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Kraken skyscraper?

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Wed Oct 21, 2009 3:22 pm    Post subject: Kraken skyscraper? Reply with quote

While working the Vanhegan Insane puzzle today, I noticed the following pattern:
Code:

*--------------------------------------------------*
 | 5    7    9    | 348  348  2    | 1    6    48   |
 | 6    2    48   | 1    7    5    | 9    48   3    |
 | 48*  1    3    | 48*  9    6    | 7    2    5    |
 |----------------+----------------+----------------|
 | 7    6    1    | 2    5    38   | 34   9    48   |
 | 348* 5    2    | 7    348* 9    | 6    38f  1    |
 | 348  9    48   | 348  6    1    | 2    5    7    |
 |----------------+----------------+----------------|
 | 9    4    7    | 6    38   38   | 5    1    2    |
 | 1    8    6    | 5    2    7    | 34   34   9    |
 | 2    3    5    | 9    1    4    | 8    7    6    |
 *--------------------------------------------------*

A finned skyscraper on 8 is in r35c1 (marked *) and the external fin is in r5c8 (marked f). In this code, the skyscraper will delete 8 from r1c5 and r6c4. If the fin is true, both of the same two cells can not be true.

Although I have never seen any comments on a finned or Kraken skyscraper, I assume that such a pattern is valid. Thus, for this specific code, 8 can be deleted from both r1c5 and r6c4.

Comments?

Ted

ps: this is an unusually easy Vanhegan Insame
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arkietech



Joined: 31 Jul 2008
Posts: 1717
Location: Northwest Arkansas USA

PostPosted: Wed Oct 21, 2009 5:53 pm    Post subject: Reply with quote

Interesting. I would use:
Code:
 *--------------------------------------------------*
 | 5    7    9    | 348  348  2    | 1    6    48   |
 | 6    2   *48   | 1    7    5    | 9    48   3    |
 |*48   1    3    |*48   9    6    | 7    2    5    |
 |----------------+----------------+----------------|
 | 7    6    1    | 2    5    38   | 34   9    48   |
 | 348  5    2    | 7    348  9    | 6    38   1    |
 | 348  9   *48   | 3-48 6    1    | 2    5    7    |
 |----------------+----------------+----------------|
 | 9    4    7    | 6    38   38   | 5    1    2    |
 | 1    8    6    | 5    2    7    | 34   34   9    |
 | 2    3    5    | 9    1    4    | 8    7    6    |
 *--------------------------------------------------*
Remote pair
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Wed Oct 21, 2009 8:00 pm    Post subject: Reply with quote

arkietech wrote:
Interesting. I would use:
Code:
 *--------------------------------------------------*
 | 5    7    9    | 348  348  2    | 1    6    48   |
 | 6    2   *48   | 1    7    5    | 9    48   3    |
 |*48   1    3    |*48   9    6    | 7    2    5    |
 |----------------+----------------+----------------|
 | 7    6    1    | 2    5    38   | 34   9    48   |
 | 348  5    2    | 7    348  9    | 6    38   1    |
 | 348  9   *48   | 3-48 6    1    | 2    5    7    |
 |----------------+----------------+----------------|
 | 9    4    7    | 6    38   38   | 5    1    2    |
 | 1    8    6    | 5    2    7    | 34   34   9    |
 | 2    3    5    | 9    1    4    | 8    7    6    |
 *--------------------------------------------------*
Remote pair


As I indicated,
Quote:
ps: this is an unusually easy Vanhegan Insame

But I am still interested in the (possible) Kraken skyscraper. In fact, this move does not solve the puzzle, but others do.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Oct 22, 2009 3:49 am    Post subject: Reply with quote

Hello Ted,

Kraken Fish have been around for some time. Since a Skyscraper is just the combination of two Sashimi X-Wings, a Kraken version is definitely possible.

Regards, Danny
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Thu Oct 22, 2009 3:56 am    Post subject: Reply with quote

daj95376 wrote:
Hello Ted,

Kraken Fish have been around for some time. Since a Skyscraper is just the combination of two Sashimi X-Wings, a Kraken version is definitely possible.

Regards, Danny


Thanks for the feedback kind sir.

Ted
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Thu Oct 22, 2009 9:24 pm    Post subject: Reply with quote

I agree that it works, I don't see a pattern.

Give us a general case?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 23, 2009 12:25 am    Post subject: Reply with quote

wapati wrote:
I agree that it works, I don't see a pattern.

Give us a general case?

I don't believe that Kraken has a pattern. It's strickly an extension based on what ronk calls a remote fin cell.

