The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . 9 | . . . | . . . |
| 8 . . | . . 7 | 6 . . |
| . 5 . | . 4 . | . 3 . |
+-------+-------+-------+
| . 3 . | . 5 . | . 4 . |
| 2 . . | . . 6 | 8 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . 1 | 3 2 . | . . . |
| 6 . . | . . 8 | 7 . . |
| . 4 . | . . . | . 5 . |
+-------+-------+-------+
..9......8....76...5..4..3..3..5..4.2....68.............132....6....87...4.....5.

[denis_berthier]

One more champion of Subsets.

Code: Select all

(solve "..9......8....76...5..4..3..3..5..4.2....68.............132....6....87...4.....5.")
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
***  Using CLIPS 6.32-r770
***********************************************************************************************
232 candidates, 1601 csp-links and 1601 links. Density = 5.97%
whip[1]: r7n6{c9 .} ==> r9c9 ≠ 6
whip[1]: r7n7{c2 .} ==> r9c3 ≠ 7, r9c1 ≠ 7
naked-pairs-in-a-block: b8{r8c5 r9c6}{n1 n9} ==> r9c5 ≠ 9, r9c5 ≠ 1, r9c4 ≠ 9, r9c4 ≠ 1, r8c4 ≠ 9, r8c4 ≠ 1, r7c6 ≠ 9
hidden-pairs-in-a-block: b1{r1c1 r2c3}{n3 n4} ==> r2c3 ≠ 2, r1c1 ≠ 7, r1c1 ≠ 1
naked-triplets-in-a-row: r8{c2 c5 c8}{n2 n9 n1} ==> r8c9 ≠ 9, r8c9 ≠ 2, r8c9 ≠ 1, r8c3 ≠ 2
naked-triplets-in-a-column: c6{r3 r4 r9}{n9 n2 n1} ==> r6c6 ≠ 9, r6c6 ≠ 2, r6c6 ≠ 1, r1c6 ≠ 2, r1c6 ≠ 1
swordfish-in-columns: n3{c1 c6 c7}{r9 r1 r6} ==> r9c9 ≠ 3, r9c3 ≠ 3, r6c9 ≠ 3, r6c5 ≠ 3, r1c5 ≠ 3
swordfish-in-columns: n8{c2 c5 c8}{r7 r6 r1} ==> r7c9 ≠ 8, r6c4 ≠ 8, r6c3 ≠ 8, r1c9 ≠ 8, r1c4 ≠ 8
swordfish-in-columns: n5{c1 c6 c7}{r6 r7 r1} ==> r6c9 ≠ 5, r6c3 ≠ 5, r1c9 ≠ 5, r1c4 ≠ 5
hidden-pairs-in-a-block: b6{r5c9 r6c7}{n3 n5} ==> r6c7 ≠ 9, r6c7 ≠ 2, r6c7 ≠ 1, r5c9 ≠ 9, r5c9 ≠ 7, r5c9 ≠ 1
swordfish-in-rows: n4{r2 r5 r8}{c9 c3 c4} ==> r7c9 ≠ 4, r6c4 ≠ 4, r6c3 ≠ 4, r1c9 ≠ 4
hidden-pairs-in-a-block: b3{r1c7 r2c9}{n4 n5} ==> r2c9 ≠ 9, r2c9 ≠ 2, r2c9 ≠ 1, r1c7 ≠ 2, r1c7 ≠ 1
hidden-pairs-in-a-block: b4{r5c3 r6c1}{n4 n5} ==> r6c1 ≠ 9, r6c1 ≠ 7, r6c1 ≠ 1, r5c3 ≠ 7
swordfish-in-columns: n1{c1 c6 c7}{r3 r4 r9} ==> r9c9 ≠ 1, r4c9 ≠ 1, r4c4 ≠ 1, r3c9 ≠ 1, r3c4 ≠ 1
swordfish-in-columns: n2{c3 c6 c7}{r9 r3 r4} ==> r9c9 ≠ 2, r4c9 ≠ 2, r4c4 ≠ 2, r3c9 ≠ 2, r3c4 ≠ 2
hidden-pairs-in-a-column: c9{n1 n2}{r1 r6} ==> r6c9 ≠ 9, r6c9 ≠ 7, r6c9 ≠ 6, r1c9 ≠ 7
hidden-pairs-in-a-block: b3{r1c8 r3c9}{n7 n8} ==> r3c9 ≠ 9, r1c8 ≠ 2, r1c8 ≠ 1
hidden-pairs-in-a-block: b9{r8c8 r9c7}{n1 n2} ==> r9c7 ≠ 9, r9c7 ≠ 3, r8c8 ≠ 9
singles ==> r8c9 = 3, r5c9 = 5, r2c9 = 4, r1c7 = 5, r1c6 = 3, r1c1 = 4, r6c1 = 5, r6c6 = 4, r7c6 = 5, r8c4 = 4, r2c3 = 3, r5c3 = 4, r6c7 = 3, r8c3 = 5, r2c4 = 5, r7c7 = 4, r9c1 = 3, r5c5 = 3
naked-pairs-in-a-column: c5{r2 r8}{n1 n9} ==> r6c5 ≠ 9, r6c5 ≠ 1, r1c5 ≠ 1
x-wing-in-columns: n2{c4 c9}{r1 r6} ==> r6c8 ≠ 2, r1c2 ≠ 2
jellyfish-in-columns: n9{c1 c7 c6 c9}{r7 r4 r3 r9} ==> r7c8 ≠ 9, r7c2 ≠ 9, r4c4 ≠ 9, r3c4 ≠ 9
whip[1]: c4n9{r6 .} ==> r4c6 ≠ 9
whip[1]: b9n9{r9c9 .} ==> r4c9 ≠ 9
naked-pairs-in-a-block: b2{r1c5 r3c4}{n6 n8} ==> r1c4 ≠ 6
naked-pairs-in-a-row: r1{c4 c9}{n1 n2} ==> r1c2 ≠ 1
naked-pairs-in-a-block: b5{r4c4 r6c5}{n7 n8} ==> r6c4 ≠ 7, r5c4 ≠ 7
x-wing-in-rows: n7{r1 r5}{c2 c8} ==> r7c2 ≠ 7, r6c8 ≠ 7, r6c2 ≠ 7
stte

