## An extreme puzzle with a lot of fish

Post puzzles for others to solve here.

### An extreme puzzle with a lot of fish

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

Posts: 406
Joined: 13 April 2020

### Re: An extreme puzzle with a lot of fish

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
pjb
2014 Supporter

Posts: 2310
Joined: 11 September 2011
Location: Sydney, Australia

### Re: An extreme puzzle with a lot of fish

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:
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`   +----------------------+----------------------+----------------------+    ! 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
denis_berthier
2010 Supporter

Posts: 2206
Joined: 19 June 2007
Location: Paris

### Re: An extreme puzzle with a lot of fish

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.
DEFISE

Posts: 93
Joined: 16 April 2020
Location: France

### Re: An extreme puzzle with a lot of fish

I tried to solve this puzzle manually, and after the lcls steps I saw an ALS-chain eliminating the 7 from r1c9.
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`.--------------------.-------------------.-------------------.| 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.
Bogdan
AnotherLife

Posts: 48
Joined: 07 January 2021
Location: Moscow, Russia

### Re: An extreme puzzle with a lot of fish

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?
denis_berthier
2010 Supporter

Posts: 2206
Joined: 19 June 2007
Location: Paris

### Re: An extreme puzzle with a lot of fish

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
Cenoman
Cenoman

Posts: 1637
Joined: 21 November 2016
Location: Paris, France

### Re: An extreme puzzle with a lot of fish

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

Posts: 93
Joined: 16 April 2020
Location: France

### Re: An extreme puzzle with a lot of fish

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
2010 Supporter

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Location: Paris

### Re: An extreme puzzle with a lot of fish

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

Posts: 93
Joined: 16 April 2020
Location: France