Code:
 Skyscraper  r35\c1+(4|5) => r1c5,r6c4<>8
 remote fin r5c8 is one end of a Blue/Green X-Chain ...
 ... where r1c4 is the same color => same eliminations
 *--------------------------------------------------*
 | 5    7    9    | 348  348  2    | 1    6    48   |
 | 6    2   B48   | 1    7    5    | 9   G48   3    |
 |G48*  1    3    |B48*  9    6    | 7    2    5    |
 |----------------+----------------+----------------|
 | 7    6    1    | 2    5    38   | 34   9    48   |
 | 348* 5    2    | 7    348* 9    | 6   B38#  1    |
 | 348  9    48   | 348  6    1    | 2    5    7    |
 |----------------+----------------+----------------|
 | 9    4    7    | 6    38   38   | 5    1    2    |
 | 1    8    6    | 5    2    7    | 34   34   9    |
 | 2    3    5    | 9    1    4    | 8    7    6    |
 *--------------------------------------------------*

Note: There's no rule keeping a Kraken Fish from having more than one remote fin cell ... or from having what ronk calls endo-/exo- fin cells.

----- ----- ----- (my editing of) ronk fin types

Code:
endo-  fin cell  <-->   A cell inside  the intersection of two or more Base sectors
exo-   fin cell  <-->   A cell outside the intersection of the Base and Cover sectors
remote fin cell  <-->   A cell that only sees an elimination cell indirectly -- Kraken cell
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Fri Oct 23, 2009 6:03 am    Post subject: Reply with quote

Thanks Danny,

It seems to me that Kraken covers extensions too, so extended W-wings are a kraken form ?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 23, 2009 7:30 am    Post subject: Reply with quote

wapati wrote:
Thanks Danny,

It seems to me that Kraken covers extensions too, so extended W-wings are a kraken form ?

I've always used Kraken with Fish. That's what Sudopedia seems to do as well. However, I've seen it used on non-Fish and never quite understood how it applied.

Regards, Danny
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Oct 23, 2009 2:06 pm    Post subject: Reply with quote

Danny, thanks for responding to the question by Wapati. I was trying to work up a response but was hopping that someone with a solid fundamental and historical understanding would step in and address the issue. I am definitely more of a mechanical do it person than someone with a sound basic knowledge of sudoku.

However, now that you have gotten involved, would you please also explain the terms "base" and "cover" as used in the definitions by ronk?

Thanks again,

T
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 23, 2009 10:10 pm    Post subject: Reply with quote

tlanglet wrote:
Danny, thanks for responding to the question by Wapati. I was trying to work up a response but was hopping that someone with a solid fundamental and historical understanding would step in and address the issue. I am definitely more of a mechanical do it person than someone with a sound basic knowledge of sudoku.

However, now that you have gotten involved, would you please also explain the terms "base" and "cover" as used in the definitions by ronk?

Ouch!!! Your request is far from easy to answer. Any discussion about Fish gets bogged down in definitions and details very quickly. Also, it doesn't help that I don't know the proof behind the use of a Base Set and a Cover Set for Fish. What I do know is how to find/manipulate the Sets to determine eliminations. (Thanks to many hours of discussions with RonK and a couple of threads by Obi-Wahn!)

Everything discussed is limited to one candidate value!!!

In the world of Fish, a house/unit -- i.e., row/column/box -- is called a sector. I don't know why!

You can select N (base) sectors and they are called a Base Set (for a candidate value).

You can select N (cover) sectors and they are called a Cover Set (for a candidate value).

If you select your Sets wisely, then eliminations can be derived using an NxN Fish. Consider the following (N=2) X-Wing from RonK's exemplars.

Code:
 "\" -- an empty cell for the candidate value
 "X" -- a cell that's considered to be part of the Fish pattern
 "." -- a cell where the candidate value may or may not exist
 "*" -- a cell where an elimination can occur in a grid for the candidate

Code:
 .  *  . |  .  .  . |  .  *  .
 /  X  / |  /  /  / |  /  X  /
 .  *  . |  .  .  . |  .  *  .
---------+----------+----------
 .  *  . |  .  .  . |  .  *  .
 .  *  . |  .  .  . |  .  *  .
 .  *  . |  .  .  . |  .  *  .
---------+----------+----------
 .  *  . |  .  .  . |  .  *  .
 /  X  / |  /  /  / |  /  X  /
 .  *  . |  .  .  . |  .  *  .
 Fig 2Ai: rr\cc

The Base Set consists of sectors [r2] and [r8]; i.e., r28. This set contains only four candidate cells. The remaining cells of the set are empty for this candidate! Now, consider a Cover Set that consists of sectors [c2] and [c8]; i.e., c28. This set contains all of the candidate cells in the Base Set ... plus the possibility of the candidate in the cells marked with an "*".

