Where do I go from here?????

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Postby Luke » Thu Apr 02, 2009 9:03 pm

I have never understood Kraken Fish, so all this is raising tons of questions for me. I'd like to break it down, starting with hobiwan's "Kraken Fish Type 1."
hobiwan wrote:
Code: Select all
.---------------.----------------------.----------------.
| 4   *159   2  | 6      *159     3    | *159   7   8   |
| 8    159   19 | 12459   7      *1249 |  3     6   145 |
| 6    3     7  | 1459    8      *149  |  2     49  145 |
:---------------+----------------------+----------------:
| 37  *1-9   6  | 13459   13459  *149  |  1579  8   2   |
| 37   2     8  | 1359    1359    6    |  1579  49  145 |
| 5    4    *19 | 8       2       7    | *19    3   6   |
:---------------+----------------------+----------------:
| 9    6     45 | 1234    134     124  |  8     15  7   |
| 1    8     3  | 7       6       5    |  4     2   9   |
| 2    7     45 | 149     149     8    |  6     15  3   |
'---------------'----------------------'----------------'

Kraken Fish Type 1:  => r4c2<>9
  Sashimi X-Wing: 9 r16 c27 fr1c5 fr6c3
  r1c5 -9- r23c6 =9= r4c6 -9- r4c2
  r6c3 -9- r4c2

Hookay. I imagine to have a Kraken Fish one must first have a fish. In this case, it's the most basic of all, an x-wing (potentially):
Code: Select all
 .  X  . |  .  .  . |  X  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  X  . |  .  .  . |  X  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .

The fact that r6c2 is already solved to (4) makes no difference, and it's what makes this a sashimi x-wing rather than a plain ole x-wing.

Preventing the x-wing are two fins. If there was only one fin, this would be called a finned sashimi x-wing, so I'm guessing that since there are two, then that is what makes this a "Kraken" fish. Just guessing.

Code: Select all
 .  X  . |  .  F  . |  X  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 . -X  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  X  F |  .  .  . |  X  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .

Now the two little chains come into play:
r1c5 -9- r23c6 =9= r4c6 -9- r4c2
r6c3 -9- r4c2

If the fin in row 1 is true, r4c2<>X.
If the fin in row 6 is true, r4c2<>X.
If the fish (x-wing) is true, r4c2<>X.

Is that what's going in a "Type 1 Kraken Fish"? Can I assume any fish will do, although the bigger, the tougher to spot (an x-wing is tuff enuf...)? How many fins can be involved? Is a two pound robin fat?
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Postby Gee » Thu Apr 02, 2009 9:56 pm

After working with all of the help you submitted, I do understand how r6c3 has to be a (9). In an actual puzzle I don’t know if I would even look for this or even find it.

Mentally, I found a different way that I could arrive at the same conclusion albeit a “backdoor” approach to what was described above in your posts.

We have four cells containing (19). That is, r2c3,r4c2,r6c3,r6c7. R6c3 seems to be a “pivotal” cell in that if a (1) is placed there, the other three cells will be (9). Conversely, if a 9 is placed there, the other three cells will be (1).

When I mentally placed a (9) in r6c3, I could not find a contradiction. That doesn’t mean that there may not be one but not as far as I could go mentally.

Different story if I mentally placed a (1) in r6c3. At this point, all the other three cells became a (9). So r6c7 becomes a 9, r5c8 becomes a (4), r3c8 becomes a (9). Therefore all (9’s) are removed from row (3).

Then the (9) in r4c2 eliminates all the (9’s) in row (4).

Next, the (9) in r2c3 eliminates all the (9’s) in row (2).

So now there are no (9’s) in column (6). So a (1) definitely cannot go in r6c3 and it must be a (9).

This seems an easier way for me but whether it would be a viable way to approach other puzzles, I don’t know.

Any comments or corrections will be appreciated. If I goofed-up in the above, I sure want to know it. Thanks.

Code: Select all

 
 *--------------------------------------------------------------------*
 | 4      159    2      | 6      159    3      | 159    7      8      |
 | 8      159    19     | 12459  7      1249   | 3      6      145    |
 | 6      3      7      | 1459   8      149    | 2      49     145    |
 |----------------------+----------------------+----------------------|
 | 37     19     6      | 13459  13459  149    | 57     8      2      |
 | 37     2      8      | 1359   1359   6      | 1579   49     145    |
 | 5      4      19     | 8      2      7      | 19     3      6      |
 |----------------------+----------------------+----------------------|
 | 9      6      45     | 1234   134    124    | 8      15     7      |
 | 1      8      3      | 7      6      5      | 4      2      9      |
 | 2      7      45     | 149    149    8      | 6      15     3      |
 *--------------------------------------------------------------------*


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Postby hobiwan » Fri Apr 03, 2009 12:13 am

Luke451, your explanation is pretty good! There is only one small detail:
Luke451 wrote:Preventing the x-wing are two fins. If there was only one fin, this would be called a finned sashimi x-wing, so I'm guessing that since there are two, then that is what makes this a "Kraken" fish.

The number of fins is irrelevant. The fish as you wrote it is a regular finned sashimi x-wing, but it doesnt yield any eliminations since there is no 9 in c27 that is not in r16 and sees both fins.

The fish becomes a "Kraken" when chains get involved. The second chain is not really a chain (fin r6c3 sees r4c2 directly), but the first is and it is needed to do the elimination -> thus Kraken Fish.

