Intersecting X-Wings

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Intersecting X-Wings

Postby daj95376 » Wed Oct 04, 2006 3:11 pm

Suddenly, I'm hooked on Kraken fish because they explain many of the unusual eliminations found by Templates in my solver. Here's an interesting example.

Code: Select all
# Tarek's (20-stepper) after SSTS
 *--------------------------------------------------------------------------------------*
 | 6        2347     3457     |@458     @258      1        | 9        3457    #348      |
 | 2579     8        4579     | 4569     3        2456     | 1457     4567     146      |
 | 59       349      1        | 7        5689     4568     |#458      3456     2        |
 |----------------------------+----------------------------+----------------------------|
 |*189      1369     2        | 134569-8 1569-8   34568    |*458      4569     7        |
 |*789      5        3679     | 3469-8   679-8    24678    |*248      1        4689     |
 | 4        1679     679      | 15689    1256789  25678    | 3        2569     689      |
 |----------------------------+----------------------------+----------------------------|
 | 3        1247     457      |@158     @1578     9        | 6        247      14       |
 | 12579    12679    5679     | 1356     4        3567     | 127      8        39       |
 | 179      14679    8        | 2        167      367      | 147      39       5        |
 *--------------------------------------------------------------------------------------*

There are two Kraken X-Wings, (*) and (@), in <8> where the fin cells have a strong link. Since one of the fins must be false, this means that any cells common to both X-Wings, (-), can have <8> eliminated.

[Edit: updated title, changed finned to Kraken, and exchanged prefix characters in PM to be more standard.]
Last edited by daj95376 on Fri Nov 03, 2006 5:41 pm, edited 2 times in total.
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Re: Two finned X-Wings and a Strong Link

Postby ronk » Wed Oct 04, 2006 3:47 pm

daj95376 wrote:Suddenly, I'm hooked on finned fish because they explain many of the unusual eliminations found by Templates in my solver. Here's an interesting example. (I hope this isn't redundant to a posting elsewhere!)
...
There are two finned X-Wings, (*) and (#), in <8> where the fins have a strong link, (@). Since one of the fins must be false, this means that any cells common to both X-Wings, (-), can have <8> eliminated.

daj, very nice deduction. If by strong link you mean r1c9=8=r3c7, it can be a weak link. Ironically, you posted another such intersecting x-wing puzzle here ... which uses such a weak link.:)
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Postby tarek » Wed Oct 04, 2006 4:30 pm

The eliminations can be achieved using finned swordfishes.... for 8s the formation can be achieved in rows or in cloumns, which caused this link to exist...........
Code: Select all
*-----------------------------------------------------------------------------------*
| 6        2347     3457    |%458     %258      1       | 9        3457    %348     |
| 2579     8        4579    | 4569     3        2456    | 1457     4567     146     |
| 59       349      1       | 7        5689    *4568    |*458      3456     2       |
|---------------------------+---------------------------+---------------------------|
|*189      1369     2       |-1345689 -15689   *34568   |*458      4569     7       |
|*789      5        3679    |-34689   -26789   *234678  |*248      1        4689    |
| 4        1679     679     |%15689   %1256789 #25678   | 3        2569    %689     |
|---------------------------+---------------------------+---------------------------|
| 3        1247     457     |%158     %1578     9       | 6        247      14      |
| 12579    12679    5679    | 1356     4        3567    | 127      8        39      |
| 179      14679    8       | 2        167      367     | 147      39       5       |
*-----------------------------------------------------------------------------------*
Eliminating 8 From r4c4 "Finned Swordfish in Columns 167(*) or rows 167(%)"
Eliminating 8 From r4c5 "Finned Swordfish in Columns 167(*) or rows 167(%)"
Eliminating 8 From r5c4 "Finned Swordfish in Columns 167(*) or rows 167(%)"
Eliminating 8 From r5c5 "Finned Swordfish in Columns 167(*) or rows 167(%)"


1 fin is in Box 5 which still has some more fins for other FINNED swordfishes:D

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Postby daj95376 » Wed Oct 04, 2006 5:09 pm

Thanks ronk for reminding me of the finned Swordfish in another post. At that time, I didn't have a clue on how a finned fish worked, so I was describing the eliminations as Implication Chains. In that case, it was a *true* finned fish. In this case, the fins don't lie within the same box as any of the X-Wing cells. That's why I suspected that overlapping ARCS was a more accurate description of what I saw.

