two "new" techniques, Skyscraper and 2-string Kite

Advanced methods and approaches for solving Sudoku puzzles

Postby tarek » Fri Feb 10, 2006 11:38 am

Allow me Myth Jellies to give the examples (all of these are from threads in this forum):

Code: Select all
*-----------------------------------------------------------------*
| 2     -359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 47     5      2347  | 23478  9      237   |
| 7     *4     #389   |*29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3     *279    4     |*29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      279   | 47     49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 9 From r1c2 (Finned XWing in rows 3 & 4) ---- or SASHIMI Xwing

*--------------------------------------------------------*
| 6     8     2    | 3     5     7    | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2     7    |
| 5     7     9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
| 78    2     6    | 14    3     14   | 9     57    58   |
| 4     5     1    |*79    789   2    |*78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    |#479   2479  3    | 1     47    89   |
| 27    3     4    |*179  -1279  8    |*67    567   59   |
| 9     1     78   | 5     47    6    | 3     478   2    |
*--------------------------------------------------------*
Eliminating 7 From r8c5 (Finned XWing in Columns 4,7)

*--------------------------------------------------------*
| 6     8     2    | 3     5     7    | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2     7    |
| 5     7     9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
| 78    2     6    | 14    3     14   | 9     57    58   |
| 4     5     1    |*79    789   2    |*78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    |*479   2479  3    |*1    -47    89   |
| 27    3     4    | 19    129   8    |#67    567   59   |
| 9     1     78   | 5     47    6    | 3     478   2    |
*--------------------------------------------------------*
Eliminating 7 From r7c8 (Almost finned XWing in Columns 4,7)

*-----------------------------------------------*
| 6    8    2   | 3    5    7   | 4    9    1   |
| 1    4    3   | 8    6    9   | 5    2    7   |
| 5    7    9   | 2    1    4   | 68   68   3   |
|---------------+---------------+---------------|
| 3    9    78  | 6    78   5   | 2    1    4   |
|*78   2    6   | 4    3    1   |*9   -57   58  |
| 4    5    1   | 79   789  2   |#78   3    6   |
|---------------+---------------+---------------|
| 28   6    5   | 79   279  3   | 1    4    89  |
|*27   3    4   | 1    29   8   |*67   567  59  |
| 9    1    78  | 5    4    6   | 3    78   2   |
*-----------------------------------------------*
Eliminating 7 From r5c8 (Almost finned XWing in Columns 1,7)

*-----------------------------------------------------------------*
| 5      9      68    | 1     *48     7     | 346   *348    2     |
| 3      2      68    | 568    9      456   | 46     1      7     |
| 4      1      7     | 268    3      26    | 5      9      68    |
|---------------------+---------------------+---------------------|
| 2      367    19    | 35689  58     13569 | 367    3578   4     |
| 16    #346    5     | 2368   7      12346 | 9      38     68    |
| 8     *3467  -49    | 3569  *45     34569 | 2      357    1     |
|---------------------+---------------------+---------------------|
| 69    *46     2     | 379    1      39    | 8     *47     5     |
| 19     8      14    | 579    6      59    | 47     2      3     |
| 7      5      3     | 4      2      8     | 1      6      9     |
*-----------------------------------------------------------------*
Eliminating 4 From r6c3 (Finned Swordfish in Columns 258)


Th last one is an example of how it can be applied for Sworfishes, I calso have a Jellyfish if you want !!!!

