An extreme puzzle with a lot of fish

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An extreme puzzle with a lot of fish

Postby urhegyi » Mon Apr 05, 2021 10:00 am

fish.png
fish.png (14.74 KiB) Viewed 170 times

Code: Select all
1..4..8.......76....6.1.......7.1.9.4..........2.....3.....35.9..516..4.38..5..1.
urhegyi
 
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Re: An extreme puzzle with a lot of fish

Postby pjb » Tue Apr 06, 2021 1:29 am

A lot of fish??
I started with two double finned mutant SFs:

Finned mutant swordfish of 7s (c37r3\r9b16), fin at r3c8, r5c3 => -7 r5c8

Finned mutant swordfish of 9s (c16r1\r8b15), fin at r1c5, r6c1 => -9 r6c5

and then came to a grinding halt, requiring messy chains to advance

Phil
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Re: An extreme puzzle with a lot of fish

Postby denis_berthier » Tue Apr 06, 2021 4:36 am

SER = 9.0
This puzzle is a typical one in the SER 9.0 category. I've found nothing noticeable (in particular, not a lot of fish - fortunately, I didn't rely on it for lunch).
Generally, this type of puzzle is not proposed to human solvers; but it can be useful from time to time to recall that this is the reality of Sudoku solving when you don't restrict your puzzles to pre-digested ones.
Resolution state after Singles:
Code: Select all
   +----------------------+----------------------+----------------------+
   ! 1      23579  379    ! 4      239    6      ! 8      2357   257    !
   ! 2589   23459  3489   ! 23589  2389   7      ! 6      235    1      !
   ! 2578   2357   6      ! 2358   1      258    ! 9      2357   4      !
   +----------------------+----------------------+----------------------+
   ! 568    356    38     ! 7      2348   1      ! 24     9      258    !
   ! 4      135679 13789  ! 235689 2389   2589   ! 127    25678  2578   !
   ! 56789  15679  2      ! 5689   489    589    ! 147    5678   3      !
   +----------------------+----------------------+----------------------+
   ! 26     1246   14     ! 28     7      3      ! 5      28     9      !
   ! 279    279    5      ! 1      6      289    ! 3      4      278    !
   ! 3      8      79     ! 29     5      4      ! 27     1      6      !
   +----------------------+----------------------+----------------------+
181 candidates, 1002 csp-links and 1002 links. Density = 6.15%