Thanks tarek for including the finned Swordfish. I'm luck to spot a finned X-Wing. Your eliminations don't require ARCS or my complicate overlapping relationship.
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Postby daj95376 » Fri Nov 03, 2006 6:54 pm

Code: Select all
..1..2....3..4..5.6..7..8....6.....7.1.....2.9.....5....3..1..6.4..5..3....8..9.. # Ocean

Code: Select all
# after SSTS
# Kraken X-Wing [R28c45]:[r2c7]
 *--------------------------------------------------------------------------------------*
 | 4578     5789     1        | 3569     3689     2        | 3467     4679     349      |
 | 278      3        2789     |*169      4       *689      |#1267     5        129      |
 | 6        259      2459     | 7        139      359      | 8        149      12349    |
 |----------------------------+----------------------------+----------------------------|
 | 23458    258      6        | 123459   12389    34589    | 134      1489     7        |
 | 34578    1        4578     | 3469     36789    3456789  | 346      2        3489     |
 | 9        278      2478     | 1234-6    123678  3478-6   | 5        1468     1348     |
 |----------------------------+----------------------------+----------------------------|
 | 2578     25789    3        | 249      279      1        | 247      478      6        |
 | 1278     4        2789     |*269      5       *679      | 127      3        128      |
 | 127      6        27       | 8        237      347      | 9        147      5        |
 *--------------------------------------------------------------------------------------*

Code: Select all
# -and-
# Intersecting Kraken X-Wings (*)[R39c56]:[r3c9] and (@)[r45C17]:[r1c7]
# fin cells are in [b3] and have a weak link, therefore ...
# either fin cell forces conjugate X-Wing
 *--------------------------------------------------------------------------------------*
 | 4578     5789     1        | 3569     3689     2        |#3467     4679     349      |
 | 278      3        2789     | 169      4        689      | 1267     5        129      |
 | 6        259      2459     | 7       *139     *359      | 8        149     #12349    |
 |----------------------------+----------------------------+----------------------------|
 |@23458    258      6        | 123459   1289-3   4589-3   |@134      1489     7        |
 |@34578    1        4578     | 3469     6789-3   456789-3 |@346      2        3489     |
 | 9        278      2478     | 12346    123678   34678    | 5        1468     1348     |
 |----------------------------+----------------------------+----------------------------|
 | 2578     25789    3        | 249      279      1        | 247      478      6        |
 | 1278     4        2789     | 269      5        679      | 127      3        128      |
 | 127      6        27       | 8       *237     *347      | 9        147      5        |
 *--------------------------------------------------------------------------------------*
Last edited by daj95376 on Fri Nov 03, 2006 6:37 pm, edited 2 times in total.
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Postby ronk » Fri Nov 03, 2006 7:19 pm

daj, that's another nice example of intersecting x-wings, but I question the use of the term "conjugate."

Conjugate implies only one of two can be true. In the case of intersecting x-wings, might not both be true?
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Postby daj95376 » Fri Nov 03, 2006 9:38 pm

ronk wrote:daj, that's another nice example of intersecting x-wings, but I question the use of the term "conjugate."

Conjugate implies only one of two can be true. In the case of intersecting x-wings, might not both be true?

Good point Ron. In the case of the first puzzle I posted, the fin cells form a conjugate relationship and so both X-Wings can not be true. In the latest puzzle, it is possible for both X-Wings to be true because both fin cells could be false in [b3] and [r1c9]=3 be true.

What I was trying (imperfectly) to describe is the relationship between a row X-Wing and a column X-Wing where at least one must be true -- thus forcing eliminations in cells common to both X-Wings. Because of the alternating row/column relationship with overlapping cells, I think of them as being conjugates -- in a non-technical sense. I have changed the title to use your 'intersecting' description.

I'd appreciate knowing for sure if these are Kraken X-Wings. It's no longer sufficient to just call them finned X-Wings, and I don't understand the terminology used to describe/define more advanced fish.

BTW: What do you think of my shorthand for defining the fish and fin cell(s)? If it's a row fish, then I use a capital 'R'. If it's a column fish, then I use a capital 'C'. Any fin cells are listed after the colon ':'.
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Postby ronk » Sat Nov 04, 2006 12:11 am

daj95376 wrote:I'd appreciate knowing for sure if these are Kraken X-Wings. It's no longer sufficient to just call them finned X-Wings, and I don't understand the terminology used to describe/define more advanced fish.

I think Kraken X-Wing applies. My understanding is ... if an excluded candidate does not directly see all the fin cells, then it's a Kraken fish. IOW a chain is required for a Kraken fish. But since it is a fish, the chain should be a single-digit chain as yours is.

daj wrote:BTW: What do you think of my shorthand for defining the fish and fin cell(s)? If it's a row fish, then I use a capital 'R'. If it's a column fish, then I use a capital 'C'. Any fin cells are listed after the colon ':'.

Didn't notice the caps, but I like both ideas. I used to have problems with the row/col thing, but looking for the exclusion(s) first makes it pretty easy. The cap 'R' or 'C' would make it even easier.
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