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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Tue Jan 13, 2009 12:40 am    Post subject: Reply with quote

Wapati,

I am enjoying this discussion!

However,

Do you have a real example? A swordfish (6 cells in 3 rows or columns) plus two essential extra "fin" cells that make an elimination not made by more elementary methods? Where both fins and the swordfish are required in the logic?

In my practical experience, almost all of these "almost fish" turn out to be simplified by line - box interactions. No higher theory needed.

Keith
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wapati



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

PostPosted: Tue Jan 13, 2009 2:18 am    Post subject: Reply with quote

keith wrote:
Wapati,

I am enjoying this discussion!

However,

Do you have a real example? A swordfish (6 cells in 3 rows or columns) plus two essential extra "fin" cells that make an elimination not made by more elementary methods? Where both fins and the swordfish are required in the logic?

In my practical experience, almost all of these "almost fish" turn out to be simplified by line - box interactions. No higher theory needed.

Keith


They are rare, partly because most people, and some solvers will not spot them. Further, there are always ways around big fish, so no-one needs to spot them.

I don't agree that skyscraper can be worked around easily. It cracks many puzzles formerly thought to be difficult. Skyscraper, sashimi x-wing, turbot ... all names for the same idea, and a powerful tool.

Any swordfish being needed is pretty rare.

I have no example at hand but will look.
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wapati



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

PostPosted: Tue Jan 13, 2009 3:22 am    Post subject: Reply with quote

Here is a puzzle with some finned swordfish.


Code:
. . .|4 . .|. . 3
. . .|. 1 .|5 6 9
. . 6|. . .|4 2 .
-----+-----+-----
6 . .|. . .|9 3 .
. 2 .|. . 4|. . .
. . .|. 7 2|6 . .
-----+-----+-----
. 6 7|5 . 1|. . .
. 5 2|7 . .|. . .
1 4 .|. . .|. . 6

.------------------.------------------.------------------.
| 2     19    5    | 4     689   689  | 18    7     3    |
| 4     38    38   | 2     1     7    | 5     6     9    |
| 7     19    6    | 389   3589  3589 | 4     2     18   |
:------------------+------------------+------------------:
| 6     7     4    | 1     58    58   | 9     3     2    |
| 5     2     39   | 6     39    4    | 18    18    7    |
| 89    38    1    | 39    7     2    | 6     4     5    |
:------------------+------------------+------------------:
| 3     6     7    | 5     489   1    | 2     89    48   |
| 89    5     2    | 7     4689  689  | 3     189   148  |
| 1     4     89   | 389   2     389  | 7     5     6    |
'------------------'------------------'------------------'


I've marked one of the swordfish below. As far as I'm concerned any one of the cells marked "@" may be considered as part of the pattern.
The elimination is made when all the fins are true or when the pattern is true.
Code:

.------------------.------------------.------------------.
| 2     19    5    | 4     689   689  | 18    7     3    |
| 4     38    38   | 2     1     7    | 5     6     9    |
| 7     19    6    | 389   3589  3589 | 4     2     18   |
:------------------+------------------+------------------:
| 6     7     4    | 1     58    58   | 9     3     2    |
| 5     2     39   | 6     39    4    | 18    18    7    |
|#89    38    1    |@39    7     2    | 6     4     5    |
:------------------+------------------+------------------:
| 3     6     7    | 5    @489   1    | 2    #89    48   |
|#89    5     2    | 7    @4689 @689  | 3    #189   148  |
| 1     4     89   | 38-9  2     389  | 7     5     6    |
'------------------'------------------'------------------'


I can make the same elimination with other steps but none I'd call basic.

Edited to add: Here is another.

Code:
. . 6|8 . 7|. . 2
. . .|4 . .|. 5 3
8 . .|2 . .|. 9 .
-----+-----+-----
2 3 8|9 7 .|. . 5
. . .|6 . 5|. . .
5 . .|. 2 .|. . 7
-----+-----+-----
. . .|. . .|. . .
. 4 5|. . .|. 3 .
7 1 .|5 . 8|. . 4

.---------------.---------------.---------------.
| 3    9    6   | 8    5    7   | 14  *14   2   |
| 1    2    7   | 4    69   69  | 8    5    3   |
| 8    5    4   | 2    13   13  | 7    9    6   |
:---------------+---------------+---------------:
| 2    3    8   | 9    7    14  | 6   @14   5   |
| 4    7    19  | 6    8    5   | 3    2   @19  |
| 5    6    19  |@13   2    134 | 49-1 8    7   |
:---------------+---------------+---------------:
| 69   8    23  |*13   4    269 | 5    7   *19  |
| 69   4    5   | 7    169  269 | 129  3    8   |
| 7    1    23  | 5    39   8   | 29   6    4   |
'---------------'---------------'---------------'
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Jan 13, 2009 5:01 am    Post subject: Reply with quote

The commonality between a Skyscraper, Sashimi X-Wings, and a Siamese Sashimi X-Wing.

