Big fish

Advanced methods and approaches for solving Sudoku puzzles

Postby tarek » Mon Mar 13, 2006 2:37 pm

vidarino wrote:Fixed, and the hunt continues... ;-)


good, could you retest your first squirmbag ?
It looks like a pure one....unless there is a lesser fish with 2 vertices in the box next to the fin which I've miseed.

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Postby vidarino » Mon Mar 13, 2006 2:40 pm

tarek wrote:It looks like a pure one....unless there is a lesser fish with 2 vertices in the box next to the fin which I've miseed.


The first one was a false positive, unfortunately;
Code: Select all
 2       159     1579    |  8       1367    4       | #167     379     13679 
 4       3       17      |  167     9       2       |  5       8       167   
*78      189     6       |  157     137    *357     | *4       2      -1379   
-------------------------+--------------------------+--------------------------
*568     45689   2589    |  124679  12367  *367     | *167     34579   13569 
 56      7       259     |  12469   1236    36      |  16      3459    8     
 1       469     3       |  4679    5       8       |  2       479     679   
-------------------------+--------------------------+--------------------------
*5678    568     578     |  3       4      *567     | *9       1       2     
 9       2       4       |  57      8       1       |  3       6       57     
 3       156     157     |  2567    267     9       |  8       57      4     

Finned Swordfish with 7 in R347C167 + fin R1C7
   -> R3C9 <> 7



But again, how about this one?

Code: Select all
 1358   7      138    |  2      6      4      |  35     389    389   
 2      9     *4      |  3     *5     *78     | *6     *78     1     
 3568   68    *368    |  1     *78    *9      | *357   *4      2     
----------------------+-----------------------+-----------------------
-379    5     *2      |  6     *789   *78     | *1     *37     4     
 3678   68    #3678   |  4      1      2      |  9      5      367   
 4      1     #679    |  79     3      5      |  8      2      67   
----------------------+-----------------------+-----------------------
 6789   2     *678    |  5     *79    *36     | *4     *1      389   
 16789  4     *16789  |  89    *2     *36     | *37    *3789   5     
 89     3      5      |  789    4      1      |  2      6      789   

Finned Squirmbag with 7 in R23478C35678 + fin R56C3
   -> R4C1 <> 7


I *think* (again, heh) it's legit.:)

Vidar
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Postby ravel » Mon Mar 13, 2006 2:51 pm

Must be easier, i dont need the upper 3 boxes for the elimination.
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Postby Havard » Mon Mar 13, 2006 2:56 pm

vidarino wrote:
Code: Select all
 7      456    346    |  45     2      8      |  36     9      1     
 8      9      23     |  67     67     1      |  23     5      4     
*56     1     *2456   |  9     *45    *3      |  268    7     *28   
----------------------+-----------------------+-----------------------
 2      3456   8      |  356    1      9      |  45     46     7     
*56     34567 *9      |  367   *8     *47     |  1245   146   *25   
*1      467   *4567   |  2     *567   *457    |  9      8     *3     
----------------------+-----------------------+-----------------------
*3      578   *57     | -1457  *457   *6      |  14578  2     *9     
 4      2      1      |  8      9     #57     |  57     3      6     
*9      5678  *567    | -1457  *3     *2      |  14578  14    *58   
Finned Squirmbag with 5 in R35679C13569 + fin R8C6
   -> R7C4 <> 5
   -> R9C4 <> 5


(And yes, I know multi-coloring / an X-cycle can zap the one in R9C4. Possibly the other one, too, but I haven't studied it. (Actually, the whole thing can be solved just by cracking the 5s.:) ) )


Here is one possible way to "crack the 5s"
Code: Select all
. . . | . . . | . . .
. . . | . . . | . . .
5 . . | . * . | . . .
|-----+-------+------
| . . | . . . | . . .
5 . . | . . . | . . 5
. . 5-----5-5 | . . |
------+-------+-----|
. . . | . . . | . . |
. . . | . . 5---5 . |
. . . | . . . | . . 5
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Postby vidarino » Mon Mar 13, 2006 3:00 pm