[mith]

Yep. One of the swordfish and one of the x-wings is not needed. There is also an alternative solution that bypasses the jellyfish and x-wings.

[denis_berthier]

Yep. One of the swordfish and one of the x-wings is not needed. There is also an alternative solution that bypasses the jellyfish and x-wings.

I have a solution with no Jellyfish, but it has finned-x-wings:

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
same as above until the x-wing-in-columns: n2{c4 c9}{r1 r6} ==> r6c8 ≠ 2, r1c2 ≠ 2
finned-x-wing-in-columns: n9{c1 c9}{r4 r7} ==> r7c8 ≠ 9
whip[1]: b9n9{r9c9 .} ==> r4c9 ≠ 9
finned-x-wing-in-columns: n9{c7 c4}{r3 r4} ==> r4c6 ≠ 9
whip[1]: b5n9{r6c4 .} ==> r3c4 ≠ 9
naked-pairs-in-a-block: b2{r1c5 r3c4}{n6 n8} ==> r1c4 ≠ 6
naked-pairs-in-a-row: r1{c4 c9}{n1 n2} ==> r1c2 ≠ 1
finned-x-wing-in-columns: n7{c9 c3}{r3 r4} ==> r4c1 ≠ 7
naked-triplets-in-a-row: r4{c1 c6 c7}{n9 n1 n2} ==> r4c4 ≠ 9
naked-pairs-in-a-block: b5{r4c4 r6c5}{n7 n8} ==> r6c4 ≠ 7, r5c4 ≠ 7
x-wing-in-rows: n7{r1 r5}{c2 c8} ==> r7c2 ≠ 7, r6c8 ≠ 7, r6c2 ≠ 7
stte

[Leren]

Multifish 1: 20 Truths = { 1345R1 1345R2 1345R5 1345R6 1345R8 } 20 Links = { 1c24589 3c359 4c349 5c349 1n167 6n167 } 13 eliminations
Multifish 1: 19 Truths = { 2345R1 2345R2 345R5 2345R6 2345R8 } 19 Links = { 2c2489 3c359 4c349 5c349 1n167 6n167 } 8 eliminations
basics.

Code: Select all

*-------------------------------------------------*
| 4    1267  9   | 1268   68 3   | 5    78    12  |
| 8   a12    3   | 5     b19 7   | 6    19-2  4   |
| 17   5     267 | 689    4  129 | 129  3     78  |
|----------------+---------------+----------------|
| 179  3     678 | 789    5  129 | 129  4     679 |
| 2    179   4   | 179    3  6   | 8    179   5   |
| 5    16789 678 | 12789  78 4   | 3    12679 12  |
|----------------+---------------+----------------|
| 79   789   1   | 3      2  5   | 4    689   689 |
| 6    9-2   5   | 4     c19 8   | 7   d12    3   |
| 3    4     28  | 67     67 19  | 12   5     89  |
*-------------------------------------------------*

W Wing : (2=1) r2c2 - r2c5 = r8c5 - (1=2) r8c8 => - 2 r2c8, r8c2; stte

Leren

[mith]

Yep; there's also a pair of XY-Wings on r28c25 that accomplish the same thing.

