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Fin transport
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Tue Oct 21, 2008 10:36 pm    Post subject: Fin transport Reply with quote

Asellus wrote:
Marty wrote:
I thought a fin had to be in the same box.

It does if you ignore transporting. However, with transporting in the picture, the Fin can be located anywhere. It just needs to be in an either/or relationship with the potential X-Wing (to be a legitimate Fin). Then, if it can be transported to a location where it "sees" candidates that would also be eliminated by that potential X-Wing, those candidates can be eliminated.

Can I assume that if there are two fins, then transport can't be used? Because neither fin by itself causes the either/or relationship, i.e., remove one fin and there still isn't an X-Wing.

Code:

+----------+---------+--------------+
| 36 236 9 | 7 1  8  | 4  5    23   |
| 7  38  5 | 2 4  9  | 6  1    38   |
| 4  28  1 | 6 3  5  | 27 278  9    |
+----------+---------+--------------+
| 38 34  2 | 9 67 1  | 5  3678 4678 |
| 1  35  7 | 8 56 4  | 9  236  26   |
| 89 459 6 | 3 57 2  | 1  78   478  |
+----------+---------+--------------+
| 2  67  4 | 1 9  3  | 8  67   5    |
| 69 679 8 | 5 2  67 | 3  4    1    |
| 5  1   3 | 4 8  67 | 27 9    267  |
+----------+---------+--------------+

Play this puzzle online at the Daily Sudoku site

There are two extra 3s in c2 (also see c9). If my assumption were wrong, then I believe the 3 in r5c2 could be transported and knock out the 3 from r4c2.
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Asellus



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PostPosted: Thu Oct 23, 2008 7:11 am    Post subject: Reply with quote

Marty wrote:
Can I assume that if there are two fins, then transport can't be used? Because neither fin by itself causes the either/or relationship, i.e., remove one fin and there still isn't an X-Wing.

To be clear, we can deal with a 2-cell Fin, not with "2 Fins". A Fin with 2 or more cells is a single Fin of grouped candidates. Provided that each one of those candidates, if true, destroys the potential X-Wing then you have a proper Fin with the required either/or relationship: Either one or more of the (grouped) Fin cells is true or the X-Wing is true. (The grouped Fin is false if ALL of its cells are false. It is true if at least one of its cells is true.)

The grouped Fin cells can be transported to any other cell (or grouped cells) through alternating weak-strong-weak-strong links as usual. If the Fin is multi-celled, every cell in the Fin must be weakly linked to the next cell in the transport chain sequence (as is always the case with grouped links).

There is no usable Finned X-Wing structure in your grid (using single or multi-celled Fins, with or without transporting). Also, even if r5c2 was a Fin, it wouldn't need any transporting to eliminate <3> from r4c2 since these two cells are already peers. (I'm not sure which cell you considered to be the second cell of your Fin since there isn't really such a critter in the grid.)

I gave an example of a Finned X-Wing with a 2-celled Fin and transport in the thread from which you quoted me above. Here it is again:
Code:
+--------------------+---------------+----------------+
| 6    5      7      | 1    9    2   | 4     3    8   |
| 349 #123-49 1239   | 34   6    8   | 1259  7    125 |
| 8   @12349 F1234   | 5   @34   7   | 1269  69   12  |
+--------------------+---------------+----------------+
| 1    6      23459  | 7    23   359 | 8     45   234 |
| 7   f234    2345   | 36   8    1   | 236   456  9   |
| 39   239    8      | 369  25   4   | 2356  1    7   |
+--------------------+---------------+----------------+
| 5   @13479 F1349   | 2   @134  39  | 379   8    6   |
| 2    8      6      | 349  7    359 | 139   459  134 |
| 349 #13-479 139    | 8    135  6   | 3579  2    345 |
+--------------------+---------------+----------------+

The potential X-Wing (involving <4>s) is marked @. The 2-cell Fin is marked F. Either of those cells, if true, destroys the potential X-Wing, and vice-versa. So, they can be considered as a Fin. However, as a Fin, these 2 cells are not directly useful because they are not both weakly linked to any mutual victims with the X-Wing. R3c3 is weakly linked to r2c2 but not to r9c2. r7c3 is weakly linked to r9c2 but not to r2c2.

