The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| 1 . . | . . 2 | 3 . . |
| . 4 . | . 5 . | 6 7 . |
+-------+-------+-------+
| . 5 . | . 7 . | . 4 . |
| 3 . . | . . 1 | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | 3 . . | . . . |
| . 7 . | . 4 . | . 6 . |
| 2 . . | . . 8 | 1 . . |
+-------+-------+-------+
.........1....23...4..5.67..5..7..4.3....12..............3......7..4..6.2....81..

[pjb]

Lots of fish. Here's one approach. Alternatively, could use MSLSs.

Swordfish of 1s (r348\c349) => -1 r1c49, r6c39, r7c3
Swordfish of 2s (r348\c349) => -2 r1c39, r6c34, r7c9
Swordfish of 3s (r348\c369) => -3 r1c36, r6c69, r9c39
Swordfish of 4s (r259\c349) => -4 r1c49, r6c34, r7c39
Swordfish of 7s (r259\c349) => -7 r1c34, r6c39, r7c9
Swordfish of 8s (r348\c147) => -8 r1c1, r1c4, r1c7, r5c4, r6c4, r6c7, r7c1
X-wing of 8s (r16\c39) => -8 r2c3, r2c9, r5c9, r7c3, r7c9
Swordfish of 9s (r348\c167) => -9 r1c17, r6c67, r7c16
Swordfish of 9s (r167\c349) => -9 r2c39, r5c49, r9c34
Sashimi franken swordfish of 5s (c178\r19b6), fin at r78c1 => -5 r9c3
finally:
(3)r6c8 = (3-5)r9c8 = r7c9 - (5=3469)r7c13, r9c23 => -3 r9c8; stte

Phil

[denis_berthier]

Code: Select all

(solve-sudoku-grid
   +-------+-------+-------+
   ! . . . ! . . . ! . . . !
   ! 1 . . ! . . 2 ! 3 . . !
   ! . 4 . ! . 5 . ! 6 7 . !
   +-------+-------+-------+
   ! . 5 . ! . 7 . ! . 4 . !
   ! 3 . . ! . . 1 ! 2 . . !
   ! . . . ! . . . ! . . . !
   +-------+-------+-------+
   ! . . . ! 3 . . ! . . . !
   ! . 7 . ! . 4 . ! . 6 . !
   ! 2 . . ! . . 8 ! 1 . . !
   +-------+-------+-------+
)


There's a solution with only Subsets and short bivalue-chains (length <= 3). Here's a more complicated one with only Subsets and (longer) Oddagons.
It seems that the presence of many Subsets often favours the presence of Oddagons at a later stage.