Set H Puzzle 3 after basics:

Code:
 +--------------------------------------------------------------+
 |  1368  168   7     |  4     9     126   |  5     1236  16    |
 |  4     5     16    |  8     3     126   |  7     126   9     |
 |  1369  169   2     |  67    15    57    |  8     136   4     |
 |--------------------+--------------------+--------------------|
 |  2     4     8     |  1     6     3     |  9     7     5     |
 |  7     3     5     |  9     2     8     |  14    146   16    |
 |  16    16    9     |  5     7     4     |  3     8     2     |
 |--------------------+--------------------+--------------------|
 |  15    7     3     |  2     145   9     |  6     14    8     |
 |  1568  2     16    |  67    1458  57    |  14    9     3     |
 |  1689  1689  4     |  3     18    16    |  2     5     7     |
 +--------------------------------------------------------------+
 # 54 eliminations remain

Code:
 Skyscraper c34
 +-----------------------------------+
 |  6  6  .  |  .  .  6  |  .  6  6  |
 |  .  . *6  |  .  . -6  |  .  6  .  |
 | -6 -6  .  | *6  .  .  |  .  6  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  6  |
 |  6  6  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  6  .  .  |
 |  6  . *6  | *6  .  .  |  .  .  .  |
 |  6  6  .  |  .  .  6  |  .  .  .  |
 +-----------------------------------+

Code:
 Sashimi X-Wing c34\r28 w/fin [r3c4]       Sashimi X-Wing c34\r38 w/fin [r2c3]
 +-----------------------------------+     +-----------------------------------+
 |  6  6  .  |  .  .  6  |  .  6  6  |     |  6  6  .  |  .  .  6  |  .  6  6  |
 |  .  . *6  |  .  . -6  |  .  6  .  |     |  .  .  6# |  .  .  6  |  .  6  .  |
 |  6  6  .  |  6# .  .  |  .  6  .  |     | -6 -6  .  | *6  .  .  |  .  6  .  |
 |-----------+-----------+-----------|     |-----------+-----------+-----------|
 |  .  .  .  |  .  6  .  |  .  .  .  |     |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  6  |     |  .  .  .  |  .  .  .  |  .  6  6  |
 |  6  6  .  |  .  .  .  |  .  .  .  |     |  6  6  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|     |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  6  .  .  |     |  .  .  .  |  .  .  .  |  6  .  .  |
 |  6  . *6  | *6  .  .  |  .  .  .  |     |  6  . *6  | *6  .  .  |  .  .  .  |
 |  6  6  .  |  .  .  6  |  .  .  .  |     |  6  6  .  |  .  .  6  |  .  .  .  |
 +-----------------------------------+     +-----------------------------------+

Code:
 Siamese Sashimi X-Wing c34\r(23)8
 identical to Skyscraper eliminations
 +-----------------------------------+
 |  6  6  .  |  .  .  6  |  .  6  6  |
 |  .  . *6# |  .  . -6  |  .  6  .  |
 | -6 -6  .  | *6# .  .  |  .  6  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  6  |
 |  6  6  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  6  .  .  |
 |  6  . *6  | *6  .  .  |  .  .  .  |
 |  6  6  .  |  .  .  6  |  .  .  .  |
 +-----------------------------------+

Each Sashimi X-Wing has only one fin cell. The Siamese Sashimi X-Wing combines the two Sashimi X-Wings because they are identical except for one cover set -- [r2] vs. [r3]. This produces eliminations identical to the Skyscraper.

Note: the concept of Siamese can be extended to larger fish with no problem. There is no larger pattern for Skyscraper.

wapati wrote:
They are rare, partly because most people, and some solvers will not spot them. Further, there are always ways around big fish, so no-one needs to spot them.

I would like to see your workaround for this elimination.

