The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| 9 . . | . . . | . . . |
| . 8 . | 7 . . | . 6 . |
| . . 5 | . 4 . | . . 3 |
+-------+-------+-------+
| . 7 . | 8 . . | . 9 . |
| . . 2 | . 3 . | 1 . . |
| . . . | . . 1 | . . . |
+-------+-------+-------+
| . . . | . 1 . | 2 . . |
| . 6 . | 9 . . | . 8 . |
| . . 3 | . . . | . . 4 |
+-------+-------+-------+
9.........8.7...6...5.4...3.7.8...9...2.3.1.......1.......1.2...6.9...8...3.....4

[Cenoman]

Code: Select all

 +-----------------------+---------------------------+---------------------------+
 |  9       124-3  67    |  12356   2568    23568    |  4578     12457   12578   |
 |  1234    8      14    |  7       259     2359     |  459      6       1259    |
 |  67      12     5     |  126     4       89       |  89       127     3       |
 +-----------------------+---------------------------+---------------------------+
 |  13456   7      146   |  8       256     2456     |  3456     9       256     |
 |  4568    459    2     |  456     3       79       |  1        457     5678    |
 |  34568   3459   89    |  2456    79      1        |  345678   23457   25678   |
 +-----------------------+---------------------------+---------------------------+
 |  4578    459    89    |  3456    1       345678   |  2        357     69      |
 |  12457   6      147   |  9       257     23457    |  357      8       157     |
 |  12578   1259   3     |  256     25678   25678    |  69       157     4       |
 +-----------------------+---------------------------+---------------------------+

Double Kraken column (2)r136c8 & cell (3456)r4c7
(2-4)r1c8 = r56c8 - r4c7 = [(3)r7c8 = r8c7 - (3=5|6)r4c7 - (562=4)r4c569 - r56c4 = (4)r7c4] - (3)r7c4 = (3)r1c4
(2)r3c8 - (2=1)r3c2 - r2c13 = (1-9)r2c9 = r7c9 - r9c7 = (912)r139c2
(2-3)r6c8 = r7c8 - r8c7 = r8c6 - r2c6 = (3)r2c1
=> -3 r1c2; lclste

[mith]

Nice.

(This one also has an absurd number of fish, basic and otherwise.)

[denis_berthier]

Code: Select all

+-------+-------+-------+
| 9 . . | . . . | . . . |
| . 8 . | 7 . . | . 6 . |
| . . 5 | . 4 . | . . 3 |
+-------+-------+-------+
| . 7 . | 8 . . | . 9 . |
| . . 2 | . 3 . | 1 . . |
| . . . | . . 1 | . . . |
+-------+-------+-------+
| . . . | . 1 . | 2 . . |
| . 6 . | 9 . . | . 8 . |
| . . 3 | . . . | . . 4 |
+-------+-------+-------+
9.........8.7...6...5.4...3.7.8...9...2.3.1.......1.......1.2...6.9...8...3.....4

Subsets alone are not enough here; but adding (3D) bivalue-chains will do the work:

Hidden Text: Show

(solve "9.........8.7...6...5.4...3.7.8...9...2.3.1.......1.......1.2...6.9...8...3.....4")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = BC+S
*** Using CLIPS 6.32-r770
***********************************************************************************************
236 candidates, 1589 csp-links and 1589 links. Density = 5.73%
hidden-pairs-in-a-block: b9{r7c9 r9c7}{n6 n9} ==> r9c7 ≠ 7, r9c7 ≠ 5, r7c9 ≠ 7, r7c9 ≠ 5
hidden-pairs-in-a-column: c3{n8 n9}{r6 r7} ==> r7c3 ≠ 7, r7c3 ≠ 4, r6c3 ≠ 6, r6c3 ≠ 4
hidden-pairs-in-a-block: b5{r5c6 r6c5}{n7 n9} ==> r6c5 ≠ 6, r6c5 ≠ 5, r6c5 ≠ 2, r5c6 ≠ 6, r5c6 ≠ 5, r5c6 ≠ 4
hidden-pairs-in-a-row: r3{n8 n9}{c6 c7} ==> r3c7 ≠ 7, r3c6 ≠ 6, r3c6 ≠ 2
hidden-pairs-in-a-block: b1{r1c3 r3c1}{n6 n7} ==> r3c1 ≠ 2, r3c1 ≠ 1, r1c3 ≠ 4, r1c3 ≠ 1
swordfish-in-columns: n1{c2 c4 c8}{r9 r3 r1} ==> r9c1 ≠ 1, r1c9 ≠ 1
swordfish-in-columns: n9{c3 c5 c9}{r7 r6 r2} ==> r7c2 ≠ 9, r6c2 ≠ 9, r2c7 ≠ 9, r2c6 ≠ 9
swordfish-in-columns: n3{c2 c4 c8}{r6 r1 r7} ==> r7c6 ≠ 3, r6c7 ≠ 3, r6c1 ≠ 3, r1c6 ≠ 3
biv-chain[3]: r2c3{n4 n1} - b4n1{r4c3 r4c1} - c1n3{r4 r2} ==> r2c1 ≠ 4
biv-chain[3]: r3c2{n2 n1} - b2n1{r3c4 r1c4} - r1n3{c4 c2} ==> r1c2 ≠ 2
biv-chain[4]: r2c7{n5 n4} - b1n4{r2c3 r1c2} - b1n3{r1c2 r2c1} - r4n3{c1 c7} ==> r4c7 ≠ 5
biv-chain[4]: r9n9{c2 c7} - c9n9{r7 r2} - c9n1{r2 r8} - r9n1{c8 c2} ==> r9c2 ≠ 2, r9c2 ≠ 5
hidden-single-in-a-column ==> r3c2 = 2
biv-chain[3]: c8n2{r1 r6} - c8n3{r6 r7} - c4n3{r7 r1} ==> r1c4 ≠ 2
biv-chain[4]: c3n6{r1 r4} - b4n1{r4c3 r4c1} - r2c1{n1 n3} - b2n3{r2c6 r1c4} ==> r1c4 ≠ 6
biv-chain[4]: r3c8{n7 n1} - b2n1{r3c4 r1c4} - c4n3{r1 r7} - c8n3{r7 r6} ==> r6c8 ≠ 7
biv-chain[4]: r3c8{n7 n1} - r9n1{c8 c2} - c2n9{r9 r5} - r5c6{n9 n7} ==> r5c8 ≠ 7
biv-chain[4]: r6c3{n8 n9} - r6c5{n9 n7} - r5n7{c6 c9} - r5n8{c9 c1} ==> r6c1 ≠ 8
biv-chain[4]: r5n7{c9 c6} - c6n9{r5 r3} - r2n9{c5 c9} - c9n1{r2 r8} ==> r8c9 ≠ 7
biv-chain[4]: r8c9{n5 n1} - r9n1{c8 c2} - r9n9{c2 c7} - b3n9{r3c7 r2c9} ==> r2c9 ≠ 5
biv-chain[4]: r5n7{c9 c6} - c6n9{r5 r3} - r2n9{c5 c9} - r7c9{n9 n6} ==> r5c9 ≠ 6
x-wing-in-rows: n6{r3 r5}{c1 c4} ==> r9c4 ≠ 6, r7c4 ≠ 6, r6c4 ≠ 6, r6c1 ≠ 6, r4c1 ≠ 6
whip[1]: r6n6{c9 .} ==> r4c7 ≠ 6, r4c9 ≠ 6
hidden-triplets-in-a-block: b6{r6c9 r6c7 r5c9}{n6 n7 n8} ==> r6c9 ≠ 5, r6c9 ≠ 2, r6c7 ≠ 5, r6c7 ≠ 4, r5c9 ≠ 5
biv-chain[3]: c9n6{r6 r7} - r7n9{c9 c3} - c3n8{r7 r6} ==> r6c9 ≠ 8
biv-chain[3]: r7n6{c6 c9} - r6c9{n6 n7} - b5n7{r6c5 r5c6} ==> r7c6 ≠ 7
x-wing-in-rows: n7{r3 r7}{c1 c8} ==> r9c8 ≠ 7, r9c1 ≠ 7, r8c1 ≠ 7, r1c8 ≠ 7
whip[1]: r9n7{c6 .} ==> r8c5 ≠ 7, r8c6 ≠ 7
naked-pairs-in-a-block: b8{r8c5 r9c4}{n2 n5} ==> r9c6 ≠ 5, r9c6 ≠ 2, r9c5 ≠ 5, r9c5 ≠ 2, r8c6 ≠ 5, r8c6 ≠ 2, r7c6 ≠ 5, r7c4 ≠ 5
naked-pairs-in-a-block: b8{r7c4 r8c6}{n3 n4} ==> r7c6 ≠ 4
naked-pairs-in-a-block: b9{r8c9 r9c8}{n1 n5} ==> r8c7 ≠ 5, r7c8 ≠ 5
whip[1]: r7n5{c2 .} ==> r8c1 ≠ 5, r9c1 ≠ 5
whip[1]: c7n5{r2 .} ==> r1c8 ≠ 5, r1c9 ≠ 5
naked-triplets-in-a-row: r7{c3 c6 c9}{n9 n8 n6} ==> r7c1 ≠ 8
swordfish-in-columns: n8{c1 c5 c9}{r5 r9 r1} ==> r9c6 ≠ 8, r1c7 ≠ 8, r1c6 ≠ 8
hidden-triplets-in-a-column: c7{n6 n8 n9}{r9 r6 r3} ==> r6c7 ≠ 7
whip[1]: b6n7{r6c9 .} ==> r1c9 ≠ 7
biv-chain[3]: c5n7{r9 r6} - r6c9{n7 n6} - r7n6{c9 c6} ==> r9c5 ≠ 6
whip[1]: b8n6{r9c6 .} ==> r1c6 ≠ 6, r4c6 ≠ 6
biv-chain[3]: r1c6{n5 n2} - c8n2{r1 r6} - r4c9{n2 n5} ==> r4c6 ≠ 5
whip[1]: c6n5{r2 .} ==> r1c4 ≠ 5, r1c5 ≠ 5, r2c5 ≠ 5
x-wing-in-columns: n5{c5 c9}{r4 r8} ==> r4c1 ≠ 5
biv-chain[3]: b6n2{r6c8 r4c9} - r4c6{n2 n4} - r4c7{n4 n3} ==> r6c8 ≠ 3
stte