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[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 9 . | 8 . 5 | . . . |
| . . 4 | . 7 . | 5 . . |
+-------+-------+-------+
| . 5 . | 6 . 9 | . 7 . |
| . . 3 | . 2 . | . . . |
| . 6 . | . . 7 | . 8 . |
+-------+-------+-------+
| . . 5 | . 3 . | 4 . . |
| . 8 . | 7 . 6 | . 9 . |
| . . . | . . . | . . . |
+-------+-------+-------+
..........9.8.5.....4.7.5...5.6.9.7...3.2.....6...7.8...5.3.4...8.7.6.9..........

[denis_berthier]

.
A lot of Subsets, as expected:

solution using only Subsets: Show

***********************************************************************************************
*** 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
***********************************************************************************************
hidden-single-in-a-block ==> r6c4 = 3
hidden-single-in-a-row ==> r1c1 = 5

Code: Select all

Starting non trivial part of solution with the following RESOLUTION STATE:
   5         1237      12678     1249      1469      1234      1236789   12346     12346789 
   12367     9         1267      8         146       5         12367     12346     123467   
   12368     123       4         129       7         123       5         1236      123689   
   1248      5         128       6         148       9         123       7         1234     
   14789     147       3         145       2         148       169       1456      14569     
   1249      6         129       3         145       7         129       8         12459     
   12679     127       5         129       3         128       4         126       12678     
   1234      8         12        7         145       6         123       9         1235     
   1234679   12347     12679     12459     14589     1248      123678    12356     1235678   
243 candidates, 1854 csp-links and 1854 links. Density = 6.31%

x-wing-in-rows: n5{r6 r8}{c5 c9} ==> r9c9 ≠ 5, r9c5 ≠ 5, r5c9 ≠ 5
swordfish-in-columns: n4{c2 c4 c6}{r9 r5 r1} ==> r9c5 ≠ 4, r9c1 ≠ 4, r5c9 ≠ 4, r5c8 ≠ 4, r5c1 ≠ 4, r1c9 ≠ 4, r1c8 ≠ 4, r1c5 ≠ 4
hidden-single-in-a-column ==> r2c8 = 4
swordfish-in-columns: n3{c2 c6 c8}{r9 r1 r3} ==> r9c9 ≠ 3, r9c7 ≠ 3, r9c1 ≠ 3, r3c9 ≠ 3, r3c1 ≠ 3, r1c9 ≠ 3, r1c7 ≠ 3
hidden-pairs-in-a-block: b7{n3 n4}{r8c1 r9c2} ==> r9c2 ≠ 7, r9c2 ≠ 2, r9c2 ≠ 1, r8c1 ≠ 2, r8c1 ≠ 1
swordfish-in-rows: n8{r3 r5 r7}{c9 c1 c6} ==> r9c9 ≠ 8, r9c6 ≠ 8, r4c1 ≠ 8, r1c9 ≠ 8
jellyfish-in-columns: n2{c2 c8 c4 c6}{r7 r3 r9 r1} ==> r9c9 ≠ 2, r9c7 ≠ 2, r9c3 ≠ 2, r9c1 ≠ 2, r7c9 ≠ 2, r7c1 ≠ 2, r3c9 ≠ 2, r3c1 ≠ 2, r1c9 ≠ 2, r1c7 ≠ 2, r1c3 ≠ 2
hidden-quads-in-a-column: c9{n2 n3 n5 n4}{r4 r2 r8 r6} ==> r8c9 ≠ 1, r6c9 ≠ 9, r6c9 ≠ 1, r4c9 ≠ 1, r2c9 ≠ 7, r2c9 ≠ 6, r2c9 ≠ 1
hidden-quads-in-a-row: r9{n2 n4 n3 n5}{c4 c6 c2 c8} ==> r9c8 ≠ 6, r9c8 ≠ 1, r9c6 ≠ 1, r9c4 ≠ 9, r9c4 ≠ 1
jellyfish-in-columns: n1{c2 c4 c6 c8}{r1 r3 r5 r7} ==> r7c9 ≠ 1, r7c1 ≠ 1, r5c9 ≠ 1, r5c7 ≠ 1, r5c1 ≠ 1, r3c9 ≠ 1, r3c1 ≠ 1, r1c9 ≠ 1, r1c7 ≠ 1, r1c5 ≠ 1, r1c3 ≠ 1
hidden-single-in-a-column ==> r9c9 = 1
naked-pairs-in-a-block: b6{r5c7 r5c9}{n6 n9} ==> r6c7 ≠ 9, r5c8 ≠ 6
whip[1]: r6n9{c3 .} ==> r5c1 ≠ 9
hidden-pairs-in-a-block: b7{n1 n2}{r7c2 r8c3} ==> r7c2 ≠ 7
hidden-pairs-in-a-block: b9{n7 n8}{r7c9 r9c7} ==> r9c7 ≠ 6, r7c9 ≠ 6
hidden-single-in-a-block ==> r7c8 = 6
hidden-pairs-in-a-row: r3{n6 n8}{c1 c9} ==> r3c9 ≠ 9
stte