However, the 2 Fin cells are both weakly linked to the grouped <4>s in c3 of box 4:
(4)r37c3 - (4)r45c3

These 2 <4>s are, in turn, strongly linked with the remaining <4> in box 4:
(4)r45c3=(4)r5c2

This weak-strong two-link sequence provides our transported fin, "f", at r5c2 and allows us to complete the eliminations marked #. The complete AIC (just for the heck of it, for those so interested) could be written:
(4)r29c2 - XWing[(4)r37c25]=Fin[(4)r37c3] - (4)r45c3=(4)r5c2 - (4)r29c2; r29c2<>4

In non-link language: If both Fin cells are false, the X-Wing is true and the victims are false. If either Fin cell is true, then the <4>s in r45c3 are both false and the <4> in r5c2 is true, with the victims again being false. So, the victims are false regardless.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Thu Oct 23, 2008 3:40 pm    Post subject: Reply with quote

Thank you very much!!
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Oct 24, 2008 10:41 am    Post subject: Reply with quote

I hadnít come across Asellusís interesting example before so I hope Iím not rehashing an old point by remarking that the same eliminations are made by a swordfish on 4.

Code:
+---------------------+---------------+----------------+
|  6    5      7      | 1    9    2   | 4     3    8   |
| *349  12349  1239   | 34   6    8   | 1259  7    125 |
|  8   *12349 *1234   | 5   *34   7   | 1269  69   12  |
+---------------------+---------------+----------------+
|  1    6      23459  | 7    23   359 | 8     45   234 |
|  7    234    2345   | 36   8    1   | 236   456  9   |
|  39   239    8      | 369  25   4   | 2356  1    7   |
+---------------------+---------------+----------------+
|  5   *13479 *1349   | 2   *134  39  | 379   8    6   |
|  2    8      6      | 349  7    359 | 139   459  134 |
| *349  13479  139    | 8    135  6   | 3579  2    345 |
+---------------------+---------------+----------------+

The cells marked with an asterisk are all those open to 4 in three primary houses: rows 3 and 7 and column 1. These cells are also covered by three secondary houses: column 5 and boxes 1 and 7.

Accordingly 4 may be eliminated from any other cell in the secondary houses which has it as a candidate.

Steve.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Oct 24, 2008 4:55 pm    Post subject: Reply with quote

Nice mutant Swordfish r37c1\c5b17 catch Steve. I like it better than my Franken Swordfish r37b4\c235 because it does a nice job of using the cells in column 1.

Code:
 *--------------------------------------------------------------------*
 | 6      5      7      | 1      9      2      | 4      3      8      |
 | 349    12349  1239   | 34     6      8      | 1259   7      125    |
 | 8     *12349 *1234   | 5     *34     7      | 1269   69     12     |
 |----------------------+----------------------+----------------------|
 | 1      6     *23459  | 7      23     359    | 8      45     234    |
 | 7     *234   *2345   | 36     8      1      | 236    456    9      |
 | 39     239    8      | 369    25     4      | 2356   1      7      |
 |----------------------+----------------------+----------------------|
 | 5     *13479 *1349   | 2     *134    39     | 379    8      6      |
 | 2      8      6      | 349    7      359    | 139    459    134    |
 | 349    13479  139    | 8      135    6      | 3579   2      345    |
 *--------------------------------------------------------------------*
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Asellus



Joined: 05 Jun 2007
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PostPosted: Fri Oct 24, 2008 9:36 pm    Post subject: Reply with quote

Steve R wrote:
I hadnít come across Asellusís interesting example before so I hope Iím not rehashing an old point

Well... the original thread had to do with examples of variants of Finned X-Wings, Kites, Skyscrapers and other simpler methods that, with transporting, could often be used to make the same eliminations as fish more complex than Finned X-Wings, for folks who hate looking for any fish more complex than these. So, I was deliberately ignoring those other fish.

Still, it's always nice to see Franken Swordfish pointed out.

[Edit to add link.]
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sat Oct 25, 2008 12:35 pm    Post subject: Reply with quote

There are many ways to see these eliminations. From my way of solving i pobably would have found it with grouped coloring (or grouped x-cycle) from the observation, that either r2c1 is 4 or r9c1, r7c5 and r2c4 (immediately eliminating 4 in r2c2)
Code:
+---------------------+---------------+----------------+
|  6    5      7      | 1    9    2   | 4     3    8   |
| #349  123-49 1239   |@34   6    8   | 1259  7    125 |
|  8    12349  1234   | 5   #34   7   | 1269  69   12  |
+---------------------+---------------+----------------+
|  1    6      23459  | 7    23   359 | 8     45   234 |
|  7    234    2345   | 36   8    1   | 236   456  9   |
|  39   239    8      | 369  25   4   | 2356  1    7   |
+---------------------+---------------+----------------+
|  5   #13479 #1349   | 2   @134  39  | 379   8    6   |
|  2    8      6      |#349  7    359 | 139   459  134 |
| @349  13-479 139    | 8    135  6   | 3579  2    345 |
+---------------------+---------------+----------------+

The strong links are r2c1=r9c1, r7c23=r7c5 and r3c5=r2c4 (or r8c4=r2c4). They form a cycle (r2c4 sees r2c1), so the weak links become strong and any cells, which see both # and @, cant be 4.
(4)r2c1=(4)r5c1-(4)r7c23=(4)r7c5-(4)r3c5=(4)r2c4
This also would eliminate other 4's in column 5 and box 8 (when using r8c4=r2c4).
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Thu Oct 30, 2008 10:34 pm    Post subject: Reply with quote

I just want to make sure I understand this.

