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[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . 9 | 8 . . | . . 7 |
| . 8 . | . 6 . | . 5 . |
+-------+-------+-------+
| . 6 . | . 5 . | . 4 . |
| . . 3 | 9 . . | . . 8 |
| . . . | . . 4 | 3 . . |
+-------+-------+-------+
| . 5 . | . 4 . | . 6 . |
| . 2 8 | 7 . . | . . 3 |
| . . . | . . . | 7 . . |
+-------+-------+-------+
...........98....7.8..6..5..6..5..4...39....8.....43...5..4..6..287....3......7..

[Leren]

Code: Select all

*----------------------------------------------------------------------*
| 1234567 1347  12456-7 | 1245-3 12379 123579  | 1246-89 12389  1246-9 |
| 123456  134   9       | 8      123   1235    | 1246    123    7      |
| 37-124  8    *1247    |*1234   6     379-12  |*1249    5     *1249   |
|-----------------------+----------------------+-----------------------|
| 789-12  6    *127     |*123    5     378-12  |*129     4     *129    |
| 12457   147   3       | 9      127   1267    | 56      127    8      |
| 125789  179   125-7   | 126    1278  4       | 3       1279   56     |
|-----------------------+----------------------+-----------------------|
| 379-1   5    *17      |*123    4     389-12  |*1289    6     *129    |
| 46      2     8       | 7      19    56      | 45      19     3      |
| 13469   1349  146     | 1256-3 12389 1235689 | 7       1289   45     |
*----------------------------------------------------------------------*

MSLS : 12 Truths; r347 c3479 : 12 Links; 124r3 12r4 12r7 ; 7c3 3c4 89c7 9c9 ; 19 Eliminations as marked; btte

Leren

[denis_berthier]

.
1) Simplest-first solution, with no step harder than 5, displaying what the puzzle was obviously designed for, i.e. a lot of Subsets (19)
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
Starting RESOLUTION STATE:

Code: Select all

   1234567   1347      124567    12345     12379     123579    124689    12389     12469
   123456    134       9         8         123       1235      1246      123       7
   12347     8         1247      1234      6         12379     1249      5         1249
   12789     6         127       123       5         12378     129       4         129
   12457     147       3         9         127       1267      1256      127       8
   125789    179       1257      126       1278      4         3         1279      12569
   1379      5         17        123       4         12389     1289      6         129
   1469      2         8         7         19        1569      1459      19        3
   13469     1349      146       12356     12389     1235689   7         1289      12459
246 candidates, 1887 csp-links and 1887 links. Density = 6.26%