Tarek
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Postby Havard » Fri Feb 10, 2006 12:41 pm

tarek wrote:Allow me Myth Jellies to give the examples (all of these are from threads in this forum):

Code: Select all
(1)
*-----------------------------------------------------------------*
| 2     -359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 47     5      2347  | 23478  9      237   |
| 7     *4     #389   |*29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3     *279    4     |*29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      279   | 47     49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 9 From r1c2 (Finned XWing in rows 3 & 4) ---- or SASHIMI Xwing

(2)
*--------------------------------------------------------*
| 6     8     2    | 3     5     7    | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2     7    |
| 5     7     9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
| 78    2     6    | 14    3     14   | 9     57    58   |
| 4     5     1    |*79    789   2    |*78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    |#479   2479  3    | 1     47    89   |
| 27    3     4    |*179  -1279  8    |*67    567   59   |
| 9     1     78   | 5     47    6    | 3     478   2    |
*--------------------------------------------------------*
Eliminating 7 From r8c5 (Finned XWing in Columns 4,7)

(3)
*--------------------------------------------------------*
| 6     8     2    | 3     5     7    | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2     7    |
| 5     7     9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
| 78    2     6    | 14    3     14   | 9     57    58   |
| 4     5     1    |*79    789   2    |*78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    |*479   2479  3    |*1    -47    89   |
| 27    3     4    | 19    129   8    |#67    567   59   |
| 9     1     78   | 5     47    6    | 3     478   2    |
*--------------------------------------------------------*
Eliminating 7 From r7c8 (Almost finned XWing in Columns 4,7)

(4)
*-----------------------------------------------*
| 6    8    2   | 3    5    7   | 4    9    1   |
| 1    4    3   | 8    6    9   | 5    2    7   |
| 5    7    9   | 2    1    4   | 68   68   3   |
|---------------+---------------+---------------|
| 3    9    78  | 6    78   5   | 2    1    4   |
|*78   2    6   | 4    3    1   |*9   -57   58  |
| 4    5    1   | 79   789  2   |#78   3    6   |
|---------------+---------------+---------------|
| 28   6    5   | 79   279  3   | 1    4    89  |
|*27   3    4   | 1    29   8   |*67   567  59  |
| 9    1    78  | 5    4    6   | 3    78   2   |
*-----------------------------------------------*
Eliminating 7 From r5c8 (Almost finned XWing in Columns 1,7)

(5)
*-----------------------------------------------------------------*
| 5      9      68    | 1     *48     7     | 346   *348    2     |
| 3      2      68    | 568    9      456   | 46     1      7     |
| 4      1      7     | 268    3      26    | 5      9      68    |
|---------------------+---------------------+---------------------|
| 2      367    19    | 35689  58     13569 | 367    3578   4     |
| 16    #346    5     | 2368   7      12346 | 9      38     68    |
| 8     *3467  -49    | 3569  *45     34569 | 2      357    1     |
|---------------------+---------------------+---------------------|
| 69    *46     2     | 379    1      39    | 8     *47     5     |
| 19     8      14    | 579    6      59    | 47     2      3     |
| 7      5      3     | 4      2      8     | 1      6      9     |
*-----------------------------------------------------------------*
Eliminating 4 From r6c3 (Finned Swordfish in Columns 258)


Th last one is an example of how it can be applied for Sworfishes, I calso have a Jellyfish if you want !!!!

Tarek


Thanks Tarek!

I assume that your argument is that the fish rule is superior to my skyscraper concept? Let's examine these examples you gave and compare! (i numbered your examples)

1:
This one is also a skyscraper, and the skyscraper will allow you to eliminate one more candidate from the grid:
Image

2:
Here the extended-skyscraper comes into play:
Image

3:
This elimination can also be done with a skyscraper.
Image

4:
and so can this one:
Image

notice also in all these examples that the "virtual" extra corner of the x-wing is not needed.

5 on the other hand is a really beautiful example! However, it involves three links, and I have not yet dealt with 3 links patterns in this post. One extra (or more) strong link can be added to any of the patterns belonging to the Turbot Fish in this manner, as you know:

Code: Select all
. . . | . . . | . . .
* * . | . d . | . . .
. . b | * | * | . . .
----|-----|----------
. . | | . | . | . . .
. . | | . | . | . . .
. . | | . | . | . . .
----|-----|----------
. . a | . | . | . f .
. . . | . | . | . | .
. . . | . c . | . e .