Code:

+-------------+-----------+------------+
| 568 358 48  | 1  245 7  | 346 23 9   |
| 56  1   2   | 49 3   59 | 7   8  46  |
| 9   7   34  | 6  24  8  | 1   5  234 |
+-------------+-----------+------------+
| 3   4   6   | 2  7   1  | 8   9  5   |
| 1   2   58  | 89 6   59 | 34  7  34  |
| 7   58  9   | 48 45  3  | 2   6  1   |
+-------------+-----------+------------+
| 58  6   578 | 3  1   2  | 9   4  78  |
| 4   38  1   | 7  9   6  | 5   23 28  |
| 2   9   37  | 5  8   4  | 36  1  367 |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site

There would be an X-Wing on 3 in rows 59 except for the extra 3 (fin) in r9c3. Can that fin be transported to r8c2, then r1c2 and knock out the 3 in r1c7 which would be zapped by the X-Wing? (I realize that that same 3 can be eliminated by coloring).
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Asellus



Joined: 05 Jun 2007
Posts: 865
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PostPosted: Thu Oct 30, 2008 10:44 pm    Post subject: Reply with quote

Marty R. wrote:
There would be an X-Wing on 3 in rows 59 except for the extra 3 (fin) in r9c3. Can that fin be transported to r8c2, then r1c2 and knock out the 3 in r1c7 which would be zapped by the X-Wing?

Yes. However, I would say that the Fin at r9c3 is transported directly to r1c2 (via r8c2). Candidates are transported to other candidates that are also true when they are true. Saying that the Fin is transported to r8c2 might cause an error since the <3> in r8c2 is false when the Fin is true.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Fri Oct 31, 2008 12:05 am    Post subject: Reply with quote

Quote:
Yes. However, I would say that the Fin at r9c3 is transported directly to r1c2 (via r8c2).


Thank you. I guess I was a little careless with the wording.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Sun Jan 11, 2009 6:42 pm    Post subject: Reply with quote

I just don't have enough confidence yet to do this without verification.

Code:

+----------+--------------+---------------+
| 2  4 5   | 178  38 178  | 1369 139 1369 |
| 13 9 8   | 5    2  6    | 13   4   7    |
| 6  7 13  | 19   39 4    | 5    8   2    |
+----------+--------------+---------------+
| 37 5 39  | 68   1  89   | 3679 2   4    |
| 17 6 139 | 2    4  5    | 8    379 39   |
| 4  8 2   | 69   7  3    | 169  5   169  |
+----------+--------------+---------------+
| 5  3 4   | 1789 6  1789 | 2    179 189  |
| 89 1 7   | 3    5  2    | 4    6   89   |
| 89 2 6   | 4    89 17   | 137  137 5    |
+----------+--------------+---------------+

Play this puzzle online at the Daily Sudoku site

Note the almost X-Wing on 6 in r16. There's an extra 6 (the fin) in r6c4. Can it be transported to r4c7 and knock out the 6 from r1c7?

(If this looks familiar, it's Danny's Salsa #1).
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jan 12, 2009 2:13 am    Post subject: Reply with quote

Marty R. wrote:
Note the almost X-Wing on 6 in r16. There's an extra 6 (the fin) in r6c4. Can it be transported to r4c7 and knock out the 6 from r1c7?

(If this looks familiar, it's Danny's Salsa #1).

I'm afraid not. The strong links in [r4] & [c4] make [r6c4] & [r4c7] complementary for <6>. Setting [r6c4] true forces [r4c7] true -- not what you need.

Code:
 +-----------------------------------+
 |  .  .  .  |  .  .  .  | *6  . *6  |
 |  .  .  .  |  .  .  6  |  .  .  .  |
 |  6  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  | ~6  .  .  | +6  .  .  |
 |  .  6  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  | +6  .  .  | *6  . *6  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  .  |
 |  .  .  6  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

At this point in the solution, there's an ugly fish elimination in <9>. Fortunately, there are alternate ways to get the <9> elimination.

Code:
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  9  9  9  |
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  9  9  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  9  |  .  .  9  |  9  .  .  |
 |  .  .  9  |  .  .  .  |  .  9 -9  |
 |  .  .  .  |  9  .  .  |  9  .  9  |
 |-----------+-----------+-----------|
 |  .  .  .  |  9  .  9  |  .  9  9  |
 |  9  .  .  |  .  .  .  |  .  .  9  |
 |  9  .  .  |  .  9  .  |  .  .  .  |
 +-----------------------------------+


Hint wrote:
Think extended Empty Rectangle.
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Marty R.