naked-pairs-in-a-row: r8{c5 c8}{n1 n9} ==> r8c7 ≠ 9, r8c7 ≠ 1, r8c6 ≠ 9, r8c6 ≠ 1, r8c1 ≠ 9, r8c1 ≠ 1
hidden-pairs-in-a-block: b9{n4 n5}{r8c7 r9c9} ==> r9c9 ≠ 9, r9c9 ≠ 2, r9c9 ≠ 1
hidden-pairs-in-a-block: b6{n5 n6}{r5c7 r6c9} ==> r6c9 ≠ 9, r6c9 ≠ 2, r6c9 ≠ 1, r5c7 ≠ 2, r5c7 ≠ 1
finned-x-wing-in-rows: n4{r8 r2}{c7 c1} ==> r3c1 ≠ 4, r1c1 ≠ 4
swordfish-in-columns: n4{c3 c4 c9}{r9 r3 r1} ==> r9c2 ≠ 4, r9c1 ≠ 4, r3c7 ≠ 4, r1c7 ≠ 4, r1c2 ≠ 4
swordfish-in-columns: n5{c3 c4 c9}{r6 r1 r9} ==> r9c6 ≠ 5, r6c1 ≠ 5, r1c6 ≠ 5, r1c1 ≠ 5
swordfish-in-columns: n7{c2 c5 c8}{r6 r1 r5} ==> r6c3 ≠ 7, r6c1 ≠ 7, r5c6 ≠ 7, r5c1 ≠ 7, r1c6 ≠ 7, r1c3 ≠ 7, r1c1 ≠ 7
swordfish-in-rows: n3{r3 r4 r7}{c1 c6 c4} ==> r9c6 ≠ 3, r9c4 ≠ 3, r9c1 ≠ 3, r2c6 ≠ 3, r2c1 ≠ 3, r1c6 ≠ 3, r1c4 ≠ 3, r1c1 ≠ 3
swordfish-in-rows: n6{r2 r5 r8}{c1 c7 c6} ==> r9c6 ≠ 6, r9c1 ≠ 6, r1c7 ≠ 6, r1c1 ≠ 6
hidden-pairs-in-a-block: b1{n5 n6}{r1c3 r2c1} ==> r2c1 ≠ 4, r2c1 ≠ 2, r2c1 ≠ 1, r1c3 ≠ 4, r1c3 ≠ 2, r1c3 ≠ 1
hidden-pairs-in-a-block: b7{n4 n6}{r8c1 r9c3} ==> r9c3 ≠ 1
hidden-pairs-in-a-block: b8{n5 n6}{r8c6 r9c4} ==> r9c4 ≠ 2, r9c4 ≠ 1
hidden-triplets-in-a-column: c1{n4 n5 n6}{r8 r5 r2} ==> r5c1 ≠ 2, r5c1 ≠ 1
hidden-triplets-in-a-row: r1{n4 n5 n6}{c9 c4 c3} ==> r1c9 ≠ 9, r1c9 ≠ 2, r1c9 ≠ 1, r1c4 ≠ 2, r1c4 ≠ 1
naked-triplets-in-a-column: c9{r1 r6 r9}{n4 n6 n5} ==> r3c9 ≠ 4
hidden-pairs-in-a-block: b3{n4 n6}{r1c9 r2c7} ==> r2c7 ≠ 2, r2c7 ≠ 1
swordfish-in-rows: n2{r2 r5 r9}{c8 c6 c5} ==> r7c6 ≠ 2, r6c8 ≠ 2, r6c5 ≠ 2, r4c6 ≠ 2, r3c6 ≠ 2, r1c8 ≠ 2, r1c6 ≠ 2, r1c5 ≠ 2
biv-chain[4]: r4n8{c1 c6} - c5n8{r6 r9} - r9n3{c5 c2} - c2n9{r9 r6} ==> r4c1 ≠ 9
whip[1]: r4n9{c9 .} ==> r6c8 ≠ 9
z-chain[5]: r6n5{c3 c9} - r6n6{c9 c4} - r6n2{c4 c1} - r4c3{n2 n7} - r7c3{n7 .} ==> r6c3 ≠ 1
finned-swordfish-in-columns: n1{c3 c9 c4}{r3 r7 r4} ==> r4c6 ≠ 1
t-whip[5]: c8n9{r9 r1} - r3n9{c9 c6} - c6n7{r3 r4} - c6n3{r4 r7} - r7n8{c6 .} ==> r7c7 ≠ 9
t-whip[5]: r4n3{c4 c6} - r4n8{c6 c1} - r4n7{c1 c3} - r7n7{c3 c1} - r7n3{c1 .} ==> r3c4 ≠ 3
z-chain[4]: r3n3{c1 c6} - r3n7{c6 c3} - r7n7{c3 c1} - c1n3{r7 .} ==> r3c1 ≠ 2
z-chain[4]: r3n3{c1 c6} - r3n7{c6 c3} - r7n7{c3 c1} - c1n3{r7 .} ==> r3c1 ≠ 1
t-whip[4]: r3n9{c9 c6} - b2n7{r3c6 r1c5} - b2n3{r1c5 r2c5} - c8n3{r2 .} ==> r1c8 ≠ 9
whip[1]: c8n9{r9 .} ==> r7c9 ≠ 9
biv-chain[3]: r8c5{n1 n9} - b9n9{r8c8 r9c8} - r9c1{n9 n1} ==> r9c5 ≠ 1, r9c6 ≠ 1
biv-chain[3]: r9c1{n1 n9} - r7n9{c1 c6} - r1c6{n9 n1} ==> r1c1 ≠ 1
naked-single ==> r1c1 = 2
hidden-triplets-in-a-row: r6{n2 n5 n6}{c4 c3 c9} ==> r6c4 ≠ 1
swordfish-in-columns: n1{c3 c4 c9}{r3 r4 r7} ==> r7c7 ≠ 1, r7c6 ≠ 1, r7c1 ≠ 1, r4c7 ≠ 1, r4c1 ≠ 1, r3c7 ≠ 1, r3c6 ≠ 1
stte