Code:
 +--------------------------------------------------------------------------------+
 |  6       78      2       |  3       478     9       |  1       5       478     |
 |  17      3       18      |  2       4578    578     |  789     489     6       |
 |  9       5       4       |  78      1       6       |  278     3       278     |
 |--------------------------+--------------------------+--------------------------|
 |  2       6       789     |  5       789     4       |  3       789     1       |
 |  4       1       789     |  6789    2       3       |  5       6789    789     |
 |  5       789     3       |  1       6789    78      |  2789    246789  24789   |
 |--------------------------+--------------------------+--------------------------|
 |  3       79      679     |  4       6789    2       |  789     1       5       |
 |  8       4       15      |  79      3       15      |  6       279     279     |
 |  17      2       1569    |  6789    56789   1578    |  4       789     3       |
 +--------------------------------------------------------------------------------+

7-Fish r1458c16b7\r2c2389b5+r9|c5|b8  <> 7  [r9c5]
7-Fish r1458c1b27\r2c234589           <> 7  [r9c5]
7-Fish r18c167b47\r26c23b39+r9|c5|b8  <> 7  [r9c5]
7-Fish r18c16b467\r269c2389+r9|c5|b8  <> 7  [r9c5]
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wapati



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

PostPosted: Tue Jan 13, 2009 5:44 am    Post subject: Reply with quote

daj95376 wrote:

I would like to see your workaround for this elimination.
Code:
 +--------------------------------------------------------------------------------+
 |  6       78      2       |  3       478     9       |  1       5       478     |
 |  17      3       18      |  2       4578    578     |  789     489     6       |
 |  9       5       4       |  78      1       6       |  278     3       278     |
 |--------------------------+--------------------------+--------------------------|
 |  2       6       789     |  5       789     4       |  3       789     1       |
 |  4       1       789     |  6789    2       3       |  5       6789    789     |
 |  5       789     3       |  1       6789    78      |  2789    246789  24789   |
 |--------------------------+--------------------------+--------------------------|
 |  3       79      679     |  4       6789    2       |  789     1       5       |
 |  8       4       15      |  79      3       15      |  6       279     279     |
 |  17      2       1569    |  6789    56789   1578    |  4       789     3       |
 +--------------------------------------------------------------------------------+

7-Fish r1458c16b7\r2c2389b5+r9|c5|b8  <> 7  [r9c5]
7-Fish r1458c1b27\r2c234589           <> 7  [r9c5]
7-Fish r18c167b47\r26c23b39+r9|c5|b8  <> 7  [r9c5]
7-Fish r18c16b467\r269c2389+r9|c5|b8  <> 7  [r9c5]

SE does it this way. (It never finds big fish.)

Analysis results
Difficulty rating: 8.4
This Sudoku can be solved using the following logical methods:
39 x Hidden Single
2 x Claiming
2 x Naked Pair
1 x Hidden Pair
2 x XY-Wing
2 x Turbot Fish
2 x Bidirectional Cycle
13 x Forcing Chain
6 x Nishio Forcing Chains
1 x Cell Forcing Chains
3 x Region Forcing Chains

Soduko Cue finds Medusas and Nishio chains.

I see nothing that I know how to do, including whatever you are showing above. Smile
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Jan 13, 2009 5:55 am    Post subject: Reply with quote

wapati: When your first puzzle is solved for basics and all smaller fish, the remaining Finned/Sashimi Swordfish have one fin cell each. (Your second puzzle contains an unfinned Swordfish after basics.)

Code:
 *-----------------------------------------------------------*
 | 2     19    5     | 4     69    68    | 18    7     3     |
 | 4     38    38    | 2     1     7     | 5     6     9     |
 | 7     19    6     | 389   3589  358   | 4     2     18    |
 |-------------------+-------------------+-------------------|
 | 6     7     4     | 1     58    58    | 9     3     2     |
 | 5     2     39    | 6     39    4     | 18    18    7     |
 | 89    38    1     | 39    7     2     | 6     4     5     |
 |-------------------+-------------------+-------------------|
 | 3     6     7     | 5     48    1     | 2     9     48    |
 | 89    5     2     | 7     468   689   | 3     18    148   |
 | 1     4     89    | 38    2     389   | 7     5     6     |
 *-----------------------------------------------------------*

 Sashimi Swordfish r147\c567 w/fin [r7c9]    [r3c9]<>8
 Sashimi Swordfish r147\c569 w/fin [r1c7]    [r3c9]<>8

 Finned  Swordfish r347\c569 w/fin [r1c4]    [r1c6]<>8

Keith: Consider the following Empty Rectangle elimination. It can also be viewed as ...