. . . | . . . | . . .
. . c-----------d . .
. a . | . . . | . . .
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. b . | e . . | . . .
--------|------------
. . . | f . . | * . .
. . . | . . . | . . .
. . . | . . . | . . .

. . . | . . . | c . .
. . . | . . . | . \ .
. a . | . . . | . . d
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. b . | . . e | . . .
------------|--------
. . . | . . f | * . .
. . . | . . . | . . .
. . . | . . . | . . .


so instead of proposing a "virtual" (finned) swordfish, I would just call it an extended skyscraper with one extra strong link:

Code: Select all
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . a | . . . | . . .
* * | | . e . | . . .
. . b | . | . | . . .
----|-+---|---+------
. . | | . d . | . f .
. . | | . . . | . | .
. . c | . . . | . g .


So what's easy to identify or not is always bound to be a subjective judgement, but I don't think that the skyscraper is any harder to find than the method you propose? Specially since it does not need the insertion of a "virtual" candidate to be able to use a x-wing that is not really there. The skyscrapers are there for everyone to enjoy!

...and yes, I would love your jellyfish. Your finned swordfish example was really good!:) I would also like a finned x-wing that my skyscraper (normal and extended) can't handle.

havard
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Posts: 377
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Postby ronk » Fri Feb 10, 2006 1:31 pm

Havard wrote:
Code: Select all
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . a | . . . | . . .
* * | | . e . | . . .
. . b | . | . | . . .
----|-+---|---+------
. . | | . d . | . f .
. . | | . . . | . | .
. . c | . . . | . g .

Nice post. It's obvious now, but it took me a while to figure out that 'a' and 'b' above were being treated as 'grouped candidates'. Perhaps tagging them both 'a' would help.
ronk
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Postby vidarino » Fri Feb 10, 2006 2:18 pm

Hmm, I guess this counts as beating a dead horse, but is this extended skyscraper thing really needed? I liked the idea of the simple skyscraper, because it's fairly easy to spot, but as soon as the complexity goes beyond that, the Turbot Fish (or perhaps even short, general X-Cycles) is just as easy to find, and much more flexible and powerful.
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Postby Neunmalneun » Fri Feb 10, 2006 4:36 pm

Maybe I am stating the obvious, but I think all these constellations could be solved in an easier way (or at least as easily) by Angus' multi-coloring technique.
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Postby Wolfgang » Fri Feb 10, 2006 7:17 pm

Not the last sample with the grouped strong link, i think. I was not aware that this can be expressed as an x-cycle also (thought it is equivalent to multicoloring), but at least it seems no problem to notate it.
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Postby vidarino » Fri Feb 10, 2006 7:59 pm

Code: Select all
. . . | . . . | c . .
. . . | . . . | . \ .
. a . | . . . | . . d
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. b . | . . e | . . .
------------|--------
. . . | . . f | * . .
. . . | . . . | . . .
. . . | . . . | . . .


The discontinuous X-Cycle here is:

*-f=e-b=a-d=c-*

or expressed as a Nice Loop:

R7C7-x-R7C6=x=R6C6-x-R6C2=x=R3C2-x-R3C9=x=R1C7-x-R7C7 -> R7C7 <> x
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Postby tarek » Fri Feb 10, 2006 8:57 pm

Hi Havard,

I am not saying that the Filet-O-Fish is JUST superior to your skyscraper, the whole skyscraper concept FOLLOWS the Finned X-wing concept in EVERY aspect.

The example that you said that the Filet-O-fish rule missed an elimination. It actually didn't, It can also be eliminated using the same rule.

I will post the finned jellyfish (if no one does it before me:D ) as soon as I find it in my database.