The pair of finned x-wings in the jellyfish I didn't notice though, that's nice as well.

[Cenoman]

A solution in two steps:

Code: Select all

 +--------------------------+-------------------------+----------------------------+
 |  34      1267    9       |  12568    1368    35    |  1245    1278    12457-8   |
 |  8       12      34      |  1259     139     7     |  6       129     12459     |
 |  17      5     fa26-7    | e68-129   4       129   |  129     3      d12789     |
 +--------------------------+-------------------------+----------------------------+
 |  179     3       678     |  12789    5       129   |  129     4       12679     |
 |  2       179     457     |  1479     1379    6     |  8       179     13579     |
 |  14579   16789   45678   |  124789   13789   34    |  12359   12679   1235679   |
 +--------------------------+-------------------------+----------------------------+
 |  579     789     1       |  3        2       45    |  49      689     469-8     |
 |  6       29      35      |  45       19      8     |  7       129     34        |
 |  39      4      b28-3    |  67       67      19    |  1239    5      c12389     |
 +--------------------------+-------------------------+----------------------------+

1. (2)r3c3 = (2-8)r9c3 = r9c9 - r3c9 = (8-6)r3c4 = (6)r3c3 loop => -7 r3c3, -3 r9c3, -8 r17c9, -129 r3c4

Code: Select all

 +---------------------+-----------------------+----------------------------+
 | b34   C67   9       |  125    68      35    |  1245    1278    12457     |
 |  8     12   34      |  1259   139     7     |  6       129     12459     |
 |  17    5   C26      |  68     4      B129   |  129     3       12789     |
 +---------------------+-----------------------+----------------------------+
 | a19    3    678     |  78     5      A129   | y129     4       67        |
 |  2     19   457     |  149    1379    6     |  8       179     13579     |
 | b45    68   45678   |  1249   13789   34    |  12359   12679   1235679   |
 +---------------------+-----------------------+----------------------------+
 | E79-5 D78   1       |  3      2      z45    | z49      689     469       |
 |  6     29   35      |  45     19      8     |  7       129     34        |
 | b39    4    28      |  67     67      19    |  1239    5       12389     |
 +---------------------+-----------------------+----------------------------+

2. Kraken row (9)r4c167
(9)r4c1 - (9=345)r169c1
(9-2)r4c6 = r3c6 - (2=67)b1p29 - r7c2 = (7)r7c1
(9)r4c7 - (9=45)r7c67
=> -5 r7c1; lclste

After step 1, puzzle solved in two further steps, with four swordfishes:

Code: Select all

 +---------------------+-----------------------+----------------------------+
 |  34    67   9       |  12-5   68      35    |  1245    1278    1247-5    |
 |  8     12  <34      | <1259  <139     7     |  6       129    <12459     |
 | *17    5   *26      |  68     4      *129   | *129     3       789-12    |
 +---------------------+-----------------------+----------------------------+
 | &19    3    678     |  78     5      *129   | *129     4       67        |
 |  2     19  <457     | <149   <1379    6     |  8       179    <35(179)   |
 |  45    68   4678-5  |  1249   1789-3  34    |  35(129) 12679   12679-35  |
 +---------------------+-----------------------+----------------------------+
 |  579   78   1       |  3      2       45    |  49      689     469       |
 |  6     29  <35      | <45     19      8     |  7       129    <34        |
 |  39    4   *28      |  67     67     *19    | *1239    5       89-123    |
 +---------------------+-----------------------+----------------------------+

2a. SF(3)r258\c359 or (3)r2c3 = r2c5 - r5c5 = r5c9 - r8c9 = r8c3 loop => -3 r6c59, r9c9
2b. SF(5)r258\c349 or (5)r2c4 = r2c9 - r5c9 = r5c2 - r8c2 = r8c3 loop => -5 r1c49, r6c39
=> HP(35)b6p67, -129 r6c7, -179 r5c9; HP(45)b4p67, -7 r5c3; NT(345)r6c167, -4 r6c34
3a. SF(1)c167\r349 => -1 r39c9
3b. SF(2)c367\r349 => -2 r39c9
=> HP(12)b9p57; NT(129)r349c7; singles to the end

Note: there are also two SF's (4)r258\c359 and (8)r349\c349 but they are useless.