The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| 9 . . | . . . | . . . |
| . . 8 | 7 . . | . . 6 |
| . 5 . | . 4 . | . 3 . |
+-------+-------+-------+
| . 2 . | . 1 . | . 5 . |
| . . 6 | 8 . . | . . 7 |
| 5 . . | . . . | . . . |
+-------+-------+-------+
| . . 7 | 1 . . | . . 8 |
| . . . | . 2 . | . 4 . |
| 2 . . | . . 4 | . . 1 |
+-------+-------+-------+
9..........87....6.5..4..3..2..1..5...68....75..........71....8....2..4.2....4..1

[Hajime]

Hmmm, delicious, lots of fishes.

[denis_berthier]

.
First trying to get as many Subsets as possible (I find 20)

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************

Code: Select all

Starting non trivial part of solution with the following RESOLUTION STATE:
   9         13467     1234      2356      3568      123568    124578    1278      245       
   134       134       8         7         359       12359     12459     129       6         
   167       5         12        269       4         12689     12789     3         29       
   3478      2         349       3469      1         3679      34689     5         349       
   134       1349      6         8         359       2359      12349     129       7         
   5         134789    1349      23469     3679      23679     1234689   12689     2349     
   346       3469      7         1         3569      3569      23569     269       8         
   1368      13689     1359      3569      2         356789    35679     4         359       
   2         3689      359       3569      356789    4         35679     679       1       

242 candidates, 1738 csp-links and 1738 links. Density = 5.96%

hidden-pairs-in-a-block: b8{n7 n8}{r8c6 r9c5} ==> r9c5 ≠ 9, r9c5 ≠ 6, r9c5 ≠ 5, r9c5 ≠ 3, r8c6 ≠ 9, r8c6 ≠ 6, r8c6 ≠ 5, r8c6 ≠ 3
hidden-pairs-in-a-block: b4{n7 n8}{r4c1 r6c2} ==> r6c2 ≠ 9, r6c2 ≠ 4, r6c2 ≠ 3, r6c2 ≠ 1, r4c1 ≠ 4, r4c1 ≠ 3
hidden-pairs-in-a-block: b1{n6 n7}{r1c2 r3c1} ==> r3c1 ≠ 1, r1c2 ≠ 4, r1c2 ≠ 3, r1c2 ≠ 1
swordfish-in-columns: n5{c3 c4 c9}{r8 r9 r1} ==> r9c7 ≠ 5, r8c7 ≠ 5, r1c7 ≠ 5, r1c6 ≠ 5, r1c5 ≠ 5
swordfish-in-rows: n7{r3 r4 r8}{c7 c1 c6} ==> r9c7 ≠ 7, r6c6 ≠ 7, r1c7 ≠ 7
swordfish-in-columns: n2{c3 c4 c9}{r3 r1 r6} ==> r6c8 ≠ 2, r6c7 ≠ 2, r6c6 ≠ 2, r3c7 ≠ 2, r3c6 ≠ 2, r1c8 ≠ 2, r1c7 ≠ 2, r1c6 ≠ 2
swordfish-in-rows: n4{r2 r5 r7}{c2 c7 c1} ==> r6c7 ≠ 4, r4c7 ≠ 4, r1c7 ≠ 4
hidden-pairs-in-a-block: b3{n4 n5}{r1c9 r2c7} ==> r2c7 ≠ 9, r2c7 ≠ 2, r2c7 ≠ 1, r1c9 ≠ 2
hidden-triplets-in-a-column: c7{n2 n4 n5}{r7 r5 r2} ==> r7c7 ≠ 9, r7c7 ≠ 6, r7c7 ≠ 3, r5c7 ≠ 9, r5c7 ≠ 3, r5c7 ≠ 1
hidden-triplets-in-a-row: r1{n2 n4 n5}{c4 c3 c9} ==> r1c4 ≠ 6, r1c4 ≠ 3, r1c3 ≠ 3, r1c3 ≠ 1
whip[1]: r1n3{c6 .} ==> r2c5 ≠ 3, r2c6 ≠ 3
jellyfish-in-columns: n3{c3 c9 c4 c7}{r9 r8 r6 r4} ==> r9c2 ≠ 3, r8c2 ≠ 3, r8c1 ≠ 3, r6c6 ≠ 3, r6c5 ≠ 3, r4c6 ≠ 3
naked-triplets-in-a-block: b5{r4c6 r6c5 r6c6}{n6 n7 n9} ==> r6c4 ≠ 9, r6c4 ≠ 6, r5c6 ≠ 9, r5c5 ≠ 9, r4c4 ≠ 9, r4c4 ≠ 6
naked-triplets-in-a-row: r4{c3 c4 c9}{n9 n3 n4} ==> r4c7 ≠ 9, r4c7 ≠ 3, r4c6 ≠ 9
whip[1]: b5n9{r6c6 .} ==> r6c3 ≠ 9, r6c7 ≠ 9, r6c8 ≠ 9, r6c9 ≠ 9
jellyfish-in-columns: n9{c3 c9 c4 c7}{r9 r4 r8 r3} ==> r9c8 ≠ 9, r9c2 ≠ 9, r8c2 ≠ 9, r3c6 ≠ 9
naked-triplets-in-a-block: b7{r8c1 r8c2 r9c2}{n8 n1 n6} ==> r8c3 ≠ 1, r7c2 ≠ 6, r7c1 ≠ 6
naked-triplets-in-a-column: c1{r2 r5 r7}{n3 n1 n4} ==> r8c1 ≠ 1
hidden-single-in-a-block ==> r8c2 = 1
naked-triplets-in-a-row: r9{c2 c5 c8}{n6 n8 n7} ==> r9c7 ≠ 6, r9c4 ≠ 6
x-wing-in-columns: n6{c1 c4}{r3 r8} ==> r8c7 ≠ 6, r3c6 ≠ 6
whip[1]: b9n6{r9c8 .} ==> r6c8 ≠ 6
swordfish-in-columns: n8{c2 c5 c8}{r6 r9 r1} ==> r6c7 ≠ 8, r1c7 ≠ 8, r1c6 ≠ 8
naked-single ==> r1c7 = 1
naked-pairs-in-a-block: b3{r2c8 r3c9}{n2 n9} ==> r3c7 ≠ 9
whip[1]: c7n9{r9 .} ==> r7c8 ≠ 9, r8c9 ≠ 9
PUZZLE NOT SOLVED. 57 VALUES MISSING.