Code:
 finned Franken X-Wing r8b1\c28 w/fins [r2c13]
 [r2c13] are in base set [b1] but not in cover sets [c28]
 +-----------------------------------+
 |  /  6  /  |  .  .  .  |  .  .  .  |
 | #6  6 #6  |  .  .  .  |  . -6  .  |
 |  /  6  /  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  /  6  /  |  /  /  /  |  /  6  /  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

Marty: My apologies for helping to send your thread off on a tangent. Embarassed
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Jan 13, 2009 10:59 pm    Post subject: Reply with quote

I think this question about the "number of fins" is semantics. Any sort of finned fish has just one fin, but that fin can be comprised of multiple cells. Think of it as a "grouped fin."

wapati's Sashimi Swordfish might be clearer marked this way:
Code:
.------------------.------------------.------------------.
| 2     19    5    | 4     689   689  | 18    7     3    |
| 4     38    38   | 2     1     7    | 5     6     9    |
| 7     19    6    | 389   3589  3589 | 4     2     18   |
:------------------+------------------+------------------:
| 6     7     4    | 1     58    58   | 9     3     2    |
| 5     2     39   | 6     39    4    | 18    18    7    |
|#89    38    1    |#39    7     2    | 6     4     5    |
:------------------+------------------+------------------:
| 3     6     7    |*5    F489   1    | 2    #89    48   |
|#89    5     2    |*7    F4689 F689  | 3    #189   148  |
| 1     4     89   | 38-9  2     389  | 7     5     6    |
'------------------'------------------'------------------'

The Swordfish part is marked #, with the missing bits marked *. The 3-cell fin is marked F. However...
wapati wrote:
I can make the same elimination with other steps but none I'd call basic.

Not even a Kite? The one with pincers at r6c4 and r9c3 with pivot in b4 seems much simpler than the Sashimi Swordfish to me. Or, how about the ER in b5 and the conjugate <9>s in c3? Also simpler.
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Wed Jan 14, 2009 12:27 am    Post subject: Reply with quote

Asellus:
Quote:
Any sort of finned fish has just one fin, but that fin can be comprised of multiple cells.


Aha! A grouped fin!

Keith

(I think)
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Jan 14, 2009 3:54 pm    Post subject: Reply with quote

Asellus wrote:
I think this question about the "number of fins" is semantics. Any sort of finned fish has just one fin, but that fin can be comprised of multiple cells. Think of it as a "grouped fin."

In this case, that's correct. However, sometimes all the fin cells don't "see" each other.
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wapati



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

PostPosted: Wed Jan 14, 2009 4:20 pm    Post subject: Reply with quote

keith wrote:
Wapati,

I am enjoying this discussion!

However,

Do you have a real example? A swordfish (6 cells in 3 rows or columns) plus two essential extra "fin" cells that make an elimination not made by more elementary methods? Where both fins and the swordfish are required in the logic?

In my practical experience, almost all of these "almost fish" turn out to be simplified by line - box interactions. No higher theory needed.

Keith


Found one, it took a while! Very Happy
Code:

2 . .|. . 1|. 4 .
. . 4|9 . 3|. . .
. 6 3|8 4 .|2 . .
-----+-----+-----
. 4 1|. 7 .|5 3 .
. . 8|4 . .|. . .
6 7 .|. . .|. . .
-----+-----+-----
. . 9|1 . .|. . .
4 . .|3 . .|. . 6
. . .|. . .|. 2 9

.---------------------.---------------------.---------------------.
| 2      9     *57    |*567   *56     1     | 38     4      38    |
| 1578   158    4     | 9      2      3     | 167    1567   157   |
| 157    6      3     | 8      4      57    | 2      9      157   |
:---------------------+---------------------+---------------------:
| 9      4      1     | 26     7      68    | 5      3      28    |
| 35     235    8     | 4      1      59    | 679    67     27    |
| 6      7     *25    |*25     3      89    | 1489   18     148   |
:---------------------+---------------------+---------------------:
| 3578   2358   9     | 1     #568    24567 | 3478   578    34578 |
| 4      1258  *257   | 3      9      27-5  | 178    1578   6     |
| 13578  1358   6     |#57    #58     457   | 13478  2      9     |
'---------------------'---------------------'---------------------'
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daj95376



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PostPosted: Wed Jan 14, 2009 5:44 pm    Post subject: Reply with quote

ronk: Does wapati's Sashimi Swordfish c345\r168 contains two fins (aka a fin sector, a fin unit) -- [c4] & [c5] -- and three fin cells ?

everyone else: Sorry, this discussion is a carry-over from the Players' Forums.
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keith



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PostPosted: Wed Jan 14, 2009 8:36 pm    Post subject: Reply with quote

daj95376 wrote:
everyone else: Sorry, this discussion is a carry-over from the Players' Forums.


Can you post a link?

Keith
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daj95376



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PostPosted: Wed Jan 14, 2009 9:50 pm    Post subject: Reply with quote

keith wrote:
daj95376 wrote:
everyone else: Sorry, this discussion is a carry-over from the Players' Forums.

Can you post a link?