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PostPosted: Mon Jan 12, 2009 5:58 am    Post subject: Reply with quote

Danny, what am I missing? My example seems to fit the definition provided by Asellus.

Quote:
However, with transporting in the picture, the Fin can be located anywhere. It just needs to be in an either/or relationship with the potential X-Wing (to be a legitimate Fin). Then, if it can be transported to a location where it "sees" candidates that would also be eliminated by that potential X-Wing, those candidates can be eliminated.
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Asellus



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PostPosted: Mon Jan 12, 2009 8:40 am    Post subject: Reply with quote

Quote:
My example seems to fit the definition provided by Asellus.

I'm afraid it doesn't. Here's what you are missing:
Quote:
Then, if [the Fin] can be transported to a location where it "sees" candidates that would also be eliminated by that potential X-Wing, those candidates can be eliminated.

The candidate you are trying to eliminate is part of the potential X-Wing. But the potential X-Wing cannot eliminate part of itself. If your potential X-Wing were true, there would only be one victim: the <6> at r4c7. There is no way the "Fin" at r6c4 can also eliminate the <6> at r4c7 because they have the same polarity: either they are both true or they are both false.

There are no Finned X-Wings on 6 present in this grid, with or without transporting.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jan 12, 2009 10:22 am    Post subject: Reply with quote

Code:
 +-----------------------------------+
 |  .  .  .  |  .  .  .  | *6  . *6  |
 |  .  .  .  |  .  .  6  |  .  .  .  |
 |  6  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  | ~6  .  .  | +6- .  .  |
 |  .  6  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  | +6  .  .  | *6  . *6  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  .  |
 |  .  .  6  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

I'm not going to touch Asellus' definition. Here's how I learned to think of finned fish.

Either the fish is true or else at least one of the fin cells is true.

Perform eliminations common to the fish and all fin cells being (individually) assumed true.

In this example, the fish is the X-Wing r16\c79, and it would perform an eliminate in [r4c7] (-).

If fin cell [r6c4] is true (+), then [r4c7] is also true (+) because of the strong link provided by [r4c4] (~) in [r4].

Since there aren't any eliminations in common between the X-Wing and the fin cell, there's no where to go with this pattern.
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Marty R.



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PostPosted: Mon Jan 12, 2009 4:49 pm    Post subject: Reply with quote

Quote:
The candidate you are trying to eliminate is part of the potential X-Wing. But the potential X-Wing cannot eliminate part of itself.

Of course. I never even realized I was trying to eliminate part of the X-Wing itself.

Suppose, without other considerations, there had been a 6 in r2 or 3, c7? Would the transport have been valid in that case?

Thanks to both of you for taking the time to help.
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keith



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PostPosted: Mon Jan 12, 2009 10:03 pm    Post subject: Reply with quote

Quote:
Either the fish is true or else at least one of the fin cells is true.


It seems to me that, strictly speaking, there can only be one fin. The statement should be: Either the fish (in the rows / columns) is true, or the fin is true

Keith
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wapati



Joined: 10 Jun 2008
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PostPosted: Mon Jan 12, 2009 10:44 pm    Post subject: Reply with quote

keith wrote:
Quote:
Either the fish is true or else at least one of the fin cells is true.


It seems to me that, strictly speaking, there can only be one fin. The statement should be: Either the fish (in the rows / columns) is true, or the fin is true

Keith

As one example that makes it harder...
a skyscraper is a sashimi x-wing. To get all the eliminations you have to consider that there are two fins. That's my position, anyways! Smile
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keith



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PostPosted: Mon Jan 12, 2009 11:49 pm    Post subject: Reply with quote

wapati wrote:
keith wrote:
Quote:
Either the fish is true or else at least one of the fin cells is true.


It seems to me that, strictly speaking, there can only be one fin. The statement should be: Either the fish (in the rows / columns) is true, or the fin is true

Keith

As one example that makes it harder...
a skyscraper is a sashimi x-wing. To get all the eliminations you have to consider that there are two fins. That's my position, anyways! Smile


Yes, but the two fins are associated with two different (possible) X-wings. There is no logic that derives from one possible (row or column) X-wing and two fins.

I think.

Keith
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wapati



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PostPosted: Tue Jan 13, 2009 12:21 am    Post subject: Reply with quote

Here is a swordfish. The easy way to see it is that there is one fish with fins.
Code:

. x .|. / .|. . .
. . #|. x .|. . .
x . .|. / .|. . .
-----+-----+-----
/ / .|. / .|. . .
x x .|. x .|. . .
/ / .|. / .|. . .
-----+-----+-----
/ / .|. / .|. . .
/ / .|. / .|. . .
x x .|. x .|. . .

Box 1, c12, can have more fins but doesn't require them.
"#" cannot be x because the pattern sees it as do all the fins. Very Happy
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