Since all of the Base Set candidates are contained/included in the Cover Set candidates, then the candidate value can be eliminated in the other cells of the Cover Set. (I don't know the why for the preceeding statement, but it's very important!) To my knowledge, this is how the basic Fish patterns and eliminations were derived. The above exemplar would be called:

Code:
X-Wing r28\c28

An example:

Code:
 +-----------------------+
 | 1 8 . | . . 3 | 9 . 2 |
 | 3 . . | . 8 . | . . . |
 | . . 6 | . 2 . | 8 3 . |
 |-------+-------+-------|
 | . . . | 8 . . | 5 . . |
 | . 1 5 | . . . | . 9 . |
 | 8 . . | . . 1 | 3 . . |
 |-------+-------+-------|
 | 6 . 1 | 3 . 2 | 4 . . |
 | . . 2 | . 9 . | . . . |
 | 4 . . | . . . | . . . |
 +-----------------------+

 after basics
 *-----------------------------------------------------------*
 | 1     8     7     | 56    4     3     | 9     56    2     |
 | 3     2     49    | 179   8     56    | 17    147   56    |
 | 59    45    6     | 179   2     79    | 8     3     147   |
 |-------------------+-------------------+-------------------|
 | 279   467   3     | 8     67    79    | 5     1247  147   |
 | 27    1     5     | 27    3     4     | 6     9     8     |
 | 8     467   49    | 2579  567   1     | 3     247   47    |
 |-------------------+-------------------+-------------------|
 | 6     579   1     | 3     57    2     | 4     8     59    |
 | 57    357   2     | 4     9     8     | 17    1567  356   |
 | 4     39    8     | 567   1     56    | 2     57    39    |
 *-----------------------------------------------------------*

Code:
 candidate grid for <9>
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  9  |  9  .  .  |  .  .  .  |
 |  9  .  .  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  9  .  .  |  .  .  9  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  9  .  |
 |  .  .  9  |  9  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  9  |
 |  .  .  .  |  .  9  .  |  .  .  .  |
 |  .  9  .  |  .  .  .  |  .  .  9  |
 +-----------------------------------+

Code:
 X-Wing r26\c34 => [r3c4]<>9
 +-----------------------------------+
 |  .  .  *  |  *  .  .  |  9  .  .  |
 |  /  /  9  |  9  /  /  |  /  /  /  |
 |  9  .  *  | *9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  9  .  *  |  *  .  9  |  .  .  .  |
 |  .  .  *  |  *  .  .  |  .  9  .  |
 |  /  /  9  |  9  /  /  |  /  /  /  |
 |-----------+-----------+-----------|
 |  .  9  *  |  *  .  .  |  .  .  9  |
 |  .  .  *  |  *  9  .  |  .  .  .  |
 |  .  9  *  |  *  .  .  |  .  .  9  |
 +-----------------------------------+

Later on, basic Fish were expanded into finned/Sashimi/Franken/mutant/Kraken fish.

For additional information, check my general post on Fish.


Last edited by daj95376 on Fri Oct 23, 2009 10:47 pm; edited 3 times in total
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Fri Oct 23, 2009 10:36 pm    Post subject: Reply with quote

daj95376 wrote:

In the world of Fish, a house/unit is called a sector; e.g., row/column/box. I don't know why!


OK, you introduced house/unit, what is that?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 23, 2009 10:44 pm    Post subject: Reply with quote

wapati wrote:
daj95376 wrote:

In the world of Fish, a house/unit is called a sector; e.g., row/column/box. I don't know why!


OK, you introduced house/unit, what is that?

http://www.sudopedia.org/wiki/House
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ttt



Joined: 06 Dec 2008
Posts: 42
Location: vietnam

PostPosted: Mon Oct 26, 2009 4:54 am    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------------------------*
 | 1       45679   45678   | 2       45678   456789  | 3       678     79      |
 | 689     2       5678    | 578     3       56789   | 1689    4       179     |
 | 4689    4679    3       | 478     4678    1       | 2689    2678    5       |
 |-------------------------+-------------------------+-------------------------|
 | 5       349     24      | 6      *148     48      | 7      *1238   #12349   |
 | 2346    8       2467    | 1347    9       47      | 124     5       1234    |
 | 349     3479    1       | 34578   4578    2       | 489     38      6       |
 |-------------------------+-------------------------+-------------------------|
 | 7       346     2468    | 9      *1468    468     | 5      *1236   #1234    |
 | 3468    1       4568    | 4578    2       45678   | 46      9       347     |
 | 246     456     9       | 1457    14567   3       | 1246   -1267    8       |
 *-----------------------------------------------------------------------------*

An example on using Almost X-wing (Fish), look at almost X-wing 1ís (marked with *):
(7)r9c8=(7)r8c9-(79=1)r12c9-(1)r47c9=(X-wing:1ís)r47c58 => r9c8<>1

ttt
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