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Kraken skyscraper?

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tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Wed Oct 21, 2009 3:22 pm Post subject: Kraken skyscraper?

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

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Wed Oct 21, 2009 5:53 pm Post subject:

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

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Wed Oct 21, 2009 8:00 pm Post subject:

arkietech wrote:

Interesting. I would use:

Code:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Oct 22, 2009 3:49 am Post subject:

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

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Thu Oct 22, 2009 3:56 am Post subject:

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

wapati

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

Posted: Thu Oct 22, 2009 9:24 pm Post subject:

I agree that it works, I don't see a pattern. Give us a general case?

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Oct 23, 2009 12:25 am Post subject:

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

wapati

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

Posted: Fri Oct 23, 2009 6:03 am Post subject:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Oct 23, 2009 7:30 am Post subject:

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

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Oct 23, 2009 2:06 pm Post subject:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Oct 23, 2009 10:10 pm Post subject:

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

wapati

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

Posted: Fri Oct 23, 2009 10:36 pm Post subject:

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?

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Oct 23, 2009 10:44 pm Post subject:

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

ttt

Joined: 06 Dec 2008
Posts: 42
Location: vietnam

Posted: Mon Oct 26, 2009 4:54 am Post subject:

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 1’s (marked with *):
(7)r9c8=(7)r8c9-(79=1)r12c9-(1)r47c9=(X-wing:1’s)r47c58 => r9c8<>1

ttt

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