Tarek
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Postby tarek » Sat Feb 11, 2006 1:14 am

Code: Select all
*--------------------------------------------------------*
| 6     8     2    | 3     5     7    | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2     7    |
| 5     7     9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9    *78   | 6    *78    5    | 2     1     4    |
| 78    2     6    | 14    3     14   | 9     57    58   |
| 4     5     1    |*79   *789   2    |*78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    |*479  *2479  3    |%1    -47    89   |
| 27    3     4    | 19    129   8    |#67    567   59   |
| 9     1    *78   | 5    *47    6    |%3    -478   2    |
*--------------------------------------------------------*
Eliminating 7 From r7c8 (Almost Finned Jellyfish in Columns 3457)
Eliminating 7 From r9c8 (Almost Finned Jellyfish in Columns 3457)


will this be an extended skyscraper with 2 strong links:D ?
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Postby Myth Jellies » Sat Feb 11, 2006 4:28 am

:)Nice try, Terek, but there is an accompanying X-wing filet or sideways skyscraper there:( ...
Code: Select all
*--------------------------------------------------------*
| 6     8     2    | 3     5    (7)   | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2    (7)   |
| 5    (7)    9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
|*78    2     6    | 14    3     14   | 9    *57    58   |
| 4     5     1    | 79    789   2    | 78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    | 479   2479  3    | 1    -47    89   |
|*27    3     4    | 19    129   8    |#67   *567   59   |
| 9     1     78   | 5     47    6    | 3    -478   2    |
*--------------------------------------------------------*

For a real jellyfish case you'll have to find an example where the digit has been solved for in either zero or one box, not in three.

Havard, you can apply the Filet-of-Anything concept to your patterns as well. For example, starting with your simple skyscraper...
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * |  | . c . | . . .
. . |  | . | . | . . .
----|--+---|---+------
. . |  | . | . | . . .
. . b  | . d . | . . .
. . .  | . . . | . . .

...to make eliminations for digit 'n' in the two starred cells we can apply the filet-of-anything concept and note that it doesn't matter if 'n' is a candidate or not in any of the cells marked with an x below...
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
x x x  | . . . | . . .
* * x  | x x x | x x x
x x x  | . | . | . . .
----|--+---|---+------
. . |  | . | . | . . .
. . b  | . d . | . . .
. . .  | . . . | . . .

Of course eliminating the candidate 'n' at c leaves a single, so that's not going to result in anything new, but you can add all the candidates you want in box 4 column 3. Thus
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * |  | . c . | . . .
. . a' | . | . | . . .
----|--+---|---+------
. . |  | . | . | . . .
. . b  | . d . | . . .
. . .  | . . . | . . .

and
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * a' | . c . | . . .
. . a" | . | . | . . .
----|--+---|---+------
. . |  | . | . | . . .
. . b  | . d . | . . .
. . .  | . . . | . . .

Voila! Filet of Skyscraper!?:)

This goes for your three stage case as well. You can also add an e' to go along with your a' and a"...
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * a' | . c . | . e'.
. . a" | . | . | . | .
----|--+---|---+---|--
. . |  | . d . | . e .
. . b  | . . . | . f .
. . .  | . . . | . . .

Of course these appear to be identical to the things you can do with filets of fish, resulting in many of the same patterns, but it is another way of seeing it, so it may be useful to some. You might want to try filets on your two string kite as well.
Myth Jellies
 
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Joined: 19 September 2005

Postby tarek » Sat Feb 11, 2006 10:45 am

Hi Myth Jellies,

I actually used one of the examples showing the XWing earlier, so you're right it is not needed.

I did not understand what the 0 & 1 box issue is, but this example should be a pure almost finned jellyfish:
Code: Select all
*-----------------------------------------------*
| 9    278  278 | 24   5    67  | 3    46   1   |
| 4    6    3   | 9    8    1   | 2    5    7   |
| 17   5    127 | 24   3    67  | 9    8    46  |
|---------------+---------------+---------------|
| 2   #79  *4   | 1   *679  5   |*67   3    8   |
| 5    78  -678 | 67   4    3   | 1    2    9   |
| 3    1   *679 | 8   *679  2   | 5   *467  46  |
|---------------+---------------+---------------|
| 8    29   29  | 5   *17   4   |*67  *167  3   |
| 17   3    5   | 67   167  8   | 4    9    2   |
| 6    4   *17  | 3    2    9   | 8   *17   5   |
*-----------------------------------------------*
Eliminating 7 From r5c3 (Finned Jellyfish in rows 4679)


don't tell me that you don't have zillions of them in your database, you may also have a squirmbag that you would want to share........

