different between your link and the above.

First a side remark: what you need between the two ste digits isn't a weak link "digit1 - digit2" but an inference link "digit1 => digit2", such that if digit1 is True, set1 of guardians is false, digit2 is true, set2 of guardians is false; all guardians are false (contradiction). On September 18 puzzle, such an inference link was available trough a kite. But in the above puzzle, it is not immediate (there is one through a kraken, as you mention). My suggestion of short-writing on September 18 was made with the hypothesis of implicit existence of the link.

So SpAce was right, the logic needs to explicit some inference link between "the two stte digits". The common outcome must be: "anyhow, all guardians are false".

For example, the above puzzle would be solved this way:
Code: Select all
In 8s, 5-link oddagon(*) having three guardians(#):

Kraken box (3)b8p279
(3)r9c6 - (8)r9c6
(3-5)r7c5 = r6c5  - (8)r6c5 = (8)r3c5     demonstrating " 8r9c6 => 8r3c5 " or equivalent " -8r3c5 => -8r9c6 "
(3)r9c4 - (3=8)r5c4 /
Therefore:
8r1c6,r3c8 => -8r3c5 => -8r9c6 }
  ||                           } -8 r9c6; ste
8r6c6      => -8r9c6           }

If you find me a disappointing guy, I will not protest. :(
Cenoman
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Re: December 11, 2018

Postby SpAce » Thu Dec 13, 2018 10:02 pm

Sudtyro2 wrote:In 8s, a simple 5-link oddagon(*) having three guardians(#).
Guardians 8r1c6,r3c8 directly see 8r3c5, while guardian 8r6c6 needs a network to remotely see 8r3c5. But, guardian 8r6c6 does directly see 8r9c6. Since at least one guardian must be true, let's write the following kraken column:
Code: Select all
8r1c6,r3c8 => -8r3c5; stte
  ||
8r6c6      => -8r9c6; stte
We've avoided the long network solution, but is the logic valid? My old brain wants to say yes, but SpaCe pointed out for a similar situation here that this is probably not the case. There does exist a derived weak inference between the two stte digits, so at least one must be false, but we have not shown a "common outcome" that would definitely eliminate one of the two digits. Do the Forum rules for stte eliminations specifically require that common outcome? Comments would be most welcome!

I would welcome others' comments too, because I already said my piece earlier. I haven't changed my mind, either. In my mind there are two valid ways to achieve a definite conclusion with any kraken-like logic (by "kraken" I mean any SIS, such as the set of oddagon guardians): 1) either all members of the SIS reach a consensus about some conclusion, or 2) some do and the rest self-destruct with a contradiction (but that variant doesn't seem as elegant). In both of those cases we're left with a single conclusion that must be true and we can confidently take that. If it also happens to be an stte-solution, then great, we're done.

However, if we reach two or more different conclusions (none of which is a contradiction), as in your case, it doesn't prove anything directly useful. All you know is that at least one of those conclusions must be true but that's not any different from our starting point (at least one of the SIS members must be true, but we don't know which one(s) -- that's why we try to find a point where they all agree). As I said before, it shouldn't play any part if you happen to know that all of those conclusions are valid stte-eliminations, because that's not something that the proof tells you or what a purely manual solver would be able to know. You should actually run (and notate) your chains all the way to the end to prove that they all do lead to the solution, but that wouldn't be a very satisfactory proof. On the other hand, if you use that prior knowledge without proving it, then it's a case of circular reasoning, as I said before.

Therefore, I still think that we can't accept as a solution two or more different stte-conclusions that have an OR relationship, no matter how elegant it might look, because it depends on knowing beforehand that they in fact are all stte-conclusions. That's not something a manual solver would know without running trials for all paths to the end.

(Oh, I didn't notice Cenoman had already replied.)
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Re: December 11, 2018

Postby Cenoman » Thu Dec 13, 2018 11:24 pm

Hi eleven, blue, hi all,

eleven's solution is the nicest for a single line writing.
The almost-almost-almost xy-wing is a great, great finding !

To be sure I caught it, I have translated it into a matrix:
Hidden Text: Show
Code: Select all
3r3c5 8r3c5
      8r3c9 8r5c9
            8r5c4 3r5c4
8r1c4             3r1c4 4r1c4
                  3r4c4 4r4c4 5r4c4
8r6c5             3r6c5       5r6c5
=> -8 r3c5

I also put blue's solution into a matrix:
Hidden Text: Show
Code: Select all
8r3c9 8r5c9
8r6c5 8r6c8 8r6c6
            8r9c6 3r9c6
      8r5c4             3r5c4
3r3c5             3r1c6 3r1c4
=> -8 r3c5

blue's solution has the smallest matrix, i.e. uses the least native strong links. A challenge that JC Van Hay was fond of. So, kudos for blue !

For comparison, here are matrices of SpAce's, Steve's and my own solutions:
Hidden Text: Show
Code: Select all
 SpAce's
8r3c9 8r5c9
8r6c5 8r6c8 8r6c6
            8r9c6 3r9c6
                  3r7c5 5r7c5
      8r5c4                   3r5c4
8r6c5                   5r6c5 3r6c5
=> -8 r3c5


Code: Select all
 Steve's
3r5c4 8r5c4           not a triangular matrix but juxtaposition of two smaller triangular matrices
5r7c5        3r7c5                |                                |      3r5c4 8r5c4
      8r6c5 35r67c5               |    5r7c5 3r7c5                 |            8r6c5 35r67c5
             3r3c5   8r3c5        |          3r3c5   8r3c5         |                   3r3c5   8r3c5
                     8r3c9 8r5c9  |                  8r3c9 8r5c9   |                           8r3c9 8r5c9
8r9c4                8r1c5 8r5c4  |    8r9c4         8r1c5 8r5c4   |      8r9c4                8r1c5 8r5c4
=> -35 r9c4                       |    => -5 r9c4                  |      => -3 r9c4


Code: Select all
 Cenoman's
8r3c9 8r5c9
8r6c5 8r6c8 8r6c6
            8r9c6 8r9c4
                  8r5c4 3r5c4
                  5r9c4       5r4c4
8r6c5                   3r6c5 5r6c5
=> -8 r3c5
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Re: December 11, 2018

Postby Sudtyro2 » Fri Dec 14, 2018 12:26 pm

Special thanks to Cenoman and SpaCe for their generous and positive feedback. As always, it's very much appreciated!

SteveC
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