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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Wed Nov 21, 2012 7:30 am Post subject: Sudopedia: Kraken Fish |
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Kraken Fish
A Kraken Fish is a fish pattern which is connected to a candidate elimination cell (CEC) in such a way that placing this candidate would reduce the secondary set to a size smaller than the defining set.
Here is a diagram depicting a Kraken X-Wing. It has 2 CECs.
| Code: | .-------.-------.-------.
| . / . | . / . | . . . |
| . X . | . X . | . * . |
| . / . | . / . | . . . |
:-------+-------+-------:
| . / . | . / . | . . . |
| . X . | . X . | . * . |
| . / . | . / . | . . . |
:-------+-------+-------:
| . / . | . / . | . . . |
| . X . | . / . | . . . |
| / / X | / / / | / X / |
'-------'-------'-------' |
There is a potential X-Wing in columns 2 & 5 and rows 2 & 5. The candidate in r8c2 acts as a fin, but because it does not share a box with one of the candidates forming the X-Wing, it does not cause any eliminations that would normally occur in a Finned X-Wing. The pattern has 2 columns covering 3 rows.
Now consider what would happen if either r2c8 or r5c8 would contain digit X. Both would eliminate all candidates in their own row and, through the strong link in row 9, the candidate in r8c2, leaving a pattern with 2 columns covering 1 row, an impossible situation.
A Kraken-related Extended 2-String Kite Example
Next consider the example below. This is identical to the Kraken X-wing example except the candidate has benn removed from cell r2c2. The resultant pattern is a 2-string kite consisting of conjugate pairs AB and CD and an additional conjugate pair EF. This is an example of a more general technique called the extended 2-string kite technique.
| Code: | .-------.-------.-------.
| . - . | . - . | . . . |
| . - . | . F . | . * . |
| . - . | . - . | . . . |
:-------+-------+-------:
| . - . | . - . | . . . |
| . D . | . E . | . * . |
| . - . | . - . | . . . |
:-------+-------+-------:
| . - . | . - . | . . . |
| . C . | . - . | . . . |
| - - A | - - - | - B - |
'-------'-------'-------' |
How it works. Since A and C are peers, at most only one of them can be X. This means that either or both of their conjugates B and D must be X. If B is X then r25c8 cannot be X. If B is not X, then D must be X and its peer E must be not X. Therefore E's conjugate F must be X. Therefore r25c8 cannot be X. So you get the same eliminations as the Kraken X-wing. A similar argument holds if r5c2 had been eliminated instead of r2c2. This means that either r2c2 or r5c2 but not both can be eliminated from the Kraken X-wing pattern without changing the results. The extended 2-string kite pattern occurs more often then the Kraken X=wing in puzzles.
Connection Types
In the example, the CECs are connected to the pattern with a direct weak link and an indirect connection via a strong link. However, there are several other methods to connect the CEC to the fish pattern:
Strong links
Grouped strong links
Almost Locked Sets
As a result, the CEC does not even need to be a candidate for the same digit as the pattern. The following diagram shows how an X-Wing pattern for digit X can eliminate a candidate for digit Y.
| Code: | . - . | . - . | . . .
. X . | . X . | . XY .
. - . | . - . | . . .
---------+----------+---------
. - . | . - . | . . .
. X . | . X . | . . .
. - . | . - . | . . .
---------+----------+---------
. - . | . - . | . . .
. X . | . - . | . . .
. - XY | . - . | . CEC . |
In this example, a similar Finned X-Wing is present, but r2c8 and r9c3 are both bivalue cells with candidates XY. Placing Y in the CEC at r9c8 would force both these cells to X and reduce the fish pattern to a single row and 2 columns.
External Link
Kraken Fish (New Sudoku Players' Forums)
http://forum.enjoysudoku.com/viewtopic.php?t=5143
Last edited by keith on Wed Nov 21, 2012 7:56 am; edited 4 times in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Nov 21, 2012 7:32 am Post subject: Nienhaus Comments |
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Talk: Kraken Fish
If you eliminate either r2c2 or r2c4 from the Kraken X-wing example, you still get the same eliminations. The resultant pattern is a 2 string kite and a conjugate pair, where one cell of the conjugate pair is a peer of one cell of the 2 string kite. This occurs more often than the Kraken X-wing. The Kraken X-wing pattern has one cell of an x-wing merged with a one cell of a 2 string kite. This concept of adding a conjugate pair to an existing pattern also works for the empty rectangle technique. It gives an extra cell elimination.