Tarek
User avatar
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Posts: 2622
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Postby ronk » Sat Feb 11, 2006 1:24 pm

Myth Jellies wrote:there is an accompanying X-wing filet .... there.
Code: Select all
*--------------------------------------------------------*
| 6     8     2    | 3     5    (7)   | 4     9     1    |
| 1     4     3    | 8     6     9    | 5     2    (7)   |
| 5    (7)    9    | 2     14    14   | 68    68    3    |
|------------------+------------------+------------------|
| 3     9     78   | 6     78    5    | 2     1     4    |
|*78    2     6    | 14    3     14   | 9    *57    58   |
| 4     5     1    | 79    789   2    | 78    3     6    |
|------------------+------------------+------------------|
| 278   6     5    | 479   2479  3    | 1    -47    89   |
|*27    3     4    | 19    129   8    |#67   *567   59   |
| 9     1     78   | 5     47    6    | 3    -478   2    |
*--------------------------------------------------------*

Apparently, I don't get this 'finned' and 'filet' naming. To me the x-wing (r58c17) with the extra candidate (fin at r7c7) would be a finned x-wing or alternatively, since it's been "butchered" down from a 3x3 to a 3x2 "swordfish", a filet-o-swordfish.

Ron
ronk
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Location: Southeastern USA

Postby Havard » Sat Feb 11, 2006 2:22 pm

Hi Myth Jellies!

Myth Jellies wrote:
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * a' | . c . | . . .
. . a" | . | . | . . .
----|--+---|---+------
. . |  | . | . | . . .
. . b  | . d . | . . .
. . .  | . . . | . . .

Voila! Filet of Skyscraper!?:)


Excellent! Thanks Myth Jellies! I have been so obsessed in strong links, that I did not realise that if "b" is NOT a number then the elimination of the * becomes a line-box intersection, and not just the fact that the "a"'s (if there are to of them) make a strong link in that box! Cool! That should make the "filet of Skyscraper" apply for a lot more cases then merly my "extended" version!:D

but with this one:
Myth Jellies wrote:This goes for your three stage case as well. You can also add an e' to go along with your a' and a"...
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * a' | . c . | . e'.
. . a" | . | . | . | .
----|--+---|---+---|--
. . |  | . d . | . e .
. . b  | . . . | . f .
. . .  | . . . | . . .


...would you not actually get another elimination here:
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
* * a' | . c . | . e'.
. . a" | . | . | . | .
----|--+---|---+---|--
. . |  | . d . | * e *
. . b  | . . . | . f .
. . .  | . . . | . . .

again using the extended-upside-down-skyscraper rule?:D

however if you tried to add the filet into this one you would lose your grouped-strong-link with e'-e-f and you could only go:
Code: Select all
. . .  | . . . | . . .
. . .  | . . . | . . .
. . .  | . . . | . . .
-------+-------+------
. . a  | . . . | . . .
. . a' | . c . | . e'.
. . a" | . | . | . | .
----|--+---|---+---|--
. . |  | . d . | * e *
. . b  | . . . | . f .
. . .  | . . . | . f'.

is this right?