OK, one more snack;

Code: Select all
 234    8      124    |  7      236    14     |  9      2346   5     
*5      6     *247    |  9      238   *48     | *2347  *2347   1     
*2347   9     *1247   |  345    236   *145    | *2347  *23467  8     
----------------------+-----------------------+-----------------------
 1      347    5      |  2      47     6      | #347    8      9     
 9      47     6      |  8      1      3      | #247    5      247   
*28     347   *28     |  45     9     *457    | *6     *1     -347   
----------------------+-----------------------+-----------------------
*478    2     *478    |  34     5     *9      | *1     *347    6     
*47     1     *9      |  6      38    *478    | *5     *2347   2347 
 6      5      3      |  1      47     2      |  8      9      47   

Finned Sashimi Squirmbag with 7 in R23678C13678 + fin R45C7
   -> R6C9 <> 7


And in the very same grid!
Code: Select all
*234    8     *124    | *7      236   *14     | *9     *2346   5     
*5      6     *247    | *9      238   *48     | *2347  *2347   1     
*2347   9     *1247   | *345    236   *145    | *2347  *23467  8     
----------------------+-----------------------+-----------------------
 1      347    5      |  2      47     6      | #347    8      9     
 9      47     6      |  8      1      3      | #247    5      247   
*28     347   *28     | *45     9     *457    | *6     *1     -347   
----------------------+-----------------------+-----------------------
*478    2     *478    | *34     5     *9      | *1     *347    6     
*47     1     *9      | *6      38    *478    | *5     *2347   2347 
 6      5      3      |  1      47     2      |  8      9      47   

Finned Whale with 4 in R123678C134678 + fin R45C7
   -> R6C9 <> 4


Now, obviously I'm not trusting my solver 100% yet, but they look okay to me.:)

Vidar
Last edited by vidarino on Mon Mar 13, 2006 11:21 am, edited 1 time in total.
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Postby ravel » Mon Mar 13, 2006 3:19 pm

vidarino wrote:But again, how about this one?

Code: Select all
 1358   7      138    |  2      6      4      |  35     389    389   
 2      9     *4      |  3     *5     *78     | *6     *78     1     
 3568   68    *368    |  1     *78    *9      | *357   *4      2     
----------------------+-----------------------+-----------------------
-379    5     *2      |  6     *789   *78     | *1     *37     4     
 3678   68    #3678   |  4      1      2      |  9      5      367   
 4      1     #679    |  79     3      5      |  8      2      67   
----------------------+-----------------------+-----------------------
 6789   2     *678    |  5     *79    *36     | *4     *1      389   
 16789  4     *16789  |  89    *2     *36     | *37    *3789   5     
 89     3      5      |  789    4      1      |  2      6      789   

Finned Squirmbag with 7 in R23478C35678 + fin R56C3
   -> R4C1 <> 7


Isnt there a finned swordfish in rows 569?
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Postby vidarino » Mon Mar 13, 2006 3:29 pm

ravel wrote:Isnt there a finned swordfish in rows 569?


Hmm, I don't think so... Well, there appears to be, but will that be able to make the elimination in R4C1? I was under the impression that you could only eliminate candidates in the fish's columns.

If so this particular finned swordfish could only eliminate from R4C3, which doesn't have a 7...

Hmm, you might be on to something, though. I'll experiment a bit.:)

Thanks,
Vidar
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Postby ronk » Mon Mar 13, 2006 3:31 pm

Havard wrote:Here is the simpler counterpart:
Code: Select all
. . . | . . . | 7 . .
. . . | . . . | | . .
7 . . | . . 7 | | . *
|-----+-----|-+-|----
| . . | . . 7 | 7 . .
| . . | . . | | . . .
| . . | . . | | . . .
|-----+-----|-+------
7 . . | . . 7 | . . .
. . . | . . . | . . .
. . . | . . . | . . .