[pjb]

A 5x4 msls :
r24689 c1357; 20 links: 67r2, 8r4, 9r6, r8, 6789r9, 1234c1, 12c3, 145c5, 123c7
24 Eliminations: -6 r2c89, -7 r2c9, -9 r6c9, -7 r9c2, -8 r9c6, -6 r9c89, -78 r9c9, -123 r3c1, -1 r5c1, -12 r7c1, -12 r1c3, -14 r1c5, -123 r1c7, -1 r5c7; btte

Code: Select all

 5        1237    12678  | 1249   1469   1234   | 123678912346  12346789
<123/67>  9      <12/67> | 8     <14/6>  5      |<123/67>12346  123467
 12368    123     4      | 129    7      123    | 5      1236   123689
-------------------------+----------------------+---------------------
<124/8>   5      <12/8>  | 6     <14/8>  9      |<123>   7      1234   
 14789    147     3      | 145    2      148    | 169    1456   14569 
<124/9>   6      <12/9>  | 3     <145>   7      |<12/9>  8      12459 
-------------------------+----------------------+---------------------
 12679    127     5      | 129    3      128    | 4      126    12678 
<1234>    8      <12>    | 7     <145>   6      |<123>   9      1235   
<1234/679>12347  <12/679>| 12459 <145/89>1248   |<123/678>2356  1235678

There is also a multifish:

19 Truths = {6789R1, 689R3, 6789R5, 6789R7, 6789R9}
19 Links = {7c2, 9c4, 8c6, 6c8, 6c9, 7c9, 8c9, 9c9, 1n3, 1n5, 1n7, 3n1, 5n1, 5n7, 7n1, 9n1, 9n3, 9n5, 9n7}
31 Eliminations: r1c3<>1, r1c3<>2, r1c5<>1, r1c5<>4, r1c7<>1, r1c7<>2, r1c7<>3, r3c1<>1, r3c1<>2, r3c1<>3, r5c1<>1, r5c1<>4, r5c7<>1, r7c1<>1, r7c1<>2, r9c1<>1, r9c1<>2, r9c1<>3, r9c1<>4, r9c3<>1, r9c3<>2, r9c5<>1, r9c5<>4, r9c5<>5, r9c7<>1, r9c7<>2, r9c7<>3, r2c8<>6, r2c9<>6, r2c9<>7, r6c9<>9; btte


Phil

[yzfwsf]

MSLS:16 Cells r1357c2468, 16 Links 1234r1,123r3,145r5,12r7,17c2,19c4,18c6,16c8(Digit 1 can be permutated)
37 Eliminations:r1c3579,r357c19,r9c2468,r2c8,r5c7<>1,r1c379,r37c19<>2,r1c79,r3c19<>3,r1c59,r5c19<>4,r5c9<>5,r29c8<>6,r9c2<>7,r9c6<>8,r9c4<>9

[yzfwsf]

My solver has implemented the multifish technique.

Code: Select all

,-----------------------,--------------------,--------------------------,
| 5        1237   12678 | 1249   1469   1234 | 1236789  12346  12346789 |
| 12367    9      1267  | 8      146    5    | 12367    12346  123467   |
| 12368    123    4     | 129    7      123  | 5        1236   123689   |
:-----------------------+--------------------+--------------------------:
| 1248     5      128   | 6      148    9    | 123      7      1234     |
| 14789    147    3     | 145    2      148  | 169      1456   14569    |
| 1249     6      129   | 3      145    7    | 129      8      12459    |
:-----------------------+--------------------+--------------------------:
| 12679    127    5     | 129    3      128  | 4        126    12678    |
| 1234     8      12    | 7      145    6    | 123      9      1235     |
| 1234679  12347  12679 | 12459  14589  1248 | 123678   2356   1235678  |
'-----------------------'--------------------'--------------------------'

Multi-Fish: 15 Trueth:6789c1,6789c3,689c5,6789c7,15 Links:67r2,8r4,9r6,6789r9+r1c357,r357c1,r5c7 => 38 eliminations
r1c3<>12, r1c5<>14, r1c7<>123, r3c1<>123, r5c1<>14, r5c7<>1, r7c1<>12, r2c8<>6, r2c9<>67, r6c9<>9, r9c2<>7, r9c4<>9, r9c6<>8, r9c8<>6, r9c9<>678, r9c1<>1234, r9c3<>12, r9c5<>145, r9c7<>123