whip[1]: r4n6{c2 .} ==> r6c2 ≠ 6, r5c2 ≠ 6, r6c1 ≠ 6
naked-pairs-in-a-row: r7{c4 c8}{n2 n8} ==> r7c2 ≠ 2, r7c1 ≠ 2
singles ==> r7c1 = 6, r4c2 = 6
whip[1]: b7n2{r8c2 .} ==> r8c6 ≠ 2, r8c9 ≠ 2
whip[1]: b8n2{r9c4 .} ==> r2c4 ≠ 2, r3c4 ≠ 2, r5c4 ≠ 2
z-chain[3]: b2n9{r2c5 r2c4} - c1n9{r2 r8} - c6n9{r8 .} ==> r6c5 ≠ 9
z-chain[3]: b3n7{r3c8 r1c9} - c3n7{r1 r9} - c7n7{r9 .} ==> r5c8 ≠ 7
t-whip[3]: r8c9{n7 n8} - r7c8{n8 n2} - b3n2{r3c8 .} ==> r1c9 ≠ 7
whip[1]: b3n7{r3c8 .} ==> r6c8 ≠ 7
finned-x-wing-in-rows: n7{r9 r6}{c7 c3} ==> r5c3 ≠ 7
z-chain[4]: b8n8{r7c4 r8c6} - c9n8{r8 r4} - c3n8{r4 r2} - c5n8{r2 .} ==> r5c4 ≠ 8
whip[6]: r9c3{n9 n7} - r1c3{n7 n3} - c2n3{r3 r5} - r5n1{c2 c7} - c7n7{r5 r6} - b4n7{r6c1 .} ==> r5c3 ≠ 9
t-whip[7]: r8n8{c6 c9} - r7n8{c8 c4} - r7n2{c4 c8} - b3n2{r3c8 r1c9} - r4c9{n2 n5} - r4c1{n5 n8} - r3n8{c1 .} ==> r5c6 ≠ 8, r6c6 ≠ 8
biv-chain[4]: r9c7{n2 n7} - r8c9{n7 n8} - c6n8{r8 r3} - c6n2{r3 r5} ==> r5c7 ≠ 2
biv-chain[4]: r6c5{n8 n4} - r4n4{c5 c7} - c7n2{r4 r9} - r7c8{n2 n8} ==> r6c8 ≠ 8
biv-chain[3]: r6c6{n9 n5} - r6c8{n5 n6} - b5n6{r6c4 r5c4} ==> r5c4 ≠ 9
z-chain[3]: b4n9{r6c2 r6c1} - c4n9{r6 r9} - c3n9{r9 .} ==> r2c2 ≠ 9
t-whip[4]: r9n7{c3 c7} - r5c7{n7 n1} - b4n1{r5c2 r6c2} - r6n7{c2 .} ==> r8c1 ≠ 7
z-chain[4]: c3n9{r2 r9} - c3n7{r9 r1} - c1n7{r3 r6} - b4n9{r6c1 .} ==> r1c2 ≠ 9
finned-x-wing-in-rows: n9{r9 r1}{c3 c4} ==> r2c4 ≠ 9
whip[1]: b2n9{r2c5 .} ==> r5c5 ≠ 9
z-chain[6]: r7c4{n8 n2} - r9n2{c4 c7} - r4c7{n2 n4} - r6n4{c7 c5} - r6n8{c5 c1} - r3n8{c1 .} ==> r2c4 ≠ 8
z-chain[4]: r2c4{n5 n3} - r2c8{n3 n2} - r1c9{n2 n5} - r4n5{c9 .} ==> r2c1 ≠ 5
z-chain[6]: c8n7{r3 r1} - c8n3{r1 r2} - r2c4{n3 n5} - r3c6{n5 n8} - b8n8{r8c6 r7c4} - r7n2{c4 .} ==> r3c8 ≠ 2
whip[6]: r6c6{n9 n5} - r6c8{n5 n6} - r6c4{n6 n8} - b8n8{r7c4 r8c6} - r3n8{c6 c1} - c1n7{r3 .} ==> r6c1 ≠ 9
whip[1]: b4n9{r6c2 .} ==> r8c2 ≠ 9
biv-chain[3]: c2n9{r5 r6} - r6n1{c2 c7} - r5c7{n1 n7} ==> r5c2 ≠ 7
whip[1]: r5n7{c9 .} ==> r6c7 ≠ 7
z-chain[4]: r3n2{c2 c6} - c6n8{r3 r8} - r8n9{c6 c1} - r8n2{c1 .} ==> r1c2 ≠ 2
z-chain[4]: r3n2{c2 c6} - c6n8{r3 r8} - r8n9{c6 c1} - r8n2{c1 .} ==> r2c2 ≠ 2
whip[4]: r2c4{n3 n5} - r2c8{n5 n2} - r1n2{c9 c5} - c5n9{r1 .} ==> r2c5 ≠ 3
whip[6]: r2c4{n3 n5} - r2c8{n5 n2} - r1n2{c9 c5} - r3c6{n2 n8} - b8n8{r8c6 r7c4} - r7n2{c4 .} ==> r2c2 ≠ 3
whip[6]: r2c4{n3 n5} - r2c8{n5 n2} - r1n2{c9 c5} - b5n2{r4c5 r5c6} - r5n9{c6 c2} - c2n3{r5 .} ==> r2c3 ≠ 3
z-chain[7]: r6c7{n1 n4} - c5n4{r6 r4} - r4n3{c5 c3} - r5c3{n3 n8} - c8n8{r5 r7} - r8c9{n8 n7} - r5n7{c9 .} ==> r5c7 ≠ 1
singles ==> r5c7 = 7, r9c7 = 2, r4c7 = 4, r6c7 = 1, r7c8 = 8
naked-single ==> r7c4 = 2, r8c9 = 7, r8c2 = 2, r8c1 = 9, r8c6 = 8, r9c3 = 7, r9c4 = 9, r6c5 = 4
x-wing-in-rows: n8{r3 r6}{c1 c4} ==> r4c1 ≠ 8, r2c1 ≠ 8
singles ==> r2c1 = 2, r4c1 = 5, r3c6 = 2
whip[1]: c6n5{r6 .} ==> r5c4 ≠ 5, r6c4 ≠ 5
naked-pairs-in-a-row: r1{c3 c5}{n3 n9} ==> r1c8 ≠ 3, r1c2 ≠ 3
naked-pairs-in-a-row: r2{c4 c8}{n3 n5} ==> r2c2 ≠ 5
singles ==> r2c2 = 4, r7c2 = 1, r7c3 = 4, r5c3 = 1
x-wing-in-rows: n3{r1 r4}{c3 c5} ==> r5c5 ≠ 3
biv-chain[3]: r6c8{n5 n6} - r6c4{n6 n8} - r5n8{c5 c9} ==> r5c9 ≠ 5
stte
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Re: An extreme puzzle with a lot of fish