Nienhaus |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Nov 21, 2012 2:02 pm Post subject: |
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Kraken x-wing = x-wing with extended fin
I can see the latter easier.  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Nov 21, 2012 2:49 pm Post subject: |
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| arkietech wrote: | Kraken x-wing = x-wing with extended fin
I can see the latter easier. |
Except, in the example, there is no fin:
| Code: | .-------.-------.-------.
| . / . | . / . | . . . |
| . X . | . X . | . * . |
| . / . | . / . | . . . |
:-------+-------+-------:
| . / . | . / . | . . . |
| . X . | . X . | . * . |
| . / . | . / . | . . . |
:-------+-------+-------:
| . / . | . / . | . . . |
| . X . | . / . | . . . |
| / / X | / / / | / X / |
'-------'-------'-------' |
If you take away the "extension", the strong link in R9, there are no possible eliminations from the X-wing is true or R8C2 is true.
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Wed Nov 21, 2012 5:04 pm Post subject: |
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| Who authored the main article? |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Nov 21, 2012 7:24 pm Post subject: |
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| keith wrote: | If you take away the "extension", the strong link in R9, there are no possible eliminations from the X-wing is true or R8C2 is true.
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The fin is r8c2 without it you have an x-wing
with it you have the same deletes in column 8 with the extension
What am I missing  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Nov 21, 2012 8:44 pm Post subject: |
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| arkietech wrote: | | keith wrote: | If you take away the "extension", the strong link in R9, there are no possible eliminations from the X-wing is true or R8C2 is true.
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The fin is r8c2 without it you have an x-wing
with it you have the same deletes in column 8 with the extension
What am I missing |
A finned X-wing makes eliminations without an extension.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Nov 21, 2012 9:00 pm Post subject: |
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| ronk wrote: | | Who authored the main article? |
Who knows? Nienhaus is the only discernible credit.
| Quote: | From Sudopedia, the free Sudoku reference guide
Talk:Kraken Fish
From Sudopedia
Revision history
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Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Nov 25, 2012 4:08 pm Post subject: |
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| elsewhere tlanglet wrote: |
Another x-wing, which I believe is termed a Kraken x-wing, makes the same deletion.
Kraken x-wing(9)r45c16 with fin 9r3c1
9r3c1-r2c2=9r2c9 => r5c9<>9
x-wing(9)r45c16 => r5c9<>9 |
| Code: |
au tough November 19, 2012
.5.9..7..3.....48....6........7....1.78.2.53.5....3........2....49.....5..1..4.6.
12468 5 246 | 9 34 18 | 7 12 236
3 169 67 | 2 157 157 | 4 8 69
12489 1289 247 | 6 34 178 | 1239 5 239
-----------------------+-----------------------+---------------------
2469 269 3 | 7 568 569 | 2689 249 1
1469 7 8 | 14 2 169 | 5 3 4-9
5 1269 246 | 148 168 3 | 2689 2479 24789
-----------------------+-----------------------+---------------------
678 368 5 | 138 16789 2 | 1389 1479 34789
2678 4 9 | 138 1678 167 | 1238 127 5
278 238 1 | 5 789 4 | 2389 6 23789 |
| Code: |
*. . . | . . / | . . .
/ *9 *. | / / / | / / f9
*9 . . | . . / | . . .
---------+----------+----------
*9 . . | . . *9 | . . -.
*9 . . | . . *9 | . . -9
/ . . | . . / | . . .
---------+----------+----------
/ . . | . . / | . . .
/ . . | . . / | . . .
/ . . | . . / | . . .
sashimi mutant swordfish body: 9r2c16\r45b1 + fin: 9r2c9 ==> r45c9<>9 |
According to The Ultimate Fish Guide, the pattern is formally a sashimi mutant swordfish (Fig 3V). The pattern is ...- swordfish because the defining set (base set) is comprised of three strong inference sets, 9r2c16
- mutant because the base set is composed of both rows and columns
- sashimi because the pattern would collapse (to that of an x-wing) if fin r2c9 did not exist
Note the pattern is still valid with candidates <9> at r1c1 and r2c3 and can make an additional exclustion r4c9<>9.
FWIW Nienhaus is Bud on this forum and The New Players' Forums. |
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