Given that column six has three candidates in three different boxes, how do you group candidates to end up with a strong link? Or if your vertical line in col 6 doesn't represent a strong link, what does it represent?

Ron
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Postby ravel » Mon Mar 13, 2006 3:40 pm

vidarino wrote:... Well, there appears to be, but will that be able to make the elimination in R4C1?

Im sure that i can make the elimination, but not sure about the definition of the finned swordfish.
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Postby ravel » Mon Mar 13, 2006 3:45 pm

ronk wrote:Given that column six has three candidates in three different boxes, how do you group candidates to end up with a strong link?
Ron

It gives an x-wing.
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Postby aeb » Mon Mar 13, 2006 5:07 pm

vidarino wrote:I just merely looking for high-order N-fish that didn't have a smaller counterpart. My stance on the subject is wavering badly right now, though. ;-)

Anyway, my solver has now been fixed, and the search for big fish continues.

But you have already seen the proof that big fish are equivalent to small fish, and big finned fish equivalent to small finned fish. Now what is the search for?

vidarino wrote:Here's one more for you all to scrutinize;

Code: Select all
 7      456    346    |  45     2      8      |  36     9      1     
 8      9      23     |  67     67     1      |  23     5      4     
*56     1     *2456   |  9     *45    *3      |  268    7     *28   
----------------------+-----------------------+-----------------------
 2      3456   8      |  356    1      9      |  45     46     7     
*56     34567 *9      |  367   *8     *47     |  1245   146   *25   
*1      467   *4567   |  2     *567   *457    |  9      8     *3     
----------------------+-----------------------+-----------------------
*3      578   *57     | -1457  *457   *6      |  14578  2     *9     
 4      2      1      |  8      9     #57     |  57     3      6     
*9      5678  *567    | -1457  *3     *2      |  14578  14    *58   

Finned Squirmbag with 5 in R35679C13569 + fin R8C6
   -> R7C4 <> 5
   -> R9C4 <> 5


The argument for the big finned fish is: all occurrences of digit 5 in columns 13569 are in rows 35679, with the possible exception of a 5 at (8,6). If (7,4)5 or (9,4)5 then we lose the possible exception and a row, contradiction.
But the statement that all occurrences of digit 5 in columns 13569 are in rows 35679 is precisely equivalent to the statement that all occurrences of digit 5 in rows 1248 are in columns 2478, of course with precisely the same possible exception of 5 at (8,6). If (7,4)5 or (9,4)5 then we lose the possible exception and a column, contradiction.
This argument is general - go from sets of rows and columns to the complementary sets.
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Postby tarek » Mon Mar 13, 2006 5:42 pm

aeb,

what you're saying is true only when there are more than one candidate per line......

if there exists a big fish of certain candidates in a set of lines.......
iif the the rest of the lines have a line whre the candidate has been uncovered.........

The reduction will not be possible...

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Postby aeb » Mon Mar 13, 2006 5:48 pm

tarek wrote:aeb,

what you're saying is true only when there are more than one candidate per line......

if there exists a big fish of certain candidates in a set of lines.......
iif the the rest of the lines have a line whre the candidate has been uncovered.........

The reduction will not be possible...

tarek


Hmm. I am not sure I can interpret what you are saying.
Gaining information does never harm.
Also, in the example above there is a line with only one candidate. There is nothing special about that. Since the argument holds, it holds whatever the situation.
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Postby ravel » Mon Mar 13, 2006 5:49 pm

If you have a line with a fixed candidate, it gives an N-1 fish.
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Postby aeb » Mon Mar 13, 2006 6:01 pm

ravel wrote:If you have a line with a fixed candidate, it gives an N-1 fish.

Yes. Every N-fish is equivalent to an (9-N)-fish. This holds both in the finned and non-finned case. Every N-fish with a fixed candidate is also an (N-1)-fish. Also this holds both in the finned and non-finned case. It follows that there is never the need to search for N-fish with N > 4.
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