Postby DEFISE » Tue Apr 06, 2021 12:08 pm

0 fish but an "optimized" T&E(singles only):

8 singles
T&E(8r4c9) => error => -8r4c9
T&E(8r8c9) => error => -8r8c9 => 12 singles
T&E(8r6c1) => error => -8r6c1 => STTE.
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Re: An extreme puzzle with a lot of fish

Postby AnotherLife » Tue Apr 06, 2021 12:45 pm

I tried to solve this puzzle manually, and after the lcls steps I saw an ALS-chain eliminating the 7 from r1c9.
Code: Select all
.--------------------.-------------------.-------------------.
| 1     23579  379   | 4      239   6    | 8    a2357   25-7 |
| 2589  23459  3489  | 3589   2389  7    | 6    a235    1    |
| 2578  2357   6     | 358    1     258  | 9    a2357   4    |
:--------------------+-------------------+-------------------:
| 58    6      38    | 7      2348  1    | 24   9       258  |
| 4     13579  13789 | 35689  2389  2589 | 127  25678   2578 |
| 5789  1579   2     | 5689   489   589  | 147  5678    3    |
:--------------------+-------------------+------------------:
| 6     14     14    | 28     7     3    | 5    b28     9    |
| 279   279    5     | 1      6     89   | 3    4      c78   |
| 3     8      79    | 29     5     4    | 27   1       6    |
'--------------------'-------------------'-------------------'

Then I eliminated the 7's from r56c8 by the locked candidates rule, and the 7 from r5c3 by a kite. I got stuck here.
Code: Select all
.-------------------.-------------------.-----------------.
| 1     23579  379  | 4      239   6    | 8    2357  25   |
| 2589  23459  3489 | 3589   2389  7    | 6    235   1    |
| 2578  2357   6    | 358    1     258  | 9    2357  4    |
:-------------------+-------------------+-----------------:
| 58    6      38   | 7      2348  1    | 24   9     258  |
| 4     13579  1389 | 35689  2389  2589 | 127  2568  2578 |
| 5789  1579   2    | 5689   489   589  | 147  568   3    |
:-------------------+-------------------+-----------------:
| 6     14     14   | 28     7     3    | 5    28    9    |
| 279   279    5    | 1      6     89   | 3    4     78   |
| 3     8      79   | 29     5     4    | 27   1     6    |
'-------------------'-------------------'-----------------'

HoDoKu can find here two complex fish patterns:
- Finned Franken Swordfish: 9 c16b2 r268 fr1c5 fr5c6 => r6c5<>9
- Finned Franken Jellyfish: 8 r367b8 c1468 fr6c5 efr7c4 => r5c4<>8,
but that does not help very much because now the progress can be made only with the methods of Last Resort, that is, forcing chains and forcing nets.
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Re: An extreme puzzle with a lot of fish

Postby denis_berthier » Tue Apr 06, 2021 1:50 pm

DEFISE wrote:0 fish but an "optimized" T&E(singles only):
8 singles
T&E(8r4c9) => error => -8r4c9
T&E(8r8c9) => error => -8r8c9 => 12 singles
T&E(8r6c1) => error => -8r6c1 => STTE.