tarek:
tarek wrote:...but this example should be a pure almost finned jellyfish:
Code: Select all
*-----------------------------------------------*
| 9    278  278 | 24   5    67  | 3    46   1   |
| 4    6    3   | 9    8    1   | 2    5    7   |
| 17   5    127 | 24   3    67  | 9    8    46  |
|---------------+---------------+---------------|
| 2   #79  *4   | 1   *679  5   |*67   3    8   |
| 5    78  -678 | 67   4    3   | 1    2    9   |
| 3    1   *679 | 8   *679  2   | 5   *467  46  |
|---------------+---------------+---------------|
| 8    29   29  | 5   *17   4   |*67  *167  3   |
| 17   3    5   | 67   167  8   | 4    9    2   |
| 6    4   *17  | 3    2    9   | 8   *17   5   |
*-----------------------------------------------*
Eliminating 7 From r5c3 (Finned Jellyfish in rows 4679)



It is a good example, the only annoying thing is that the elimination can be done with the orginal "fish" pattern from the turbot fish...

Image

the really good thing about the swordfish example was that there were no other "simpler" patterns that could make that elimination!:)

havard
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Posts: 377
Joined: 25 December 2005

Postby Havard » Sat Feb 11, 2006 3:22 pm

Myth Jellies wrote:You might want to try filets on your two string kite as well.


I did try it on the 2-string kite, and could not make it work...

However, when I tried similar approaches to the "fish" pattern in the Turbot Fish, I found something interesting:
Code: Select all
3: "fish" pattern
. . . | . . . | c . .
. . . | . . . | . \ .
. a . | . . . | . . d
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. | . | . . . | . . .
--|------------------
. b . | . . . | * . .
. . . | . . . | . . .
. . . | . . . | . . .


if X does NOT have a candidate in it you can go:

Code: Select all
. . . | . . . | X . X
. . . | . . . | X . X
. a . | . . . | . . .
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. | . | . . . | . . .
--|------------------
. b . | . . . | . * .
. . . | . . . | . . .
. . . | . . . | . . .

. . . | . . . | X X .
. a . | . . . | . . .
. | . | . . . | X X .
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. | . | . . . | . . .
--|------------------
. b . | . . . | . . *
. . . | . . . | . . .
. . . | . . . | . . .

. a . | . . . | . . .
. | . | . . . | . X X
. | . | . . . | . X X
--|------------------
. | . | . . . | . . .
. | . | . . . | . . .
. | . | . . . | . . .
--|------------------
. b . | . . . | * . .
. . . | . . . | . . .
. . . | . . . | . . .



Notice how the fact that the X's never are in the same row as the "a" is self-explanatory, since if there WERE one X and one or two candidates there, that would eliminate the "a". So in other words, as long as where the X's are are NOT candidates, it does not matter what the distribution of candidates are in the remanining cells in that box.

How to put this into clear writing I am not sure how to do, but it would go something like:

definition: "Empty Rectangle" (ER)-> if you have four cells in a box that does not contain one perticular candidate, and that forms a rectangle, you have an empty rectangle.

definiton: "Empty Rectangle Lines" (ERL) With an Empty Rectangle in a box you will always get two lines, one vertical and one horisontal that are not touched by the ER. These are called Empty Rectangle Lines.

Code: Select all
X | X | . . . | . . .
--|-------ERL | . . .
X | X | . . . | . . .
--|---+-------+------
. | . | . . . | . . .
. | . | . . . | . . .
.ERL. | . . . | . . .
------+-------+------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .



Rule:
If you have a strong link and an empty rectangle(ER), where one of the "ends" of the strong link ("a" in the examples) line up with one of the Empty Rectangle Lines (ERL), then you can eliminate a candidate at the intersection of the other end of the strong link ("b" in the examples) and the other ERL.

As far as I can see, this would greatly expand the third pattern of the Turbot Fish in a true "fillet" way!:)

edit: typos
Havard
 
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Joined: 25 December 2005

Postby tarek » Sat Feb 11, 2006 4:08 pm

Havard wrote:It is a good example, the only annoying thing is that the elimination can be done with the orginal "fish" pattern from the turbot fish...


You're right it is annoying:(

There should be a better example of a finned Jellyfish alone in the tank !
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tarek
 
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