Code: Select all

CURRENT RESOLUTION STATE:
   9         67        24        25        368       36        1         78        45       
   134       34        8         7         59        1259      45        29        6         
   67        5         12        269       4         18        78        3         29       
   78        2         349       34        1         67        68        5         349       
   134       349       6         8         35        235       24        129       7         
   5         78        134       234       679       69        36        18        234       
   34        349       7         1         3569      3569      25        26        8         
   68        1         359       3569      2         78        379       4         35       
   2         68        359       359       78        4         39        67        1         

At this point, a single bivalue-chain-rc[3] - an xy-chain[3] - solves the puzzle:

Code: Select all

biv-chain-rc[3]: r1c4{n2 n5} - r2c5{n5 n9} - r2c8{n9 n2} ==> r2c6 ≠ 2
stte

[mith]

Hmmm, delicious, lots of fishes.

What's the deal with all these fish, anyway? Isn't this supposed to be a desert planet?

[Hajime]

What's the deal with all these fish, anyway? Isn't this supposed to be a desert planet?

Oopsy daisy. I just wanted to express my appreciation for your puzzle. A lovely puzzle with a lot of fishes: X-wing, Swordfish and Jellyfish needed to solve it.

Code: Select all

Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    67
Naked Singles      |   0.1 |    41
Hidden Singles     |   0.2 |    38
Naked Single  [1]  |   2.5 |     1
Naked Triple  [3]  |   3.6 |    15
Naked Quad    [4]  |     5 |    22
Hidden Quad   [5]  |   5.4 |     8
Hidden Triple [6]  |     4 |     6
Locked Singles[2]  |   2.8 |     9
X-Wing        [2]  |   3.2 |     2
Swordfish     [3]  |   3.8 |    22
Jellyfish     [4]  |   5.2 |    10
XY-Wing       [3]  |   4.1 |     1
                   |-------|------
Eliminated Cand's  |   242 |   242
Sum(SER * Cand's)  | 416.7 | 416.7

Initial Candidates :   242
Maximum SER rating :   5.4 <- Approach
Labour rating      : 416.7 <- Experimental rating
Time needed        : 00:00:02.375

[x] expresses the size of the method
So 2 candidates eliminations byX-wing (1x) , 22 eliminations by Swordfishes (5x) and 10 eliminations by Jellyfishes (2x).
And also XY-chain needed to eliminate that last candidate (-2r2c6) as in previous post is also stated, before stte.
Great puzzle, sorry if you feel offended.