Did you try to find the lengths of the 3 whips or braids allowing these eliminations?
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Re: An extreme puzzle with a lot of fish

Postby Cenoman » Tue Apr 06, 2021 3:53 pm

Code: Select all
 +-------------------------+------------------------+-------------------------+
 |  1      23579  C379     |  4       239    6      |    8     2357    257    |
 |  2589   23459   3489    |  3589    2389   7      |    6     235     1      |
 |  2578   2357    6       |  358     1    a'25-8   |    9     2357    4      |
 +-------------------------+------------------------+-------------------------+
 | B58     6      C38      |  7       2348   1      |  zb24    9    wAa258    |
 |  4      13579  C13789   |  35689   2389 b'2589   |  c'127   25678   2578   |
 |  5789  D1579    2       |  5689    489    589    |   E17-4  5678    3      |
 +-------------------------+------------------------+-------------------------+
 |  6      14      14      |  28      7      3      |    5     28      9      |
 |  279    279     5       |  1       6    e'89     |    3     4      x78     |
 |  3      8      C79      |e'29      5      4      | d'y27    1       6      |
 +-------------------------+------------------------+-------------------------+

1. Kraken cell (258)r4c9 => -4 r6c7
(2)r4c9 - (2=4)r4c7
(5)r4c9 - (5=8)r4c1 - (8=3791)r1459c3 - r6c2 = (1)r6c7
(8)r4c9 - (8=7)r8c9 - (7=2)r9c7 - (2=4)r4c7
----------
=> -4 r6c7; 2 placements (+4 r6c5, r4c7)

2. (2)r3c6 = r5c6 - r5c7 = r9c7 - (2=98)b8p67 =>-8r3c6
Hidden Text: Show
Code: Select all
 +-------------------------+------------------------+-----------------------+
 |  1      23579   379     |  4       239    6      |  8     2357    257    |
 |  2589   23459   3489    |  3589    2389   7      |  6     235     1      |
 | C2578*  2357    6       | D358*    1      25     |  9     2357    4      |
 +-------------------------+------------------------+-----------------------+
 | B58     6       38      |  7       238    1      |  4     9    xAa258    |
 |  4      13579   13789   |  35689   2389   2589   | b127   25678   2578   |
 |  5789   1579    2       |  5689    4      589    |  17    5678    3      |
 +-------------------------+------------------------+-----------------------+
 |  6      14      14      | E28      7      3      |  5     28      9      |
 |  279    279     5       |  1       6      89     |  3     4      y78     |
 |  3      8       79      |  9-2     5      4      |zc27    1       6      |
 +-------------------------+------------------------+-----------------------+

3. Kraken cell (258)r4c9
(2)r4c9 - r5c7 = (2)r9c7
(5)r4c9 - (5=8)r4c1 - r3c1 = r3c4 - (8=2)r7c4
(8)r4c9 - (8=7)r8c9 - (7=2)r9c7
=>-2r9c4; 7 placements & lcls
Hidden Text: Show
Code: Select all
 +------------------------+----------------------+--------------------+
 |  1      23579   39     |  4      239    6     |  8    2357   25    |
 |  259-8  23459   3489   |  35-8   2389   7     |  6    235    1     |
 |  2578*  2357    6      |  358*   1      25    |  9    2357   4     |
 +------------------------+----------------------+--------------------+
 |  5-8    6       38     |  7      238    1     |  4    9      258   |
 |  4      13579   1389   |  356-8  238    259   |  17   256    258   |
 |  5789*  1579    2      |  568*   4      59    |  17   56     3     |
 +------------------------+----------------------+--------------------+
 |  6      14      14     |  2      7      3     |  5    8      9     |
 |  29     29      5      |  1      6      8     |  3    4      7     |
 |  3      8       7      |  9      5      4     |  2    1      6     |
 +------------------------+----------------------+--------------------+