Luke451 wrote:Is that what's going in a "Type 1 Kraken Fish"? Can I assume any fish will do, although the bigger, the tougher to spot (an x-wing is tuff enuf...)? How many fins can be involved? Is a two pound robin fat?

Thats whats going on in a Kraken Fish (the "Type 1" label is an addition from me). And yes, any fish will do. You just have to ensure that all fins lead to the elimination.
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Postby hobiwan » Fri Apr 03, 2009 12:26 am

Gee, this is definitely a valid move, it is usually called a (Multiple) Forcing Chain: One or more chains starting with the same premise and leading to a contradiction.

In Forcing Chain notation:

r6c3=1 => r6c7=9 => r5c8=4 => r3c8=9 => r3c6<>9
r6c3=1 => r2c3=9 => r2c6<>9
r6c3=1 => r4c2=9 => r4c9<>9
Contradiction in c6 => r6c3<>1
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Postby DonM » Fri Apr 03, 2009 1:04 am

The use of AAICs/Kraken cell/column/box techniques in puzzles was the subject of a lot of discussion over at Eureka when we were solving ER=8.3 to ER=8.7 (or thereabout) puzzles. Overall, they were/are looked on as nets (or subsets thereof) or 'forking' methods or methods with a quantum leap in assumptiveness depending on how one views these things:) . After all that discussion, suffice it to say that in the circles of higher difficulty level manual solving it, it is not considered particularly elegant to wantonly use these methods, especially if 'traditional' nice loops or AICs can be used.

I mention this because these are fairly powerful methods and it is easy to get carried away with their use since they can easily bring down many of the puzzles we discuss in this section of the forum, even though less powerful and more elegant methods would do the job.
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Postby Luke » Fri Apr 03, 2009 9:27 am

aran wrote:Strong sets can therefore be listed vertically and developed horizontally with the goal of seeking a common conclusion, which if found must be true.

Another example : imagine a deadly rectangle with corners 57, 571, 572, 573. Then {1,2,3} is a strong set (at least one must be true, and indeed all may be true) so
1
||
2
||
3.

Now all the AUR's I've seen notated this way make more sense:) .

So, can you develop an AUR with this idea if a corner has more than one extra?
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Postby aran » Fri Apr 03, 2009 12:17 pm

hobiwan wrote:
Code: Select all
.---------------.----------------------.----------------.
| 4   *159   2  | 6      *159     3    | *159   7   8   |
| 8    159   19 | 12459   7      *1249 |  3     6   145 |
| 6    3     7  | 1459    8      *149  |  2     49  145 |
:---------------+----------------------+----------------:
| 37  *1-9   6  | 13459   13459  *149  |  1579  8   2   |
| 37   2     8  | 1359    1359    6    |  1579  49  145 |
| 5    4    *19 | 8       2       7    | *19    3   6   |
:---------------+----------------------+----------------:
| 9    6     45 | 1234    134     124  |  8     15  7   |
| 1    8     3  | 7       6       5    |  4     2   9   |
| 2    7     45 | 149     149     8    |  6     15  3   |
'---------------'----------------------'----------------'

Kraken Fish Type 1:  => r4c2<>9
  Sashimi X-Wing: 9 r16 c27 fr1c5 fr6c3
  r1c5 -9- r23c6 =9= r4c6 -9- r4c2
  r6c3 -9- r4c2

Ah, yes, Hobiwan very fine:)
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Postby aran » Fri Apr 03, 2009 12:35 pm

Luke451 wrote:
Another example : imagine a deadly rectangle with corners 57, 571, 572, 573. Then {1,2,3} is a strong set (at least one must be true, and indeed all may be true) so
1
||
2
||
3.
Now all the AUR's I've seen notated this way make more sense:) .
So, can you develop an AUR with this idea if a corner has more than one extra?

Luke, yes, if the rectangle were 57, 571,572,5734
then we would have
1
||
2
||
3
||
4
ie one of that group of 4 must be true.
The idea though of finding something on which all 4 horizontal streams converge does become a little off-putting.
The above configuration would equally apply to a cell with candidates {1234}...and in general one wouldn't dream of taking that approach.
What Don says should be borne in mind
DonM wrote:it is easy to get carried away with their use since they can easily bring down many of the puzzles we discuss in this section of the forum, even though less powerful and more elegant methods would do the job.

I would though make a big distinction between a Deadly Rectangle {123} set up as above and say {777} in a row. With the D rectangle either one exploits the {123} or one doesn't : there's no alternative. With the {777} there may be a Sashimi Franken Kraken Jellyfish waiting in the depths:)
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Postby DonM » Fri Apr 03, 2009 7:42 pm

aran wrote:What Don says should be borne in mind
DonM wrote:it is easy to get carried away with their use since they can easily bring down many of the puzzles we discuss in this section of the forum, even though less powerful and more elegant methods would do the job.

I would though make a big distinction between a Deadly Rectangle {123} set up as above and say {777} in a row. With the D rectangle either one exploits the {123} or one doesn't : there's no alternative. With the {777} there may be a Sashimi Franken Kraken Jellyfish waiting in the depths:)


Good point (assuming I've got it correctly ie. if the following is consistent with your point:) ). The use of the multi-line, strong link notation does not mean that the underlying patterns all have similar concerns about 'forking' and 'assumptivity'. Certainly, AURs, BUG patterns and even AALSs (though farther down the line from AURs & BUGs) don't have the same concerns as AAICs/Kraken cells/columns/boxes.
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