[mith]

Oh, no, not offended at all. Just being silly. I name so many of these puzzles after a desert planet, even though they always have a ton of fish in them.

[pjb]

4 fish and 2 chains:
Swordfish of 2s (r257\c678) => -2 r1c6, r1c78, r3c67, r6c678
Swordfish of 4s (r257\c127) => -4 r146c7
Swordfish of 5s (r257\c567) => -5 r1c567, r89c7
Jellyfish of 3s (r1257\c1256) => -3 r4c6, r6c56, r8c12, r9c2
(5=2)r1c4 - (2=5)r4c4, r5c5, r6c4 => -5 r2c5
((2)r2c8 = (2-9)r3c9 = (9-8)r3c7 = (8)r3c6 - (8=7)r8c6 - (7)r4c6 = (7)r4c1 - (7=6)r3c1 - (6=2)r3c4 => -2 r2c6, r3c9; stte

Phil

[RSW]

Hmmm, delicious, lots of fishes.

What's the deal with all these fish, anyway? Isn't this supposed to be a desert planet?

Maybe they're sandtrout.

[denis_berthier]

Hmmm, delicious, lots of fishes.

What's the deal with all these fish, anyway? Isn't this supposed to be a desert planet?

Maybe they're sandtrout.

Exactly what I was thinking.

[Cenoman]

4 fish and 2 chains:

3 row-fishes (SF 2,4,5 , grouped into a MSLS) and 2 chains:

Code: Select all

 +------------------------+--------------------------+---------------------------+
 |  9      67      1234   |  2356    368-5  1368-25  |  178-245   178-2   245    |
 | <134   <134     8      |  7      <359   <12359    | <12459    <129     6      |139
 |  67     5       12     |  269     4      1689-2   |  1789-2    3       29     |
 +------------------------+--------------------------+---------------------------+
 |  78     2       349    |  3469    1      3679     |  3689-4    5       349    |
 | <134   <1349    6      |  8      <359   <2359     | <12349    <129     7      |139
 |  5      78      1349   |  23469   3679   3679-2   |  13689-24  1689-2  2349   |
 +------------------------+--------------------------+---------------------------+
 | <346   <3469    7      |  1      <3569  <3569     | <23569    <269     8      |369
 |  1368   13689   1359   |  3569    2      78       |  3679-5    4       359    |
 |  2      3689    359    |  3569    78     4        |  3679-5    679     1      |
 +------------------------+--------------------------+---------------------------+
    4       4                        5      25          245       2

1. MSLS 18 cell truths; 18 links 139r25, 369r7, 4c12, 5c5, 25c6, 245c7, 2c8
=> 16 eliminations: -5 r1c5, -25 r1c6, -2 r36c6, -245 r1c7, -2 r3c7, -4 r4c7, -24 r6c7, -5 r89c7, -2 r16c8

Code: Select all

 +------------------------+------------------------+------------------------+
 |  9     E67      24     | e5-2    B368   A368-1  | F178    F178   d45     |
 |  134    134     8      |  7       59     1259   | c45      129    6      |
 |  67     5       12     |  269     4      1689   |  1789    3      29     |
 +------------------------+------------------------+------------------------+
 |  78     2       349    |  3469    1      3679   |  3689    5      349    |
 |  134    1349    6      |  8       359    2359   | c24      129    7      |
 |  5     D78      1349   | a23469  C3679   3679   |  13689   1689  b2349   |
 +------------------------+------------------------+------------------------+
 |  346    3469    7      |  1       3569   3569   |  25      269    8      |
 |  1368   13689   1359   |  3569    2      78     |  3679    4      359    |
 |  2      3689    359    |  3569   B78     4      |  3679    679    1      |
 +------------------------+------------------------+------------------------+

2. (2)r6c4 = r6c9 - (2=45)r25c7 - r1c9 = (5)r1c4 => -2 r1c4
3. (3)r1c6 = (3-87)r19c5 = r6c5 - r6c2 = r1c2 - (7=81)r1c78 => -1 r1c6; ste

[pjb]

Cenoman wrote:

3 row-fishes (SF 2,4,5 , grouped into a MSLS) and 2 chains:

Impressed. I clearly need to add 3 x 6 MSLSs to my repertoire

Phil

[AnotherLife]

It is possible to solve this puzzle in 3 main steps but I still doubt if we can consider a forcing chain (especially, a forcing net) as one step. Also, the solution is complicated and adverse to human nature.