4. XW (8)r36\c14 => -8 r24c1, r25c4; +5r4c1, NP(29)r28c1
Hidden Text: Show
Code: Select all
 +----------------------+---------------------+--------------------+
 |  1    23579  a39     |  4     239    6     |  8   D2357   25    |
 |  29   23459   3489   | B35    2389   7     |  6   C235    1     |
 |  78   2357    6      |  358   1     A25    |  9   D357-2  4     |
 +----------------------+---------------------+--------------------+
 |  5    6      a38     |  7     238    1     |  4    9      28    |
 |  4    1379    138-9  |  356   238    259   |  17   256    258   |
 | b78  b179     2      |  568   4      59    | b17   56     3     |
 +----------------------+---------------------+--------------------+
 |  6    14      14     |  2     7      3     |  5    8      9     |
 |  29   29      5      |  1     6      8     |  3    4      7     |
 |  3    8       7      |  9     5      4     |  2    1      6     |
 +----------------------+---------------------+--------------------+

5. (9=38)r14c3-(8=179)r6c127 =>-9r5c3
6. (2=5)r3c6-(5=3)r2c4-r2c8=(37)r13c8 =>-2r3c8; 10 placements & lcls
Hidden Text: Show
Code: Select all
 +------------------+-------------------+-------------------+
 |  1    57    39   |  4     39    6    |  8    27    25    |
 |  2    4     89   |  35    89    7    |  6    35    1     |
 |  78   357   6    |  358   1     2    |  9    357   4     |
 +------------------+-------------------+-------------------+
 |  5    6     38   |  7     238   1    |  4    9     28    |
 |  4    39    1    |  36    238   59   |  7    256   258   |
 |  78   79    2    |  68    4     59   |  1    56    3     |
 +------------------+-------------------+-------------------+
 |  6    1     4    |  2     7     3    |  5    8     9     |
 |  9    2     5    |  1     6     8    |  3    4     7     |
 |  3    8     7    |  9     5     4    |  2    1     6     |
 +------------------+-------------------+-------------------+

7. UR(28)r45c59 using mixed external-internal (8)r6c4 == (5)r5c9 - (5=6)r6c8 => -6 r6c4; ste
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Re: An extreme puzzle with a lot of fish

Postby DEFISE » Tue Apr 06, 2021 9:11 pm

denis_berthier wrote:
DEFISE wrote:0 fish but an "optimized" T&E(singles only):
8 singles
T&E(8r4c9) => error => -8r4c9
T&E(8r8c9) => error => -8r8c9 => 12 singles
T&E(8r6c1) => error => -8r6c1 => STTE.

Did you try to find the lengths of the 3 whips or braids allowing these eliminations?


Yes but I gave up because of the combinatorial explosion.
But if we don't limit ourselves to singles, apart from whips, it’s becomes possible with two whips[12] and
one whip[8].
However, knowing that this puzzle is in W7, here is a more reasonable solution:

Hidden Text: Show
Singles: 6r1c6, 1r2c9, 3r8c7, 6r9c9, 7r7c5, 9r3c7, 4r3c9, 4r9c6
Alignment: 6r4b4 => -6r5c2 -6r6c1 -6r6c2
Naked pair: 28r7c48 => -2r7c1 -2r7c2
Singles: 6r7c1, 6r4c2
Alignment: 2b7r8 => -2r8c6 -2r8c9
Alignment: 2b8c4 => -2r2c4 -2r3c4 -2r5c4

whip[8]: r9c7{n2 n7}- r8c9{n7 n8}- r4c9{n8 n5}- r4c1{n5 n8}- b1n8{r2c1 r2c3}- c3n4{r2 r7}- c3n1{r7 r5}- r5c7{n1 .} => -2r4c7
Singles: 4r4c7, 4r6c5