2) Single-step solution:
FORCING{3}-T&E(W1) applied to trivalue candidates n3r1c5, n3r2c5 and n3r9c5 :
===> 1 values decided in the three cases: n2r7c9
===> 118 candidates eliminated in the three cases: n3r1c1 n4r1c1 n6r1c1 n7r1c1 n1r1c2 n4r1c2 n1r1c3 n2r1c3 n4r1c3 n7r1c3 n1r1c4 n2r1c4 n3r1c4 n1r1c5 n2r1c5 n1r1c6 n2r1c6 n3r1c6 n5r1c6 n7r1c6 n4r1c7 n6r1c7 n9r1c7 n1r1c8 n2r1c8 n9r1c8 n1r1c9 n2r1c9 n9r1c9 n1r2c1 n2r2c1 n3r2c1 n3r2c2 n1r2c5 n3r2c6 n2r2c7 n4r2c7 n1r2c8 n2r2c8 n1r3c1 n2r3c1 n4r3c1 n4r3c3 n7r3c3 n2r3c4 n3r3c4 n1r3c6 n2r3c6 n9r3c6 n1r3c7 n1r3c9 n2r3c9 n1r4c1 n2r4c1 n9r4c1 n1r4c3 n1r4c4 n2r4c4 n1r4c6 n2r4c6 n1r4c7 n2r4c9 n1r5c1 n7r5c1 n7r5c2 n2r5c5 n1r5c6 n7r5c6 n1r5c7 n2r5c7 n2r6c1 n5r6c1 n7r6c1 n1r6c2 n2r6c3 n7r6c3 n1r6c4 n2r6c5 n7r6c5 n1r6c8 n9r6c8 n1r6c9 n2r6c9 n9r6c9 n1r7c1 n2r7c4 n2r7c6 n9r7c6 n1r7c7 n2r7c7 n9r7c7 n1r7c9 n9r7c9 n1r8c1 n9r8c1 n1r8c6 n9r8c6 n1r8c7 n9r8c7 n3r9c1 n4r9c1 n6r9c1 n4r9c2 n9r9c2 n1r9c3 n1r9c4 n3r9c4 n5r9c4 n1r9c5 n9r9c5 n1r9c6 n3r9c6 n5r9c6 n9r9c6 n1r9c8 n2r9c8 n2r9c9 n9r9c9
stte

[Cenoman]

Code: Select all

 +----------------------------+----------------------------+---------------------------+
 |  1234567   1347   12456-7  |  1245-3  12379   123579    |  12468-9  12389   1246-9  |
 |  123456    134    9        |  8       123     1235      |  1246     123     7       |
 |  37-124    8     *1247     | *1234    6       379-12    | *1249     5      *1249    |
 +----------------------------+----------------------------+---------------------------+
 |  789-12    6     *127      | *123     5       378-12    | *129      4      *129     |
 |  12457     147    3        |  9       127     1267      |  56       127     8       |
 |  125789    179    125-7    |  126     1278    4         |  3        1279    56      |
 +----------------------------+----------------------------+---------------------------+
 |  379-1     5     *17       | *123     4       389-12    |  8-129    6      *129     |
 |  46        2      8        |  7       19      56        |  45       19      3       |
 |  13469     1349   146      |  1256-3  12389   1235689   |  7        1289    45      |
 +----------------------------+----------------------------+---------------------------+

The 11 cells tagged "*" can contain instances of only 6 digits (1,2,3,4,7,9)
3,4,7 can be there only once; 9 can be there at most twice; 1,2 can be there at most thrice
=> all six digits must be there at their maximum ability.
So, the 11 cells contain digits 1 & 2 in each of rows r347, digit 9 in each of columns c79, digits 3, 4, 7 in c4, r3, c3 resp. => 21 eliminations shown in the PMs, lclste.

Another presentation of the same:
MSLS 11 truths, cells r34c3479, r7c349; 11 links: 12r349, 4r3, 7c3, 3c4, 9c79; same eliminations.

It is quite the same MSLS as Leren's (cell r7c7 less).