After the basics (3 hidden pairs) we have:
1. Swordfish: 7 r348 c167 => r19c7,r6c6<>7
2. Swordfish: 2 r257 c678 => r1c678,r3c67,r6c678<>2
The resolution state becomes as follows:

Code: Select all

.-------------------.--------------------.--------------------.
| 9     67     1234 | 2356   3568  13568 | 1458    178   245  |
| 134   134    8    | 7      359   12359 | 12459   129   6    |
| 67    5      12   | 269    4     1689  | 1789    3     29   |
:-------------------+--------------------+--------------------:
| 78    2      349  | 3469   1     3679  | 34689   5     349  |
| 134   1349   6    | 8      359   2359  | 12349   129   7    |
| 5     78     1349 | 23469  3679  369   | 134689  1689  2349 |
:-------------------+--------------------+--------------------:
| 346   3469   7    | 1      3569  3569  | 23569   269   8    |
| 1368  13689  1359 | 3569   2     78    | 35679   4     359  |
| 2     3689   359  | 3569   78    4     | 3569    679   1    |
'-------------------'--------------------'--------------------'


3. Now we can prove that all three possibilities in cell r2c8 lead to r5c1<>4 and r5c2<>4, so r5c7=4. See the picture: https://disk.yandex.ru/i/nSdDHPFbuhxNGQ
3.1. The red chain. r2c8=1 => 4 is locked in the yellow ALS r2c12 => r1c3<>4 => either r4c3=4 or r6c3=4 => r5c12<>4 => r5c7=4.
3.2. The black chain. r2c8=2 => r7c8<>2 => r7c7=2 => r7c7<>5 => either r7c5 or r7c6=5 => r89c4<>5 => r1c4=5 => r1c79<>5 => r2c7=5 => r2c7<>4 => either r1c7=4 or r1c9=4 => r1c3<>4 => either r4c3=4 or r6c3=4 => r5c12<>4 => r5c7=4.
3.3. The green chain. r2c8=9 => 1 is locked in the brown ALS r3c39 => 4 is locked in the pink ALS r4689c3 => r5c12<>4 => r5c7=4.

After these steps, the puzzle is solvable by the basic methods.

[pjb]

For those with an interest in MSLSs, there is another slightly simpler one, resulting in same endpoint as Cenoman's one above:

3-5 MSLS at r257c12568 Links: 139r2 139r5 369r7 4c1 4c2 5c5 25c6 2c8 Eliminations: -1 r2c7, -9 r2c7, -1 r5c7, -3 r5c7, -9 r5c7, -3 r7c7, -6 r7c7, -9 r7c7, -5 r1c5, -2 r1c6, -5 r1c6, -2 r1c8, -2 r3c6, -2 r6c6, -2 r6c8

Phil

[jco]

Hello,

After basics

1. SF(2) r257c678 => -2 r136c6,-2 r136c7,-2 r16c8

2. SF(4) r257c127 => -4 r146c7

3. SF(5) r257c567 => -5 r1c567,-5 r89c7 (+basics)

4. AIC

Code: Select all

  1     2      3      4      5     6      7      8     9
.-------------------+-------------------+-------------------.
| 9     67    a24   | 25     368   1368 | 178    178  b45   | 1
| 134   134    8    | 7      59    1259 |c45     129   6    | 2
| 67    5      1-2  | 269    4     1689 | 1789   3    f29   | 3
|-------------------+-------------------+-------------------|
| 78    2      349  | 3469   1     3679 | 3689   5     349  | 4
| 134   1349   6    | 8      359   2359 |d24     129   7    | 5
| 5     78     1349 | 23469  3679  3679 | 13689  1689 e2349 | 6
|-------------------+-------------------+-------------------|
| 346   3469   7    | 1      3569  3569 | 25     269   8    | 7
| 1368  13689  1359 | 3569   2     78   | 3679   4     359  | 8
| 2     3689   359  | 3569   78    4    | 3679   679   1    | 9
'-------------------+-------------------+-------------------'


(2=4)r1c3-r1c9=r2c7-(4=2)r5c7-r6c9=(2)r3c9 => -2 r3c3

5. SF(7) r348c167 => -7 r6c6,-7 r19c7; lclste

Regards,
jco
EDIT: improved writing adding lclste