It starts here ... and the head message of the thread has been updated. I think it will be very confusing reading. ronk and I seemed to be on different wavelengths.

http://www.sudoku.com/boards/viewtopic.php?p=65864#65864


Last edited by daj95376 on Wed Jan 14, 2009 9:59 pm; edited 1 time in total
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ronk



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PostPosted: Wed Jan 14, 2009 9:57 pm    Post subject: Reply with quote

daj95376 wrote:
ronk: Does wapati's Sashimi Swordfish c345\r168 contains two fins (aka a fin sector, a fin unit) -- [c4] & [c5] -- and three fin cells ?

Three fin cells (as shown on your pencilmarks) in one fin unit b8.

As not one of the three fin cells sees the elimination cell via a row or a column, there's not even another possibility with that interpretation.

Using the franken fish interpretation, c345\r16b8, there would only be one fin cell r8c3.


Last edited by ronk on Wed Jan 14, 2009 10:05 pm; edited 1 time in total
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Asellus



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PostPosted: Thu Jan 15, 2009 11:23 pm    Post subject: Reply with quote

ronk wrote:
In this case, that's correct. However, sometimes all the fin cells don't "see" each other.

Short of an example, I don't see that that makes a difference. Each fin cell needs to destroy the fish and each fin cell must "see" the victim(s) in some manner or other. So, they would still function as a group even if not peers. Or, is there some other sort of multi-finned fish that works in some other way?
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jan 16, 2009 12:24 am    Post subject: Reply with quote

Asellus wrote:
ronk wrote:
In this case, that's correct. However, sometimes all the fin cells don't "see" each other.

Short of an example, I don't see that that makes a difference. Each fin cell needs to destroy the fish and each fin cell must "see" the victim(s) in some manner or other. So, they would still function as a group even if not peers. Or, is there some other sort of multi-finned fish that works in some other way?

It's just one way of looking at it, but it's also a matter of convention and notational convenience. For the below ...
Code:

 *  *  X |  .  .  . |  .  *  .
 X *X  / |  /  /  / |  #  X  /
 *  *  X |  .  .  . |  .  *  .
---------+----------+----------
 .  *  / |  .  .  . |  .  *  .
 *  *  X |  *  *  * | **  *  *
 /  X  / |  /  /  / |  #  X  #
---------+----------+----------
 .  *  / |  .  .  . |  .  *  .
 /  X  / |  /  /  / |  #  X  /
 .  *  / |  .  .  . |  .  *  .

... the fish is completely defined by r268c3\r5c278b16 ==> r5c7<>X

No need to write r268c7 and r6c9 to detail the fin locations in c7 and b6.
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keith



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PostPosted: Sat Jan 17, 2009 1:22 am    Post subject: Reply with quote

So, in simple language, what is a "fin"?

I think it is easy: Either we have a pattern (X-wing, XY-wing, ...) or we have one other feature (the "fin") that invalidates the pattern.

Either the pattern is true, or the fin is true.

My original point, and I'm sticking to it! If the logic of a fin is A OR B is true, what does C have to do with it?

What is a "fin"?

Keith
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ronk



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PostPosted: Sat Jan 17, 2009 2:09 am    Post subject: Reply with quote

keith wrote:
So, in simple language, what is a "fin"?

I think it is easy: Either we have a pattern (X-wing, XY-wing, ...) or we have one other feature (the "fin") that invalidates the pattern.

Either the pattern is true, or the fin is true.

My original point, and I'm sticking to it! If the logic of a fin is A OR B is true, what does C have to do with it?

What is a "fin"?

Extra candidate(s) in the same sector (unit) as elimination candidate(s).
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keith



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Location: near Detroit, Michigan, USA

PostPosted: Sat Jan 17, 2009 3:40 am    Post subject: Reply with quote

ronk wrote:
keith wrote:
So, in simple language, what is a "fin"?

I think it is easy: Either we have a pattern (X-wing, XY-wing, ...) or we have one other feature (the "fin") that invalidates the pattern.

Either the pattern is true, or the fin is true.

My original point, and I'm sticking to it! If the logic of a fin is A OR B is true, what does C have to do with it?

What is a "fin"?

Extra candidate(s) in the same sector (unit) as elimination candidate(s).

Really?

So my statement, "Either the pattern is true, or the fin is true", is not correct?

Keith

PS: Please define: "Extra candidate(s)", "sector", "unit", and "elimination candidate(s)".
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ronk



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PostPosted: Sat Jan 17, 2009 4:11 am    Post subject: Reply with quote

keith wrote:
Please define: "Extra candidate(s)", "sector", "unit", and "elimination candidate(s)".

I'm confident you know the definitions for at least three of those terms, so I think you are just trolling. Adios.
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