Kraken X-Wing Example

Advanced methods and approaches for solving Sudoku puzzles

Kraken X-Wing Example

Postby Bud » Thu Oct 23, 2008 3:42 pm

Some time ago, someone at the forum wanted to see a an actual puzzle with a Kraken X-Wing rather than a diagram, so here it is. This is a patially worked Sudoku9981 Extreme puzzle Book 36 #1. The digit is 2, d the cells in the pattern are marked with a ' and the elimination cells are marked with a *. This did not krack the puzzle. For those who have trouble recognizing the pattern, It is a 2-string kite and an x-wing with one cell of each merged. Edit: Oops. Thanks DaJ.

Code: Select all
 |-----------------+-----------------+-----------------|
 |  139   4  1239  |   5    6    8   |  279  17  1239  |
 |   8  '239   6   | '23    1    7   | 2459 2359 *23459|
 |   7  '123   5   | '23    4    9   |   6    8  *123  |
 |-----------------+-----------------+-----------------|
 |   4  '289   7   |   1   89    3   |  259  259   6   |
 |  139   5   139  |   6    2    4   |  79   17    8   |
 |   19   6  '1289 |   7   89    5   |   3    4  '129  |
 |-----------------+-----------------+-----------------|
 |   5   389 3489  |  89    7    6   |   1   239 2349  |
 |   2    7    89  |   4    3    1   |  589   6   59   |
 |   6  1389 13489 |  89    5    2   |  489  39    7   |
 |-----------------+-----------------+-----------------|
Last edited by Bud on Fri Oct 24, 2008 7:21 am, edited 2 times in total.
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Postby hobiwan » Fri Oct 24, 2008 5:48 am

Bud,
something is wrong here. r8c2 has to be 7 (not 89).
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Postby daj95376 » Fri Oct 24, 2008 7:55 am

hobiwan: good catch.

Simple Sudoku users: SS does not catch the error:!:

Note to self, fix my solver to catch inaccurate PMs.:(
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Re: Kraken X-Wing Example

Postby DonM » Fri Oct 24, 2008 10:00 am

Bud wrote:For those who have trouble recognizing the pattern, It is a 2-string kite and an x-wing with one cell of each merged.[code]


I find it easier to look on the Kraken X-Wing as a relatively simple variation of a finned X-wing. In the latter case, the fin sees the a digit of the X-wing and the candidate for exclusion directly (ie. they're all in the same box). In the case of the Kraken, X-Wing the fin, as usual, directly see's a member of the X-Wing, but sees the candidate for exclusion through a conjugate link (r6c3 & r6c9 above). The basis for the validity of the exclusion is exactly the same in both cases. Looked at this way, IMO the Kraken X-Wing should be much easier to remember & identify.

Having said that, there is one important difference: Whereas, with the simple finned X-Wing, the exclusion is limited to to a digit that sees one 'leg' of the X-Wing, with the Kraken X-Wing, 2 exclusions are possible- one associated withe each leg. I must admit that in my own solving, I often forget to look for the Kraken X-Wing pattern...:(
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Postby ronk » Fri Oct 24, 2008 11:14 am

sashimi mutant swordfish: (2)r6c24\r23b4 plus fin r6c9 ==> r23c9<>2
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Kraken X-Wing Example

Postby Bud » Fri Oct 24, 2008 12:15 pm

Sorry about the sloppy proofreading. Color wings and 2-string kites are one of the first things I look for in a puzzle because they occur so frequently. When I look for 2-string kites, I also look for Kraken x-wings, exteded 2-string kites and Mutant Swordfish since 2-string kites are part of the pattern for the latter two. I missed Ron's Sashimi Mutant Swordfish, and that's not all I missed. Daj pointed out that there is a 2 fin x-wing in columns 1 and 6 that gives exactly the same eliminations. so in this example the Kraken x-wing is redundant
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Postby hobiwan » Fri Oct 24, 2008 12:48 pm

ronk wrote:sashimi mutant swordfish: (2)r6c24\r23b4 plus fin r6c9 ==> r23c9<>2

Or:
Finned X-Wing: 2 r16 c39 fr1c7 => r23c9<>2
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Postby ronk » Fri Oct 24, 2008 1:02 pm

hobiwan wrote:
ronk wrote:sashimi mutant swordfish: (2)r6c24\r23b4 plus fin r6c9 ==> r23c9<>2

Or:
Finned X-Wing: 2 r16 c39 fr1c7 => r23c9<>2

I was merely showing that [edit: an N-fish krakenized by adding one strong inference of the same digit] is generally replaceable with a non-kraken (N+1)-fish.
Last edited by ronk on Fri Oct 24, 2008 11:57 am, edited 1 time in total.
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Kraken X-Wing Example

Postby Bud » Fri Oct 24, 2008 2:30 pm

Ron, Are you saying that it is not uncommon that other techniques can be used inplace of the Kraken x-wing in a puzzle? That is true of a lot of pattern techniques. I've had a lot of puzzles where a 2-string kite gave the same elimination as a fin x-wing.
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Re: Kraken X-Wing Example

Postby ronk » Fri Oct 24, 2008 3:53 pm

Bud wrote:Are you saying that it is not uncommon that other techniques can be used inplace of the Kraken x-wing in a puzzle? That is true of a lot of pattern techniques.

Sorry, including the edit above, I don't know how to make my statement any more explicit.
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