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = O+S
***  Using CLIPS 6.32-r770
***********************************************************************************************
263 candidates, 2099 csp-links and 2099 links. Density = 6.09%
hidden-pairs-in-a-block: b8{r7c5 r8c4}{n1 n2} ==> r8c4 ≠ 9, r8c4 ≠ 5, r7c5 ≠ 9, r7c5 ≠ 6
naked-triplets-in-a-row: r8{c1 c6 c7}{n8 n9 n5} ==> r8c9 ≠ 9, r8c9 ≠ 8, r8c9 ≠ 5, r8c3 ≠ 9, r8c3 ≠ 8, r8c3 ≠ 5
naked-triplets-in-a-column: c5{r2 r5 r9}{n9 n8 n6} ==> r6c5 ≠ 9, r6c5 ≠ 8, r6c5 ≠ 6, r1c5 ≠ 9, r1c5 ≠ 8, r1c5 ≠ 6
swordfish-in-columns: n3{c2 c5 c8}{r9 r1 r6} ==> r9c9 ≠ 3, r9c3 ≠ 3, r6c9 ≠ 3, r6c6 ≠ 3, r1c6 ≠ 3, r1c3 ≠ 3
swordfish-in-columns: n4{c1 c6 c7}{r7 r6 r1} ==> r7c9 ≠ 4, r7c3 ≠ 4, r6c4 ≠ 4, r6c3 ≠ 4, r1c9 ≠ 4, r1c4 ≠ 4
swordfish-in-columns: n1{c2 c5 c8}{r6 r7 r1} ==> r7c3 ≠ 1, r6c9 ≠ 1, r6c3 ≠ 1, r1c9 ≠ 1, r1c4 ≠ 1
hidden-pairs-in-a-block: b6{r4c9 r6c8}{n1 n3} ==> r6c8 ≠ 9, r6c8 ≠ 8, r6c8 ≠ 5, r4c9 ≠ 9, r4c9 ≠ 8, r4c9 ≠ 6
swordfish-in-columns: n7{c1 c6 c7}{r6 r1 r7} ==> r7c9 ≠ 7, r6c9 ≠ 7, r6c3 ≠ 7, r1c4 ≠ 7, r1c3 ≠ 7
hidden-pairs-in-a-block: b2{r1c6 r2c4}{n4 n7} ==> r2c4 ≠ 9, r2c4 ≠ 8, r2c4 ≠ 6, r1c6 ≠ 9, r1c6 ≠ 6
hidden-pairs-in-a-block: b4{r5c3 r6c1}{n4 n7} ==> r6c1 ≠ 9, r6c1 ≠ 8, r6c1 ≠ 6, r5c3 ≠ 9, r5c3 ≠ 8, r5c3 ≠ 6
hidden-pairs-in-a-block: b9{r7c7 r9c9}{n4 n7} ==> r9c9 ≠ 9, r9c9 ≠ 5, r7c7 ≠ 9, r7c7 ≠ 8, r7c7 ≠ 5
swordfish-in-rows: n2{r3 r4 r8}{c9 c3 c4} ==> r7c9 ≠ 2, r6c4 ≠ 2, r6c3 ≠ 2, r1c9 ≠ 2, r1c3 ≠ 2
hidden-pairs-in-a-block: b1{r1c2 r3c3}{n2 n3} ==> r3c3 ≠ 9, r3c3 ≠ 8, r1c2 ≠ 9, r1c2 ≠ 8, r1c2 ≠ 6
hidden-pairs-in-a-block: b3{r1c8 r3c9}{n1 n2} ==> r3c9 ≠ 9, r3c9 ≠ 8, r1c8 ≠ 9, r1c8 ≠ 8, r1c8 ≠ 5
hidden-pairs-in-a-block: b4{r4c3 r6c2}{n1 n2} ==> r6c2 ≠ 9, r6c2 ≠ 8, r6c2 ≠ 6, r4c3 ≠ 9, r4c3 ≠ 8, r4c3 ≠ 6
swordfish-in-rows: n8{r3 r4 r8}{c1 c4 c7} ==> r7c1 ≠ 8, r6c7 ≠ 8, r6c4 ≠ 8, r5c4 ≠ 8, r1c7 ≠ 8, r1c4 ≠ 8, r1c1 ≠ 8
x-wing-in-rows: n8{r1 r6}{c3 c9} ==> r7c9 ≠ 8, r7c3 ≠ 8, r5c9 ≠ 8, r2c9 ≠ 8, r2c3 ≠ 8
hidden-triplets-in-a-row: r7{n1 n2 n8}{c2 c5 c8} ==> r7c8 ≠ 9, r7c8 ≠ 5, r7c2 ≠ 9, r7c2 ≠ 6
hidden-triplets-in-a-column: c4{n1 n2 n8}{r3 r8 r4} ==> r4c4 ≠ 9, r4c4 ≠ 6, r3c4 ≠ 9
swordfish-in-rows: n9{r3 r4 r8}{c6 c1 c7} ==> r7c6 ≠ 9, r7c1 ≠ 9, r6c7 ≠ 9, r6c6 ≠ 9, r1c7 ≠ 9, r1c1 ≠ 9
hidden-pairs-in-a-column: c7{n8 n9}{r4 r8} ==> r8c7 ≠ 5
swordfish-in-rows: n9{r1 r6 r7}{c3 c4 c9} ==> r9c4 ≠ 9, r9c3 ≠ 9, r5c9 ≠ 9, r5c4 ≠ 9, r2c9 ≠ 9, r2c3 ≠ 9
naked-pairs-in-a-block: b3{r1c7 r2c9}{n4 n5} ==> r2c8 ≠ 5, r1c9 ≠ 5
naked-triplets-in-a-row: r2{c2 c5 c8}{n8 n6 n9} ==> r2c3 ≠ 6
oddagon[7]: r1c4{n6 n9},r1n9{c4 c9},r1c9{n9 n8},b3n8{r1c9 r2c8},r2n8{c8 c5},r2c5{n8 n6},b2n6{r2c5 r1c4} ==> r2c2 ≠ 9
oddagon[7]: r3c1{n8 n9},r3n9{c1 c6},c6n9{r3 r8},r8n9{c6 c7},r8c7{n9 n8},r8n8{c7 c1},c1n8{r8 r3} ==> r4c1 ≠ 9
oddagon[7]: r1n8{c3 c9},c9n8{r1 r6},b6n8{r6c9 r4c7},r4n8{c7 c4},c4n8{r4 r3},r3n8{c4 c1},b1n8{r3c1 r1c3} ==> r5c2 ≠ 8
oddagon[7]: r1c4{n6 n9},c4n9{r1 r6},b5n9{r6c4 r5c5},r5c5{n9 n8},c5n8{r5 r2},r2c5{n8 n6},b2n6{r2c5 r1c4} ==> r5c5 ≠ 9
oddagon[7]: r1c9{n8 n9},c9n9{r1 r7},b9n9{r7c9 r8c7},r8c7{n9 n8},c7n8{r8 r4},b6n8{r4c7 r6c9},c9n8{r6 r1} ==> r5c8 ≠ 9
hidden-single-in-a-row ==> r5c2 = 9
oddagon[5]: c4n6{r1 r9},r9n6{c4 c2},c2n6{r9 r2},r2n6{c2 c5},b2n6{r2c5 r1c4} ==> r9c4 ≠ 6
oddagon[7]: c4n5{r6 r9},r9c4{n5 n7},b8n7{r9c4 r7c6},r7n7{c6 c7},c7n7{r7 r6},r6c7{n7 n5},r6n5{c7 c4} ==> r6c4 ≠ 5
naked-pairs-in-a-column: c4{r1 r6}{n6 n9} ==> r5c4 ≠ 6
hidden-pairs-in-a-block: b5{r5c4 r6c6}{n4 n5} ==> r6c6 ≠ 6
x-wing-in-columns: n5{c4 c8}{r5 r9} ==> r9c3 ≠ 5, r5c9 ≠ 5
naked-triplets-in-a-row: r6{c1 c6 c7}{n7 n4 n5} ==> r6c9 ≠ 5
oddagon[5]: r4n6{c1 c6},c6n6{r4 r7},r7n6{c6 c3},c3n6{r7 r6},b4n6{r6c3 r4c1} ==> r7c3 ≠ 6
naked-pairs-in-a-row: r7{c3 c9}{n5 n9} ==> r7c6 ≠ 5, r7c1 ≠ 5
naked-pairs-in-a-block: b7{r7c1 r9c3}{n4 n6} ==> r9c2 ≠ 6
stte