whip[7]: r7n2{c4 c8}- c7n2{r9 r5}- c6n2{r5 r3}- r3n8{c6 c1}- r4c1{n8 n5}- r4c9{n5 n8}- c8n8{r5 .} => -8r7c4
Singles: 2r7c4, 8r7c8, 7r8c9, 9r9c4, 8r8c6, 7r9c3, 2r9c7
Alignment: 9c6b5 => -9r5c5
Alignment: 7c7b6 => -7r5c8 -7r6c8
Xwing: 8r36c14 => -8r2c1 -8r2c4 -8r4c1 -8r5c4
Single: 5r4c1
Naked pair: 29c1r28 => -2r3c1 -9r6c1

whip[7]: c3n4{r7 r2}- r2n8{c3 c5}- c5n9{r2 r1}- r1c3{n9 n3}- c2n3{r1 r5}- r5n1{c2 c7}- r5n7{c7 .} => -1r7c3
Singles: 4r7c3, 1r7c2, 4r2c2, 1r6c7, 7r5c7, 1r5c3
Alignment: 9c3b1 => -9r1c2 -9r2c1
Singles: 2r2c1, 9r8c1, 2r8c2
Naked pair: 35r2c48 => -3r2c3 -3r2c5

whip[5]: r4n2{c9 c5}- r4n3{c5 c3}- r5c2{n3 n9}- r5c6{n9 n5}- c9n5{r5 .} => -2r1c9
STTE
DEFISE
 
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Re: An extreme puzzle with a lot of fish

Postby denis_berthier » Wed Apr 07, 2021 4:47 am

DEFISE wrote:
denis_berthier wrote:
DEFISE wrote:0 fish but an "optimized" T&E(singles only):
8 singles
T&E(8r4c9) => error => -8r4c9
T&E(8r8c9) => error => -8r8c9 => 12 singles
T&E(8r6c1) => error => -8r6c1 => STTE.

Did you try to find the lengths of the 3 whips or braids allowing these eliminations?

Yes but I gave up because of the combinatorial explosion.


I also tried with braids but it started to take too long, so I stopped after length 15.
The solution in W8 is great. How many tries did you have to do to find it?
denis_berthier
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Re: An extreme puzzle with a lot of fish

Postby DEFISE » Wed Apr 07, 2021 9:19 am

denis_berthier wrote:The solution in W8 is great. How many tries did you have to do to find it?


I did 15 executions of my "few steps" program with parameter max_length_whip = 8.
The summarized results were as follows:

Target(length whip), Target(length whip), Target(length whip), Target(length whip),
2L4C7(8),2L7C8(8),4L7C2(8),5L1C2(6),
2L4C7(8),8L8C9(7),1L7C3(7),8L5C5(8),
2L4C7(8),2L9C4(8),1L7C3(7),2L4C5(7),
2L4C7(8),2L9C4(8),4L2C3(7),2L1C9(5),
2L4C7(8),9L8C6(8),1L7C3(7),2L4C5(7),
2L4C7(8),2L5C7(7),4L7C2(8),8L5C5(8),
2L4C7(8),8L7C4(7),4L7C2(8),8L4C9(8),
2L4C7(8),8L7C4(7),1L7C3(7),2L1C9(5),
2L4C7(8),8L7C4(7),1L7C3(7),5L5C9(5),
2L4C7(8),2L9C4(8),4L2C3(7),2L4C5(7),
2L4C7(8),2L7C8(8),4L2C3(7),8L4C9(8),
2L4C7(8),8L7C4(7),4L7C2(8),2L1C9(5),
2L4C7(8),2L9C4(8),1L7C3(7),5L5C9(5),
2L4C7(8),8L7C4(7),1L7C3(7),8L5C5(8),
2L4C7(8),2L7C8(8),4L2C3(7),8L5C5(8),
I gave the 8th resolution.
Run time <= 0,4s per execution.
N.B : with parameter max_length_whip = 7 at least 8 whips are required per resolution !
DEFISE
 
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