The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 2 . . | . . 3 |
| . 4 . | . 5 . | . 6 . |
+-------+-------+-------+
| . 6 . | . 4 . | . 7 . |
| . . 2 | 3 . . | . . 8 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . 5 | 1 . . |
| . 5 . | . 6 . | . 4 . |
| . . 3 | 9 . . | . . 2 |
+-------+-------+-------+
...........12....3.4..5..6..6..4..7...23....8..............51...5..6..4...39....2

[SpAce]

No takers? In that case I'll remove the easy option to make it more interesting for others.

Step 1. Swordfish x 5 (digits 23456):

15x15 {23r348 456r259 \ 2346c167 5c178} => -2346 c167, -5 c178 (=> +9 r6c7)

Step 2. Swordfish: (7)r259\c256 => -7 c256 (=> +7 r1c7,r6c1)

Code: Select all

.--------------.-----------------.-----------------.
| 89  23   56  | 46   1389  189  |  7     1289  45 |
| 56  789  1   | 2    789   46   |  45   b89    3  |
| 23  4    789 | 178  5     1389 |  28    6     19 |
:--------------+-----------------+-----------------:
| 13  6    89  | 158  4     1289 |  23    7     15 |
| 45  19   2   | 3    179   67   |  46    15    8  |
| 7   138  45  | 56   128   18   |  9     23    46 |
:--------------+-----------------+-----------------:
| 89  289  46  | 47   23    5    |  1   ab38'9  67 |
| 12  5    79  | 18   6     23   | a38    4     79 |
| 46  178  3   | 9    18    47   |  56    5-8   2  |
'--------------'-----------------'-----------------'


Step 3. XYZ-Wing: (83)b9p42 = (98)r72c8 => -8 r9c8; stte

[mith]

Yep, that's the easy option. Curious to see if there's some crazy short option.

There are actually more fish to find before the XYZ-Wing (in fact, SE finds Swordfish on all 9 digits for this one).

[denis_berthier]

Code: Select all

(solve-sudoku-grid
   +-------+-------+-------+
   ! . . . ! . . . ! . . . !
   ! . . 1 ! 2 . . ! . . 3 !
   ! . 4 . ! . 5 . ! . 6 . !
   +-------+-------+-------+
   ! . 6 . ! . 4 . ! . 7 . !
   ! . . 2 ! 3 . . ! . . 8 !
   ! . . . ! . . . ! . . . !
   +-------+-------+-------+
   ! . . . ! . . 5 ! 1 . . !
   ! . 5 . ! . 6 . ! . 4 . !
   ! . . 3 ! 9 . . ! . . 2 !
   +-------+-------+-------+
)


Many Subsets at the start:

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
261 candidates, 2028 csp-links and 2028 links. Density = 5.98%
hidden-pairs-in-a-block: b8{r7c5 r8c6}{n2 n3} ==> r8c6 ≠ 8, r8c6 ≠ 7, r8c6 ≠ 1, r7c5 ≠ 8, r7c5 ≠ 7
swordfish-in-columns: n6{c3 c4 c9}{r7 r1 r6} ==> r7c1 ≠ 6, r6c7 ≠ 6, r6c6 ≠ 6, r1c6 ≠ 6, r1c1 ≠ 6
swordfish-in-columns: n4{c3 c4 c9}{r6 r7 r1} ==> r7c1 ≠ 4, r6c7 ≠ 4, r6c1 ≠ 4, r1c7 ≠ 4, r1c6 ≠ 4
hidden-pairs-in-a-block: b2{r1c4 r2c6}{n4 n6} ==> r2c6 ≠ 9, r2c6 ≠ 8, r2c6 ≠ 7, r1c4 ≠ 8, r1c4 ≠ 7, r1c4 ≠ 1
hidden-pairs-in-a-block: b6{r5c7 r6c9}{n4 n6} ==> r6c9 ≠ 9, r6c9 ≠ 5, r6c9 ≠ 1, r5c7 ≠ 9, r5c7 ≠ 5
hidden-pairs-in-a-block: b7{r7c3 r9c1}{n4 n6} ==> r9c1 ≠ 8, r9c1 ≠ 7, r9c1 ≠ 1, r7c3 ≠ 9, r7c3 ≠ 8, r7c3 ≠ 7
finned-x-wing-in-rows: n5{r5 r2}{c1 c8} ==> r1c8 ≠ 5
finned-x-wing-in-columns: n5{c9 c3}{r1 r4} ==> r4c1 ≠ 5
biv-chain[2]: r5n5{c1 c8} - c9n5{r4 r1} ==> r1c1 ≠ 5
hidden-pairs-in-a-block: b1{r1c3 r2c1}{n5 n6} ==> r2c1 ≠ 9, r2c1 ≠ 8, r2c1 ≠ 7, r1c3 ≠ 9, r1c3 ≠ 8, r1c3 ≠ 7
swordfish-in-columns: n3{c2 c5 c8}{r6 r1 r7} ==> r6c7 ≠ 3, r6c1 ≠ 3, r1c6 ≠ 3, r1c1 ≠ 3
swordfish-in-rows: n2{r3 r4 r8}{c1 c7 c6} ==> r7c1 ≠ 2, r6c7 ≠ 2, r6c6 ≠ 2, r1c7 ≠ 2, r1c1 ≠ 2
hidden-pairs-in-a-block: b1{r1c2 r3c1}{n2 n3} ==> r3c1 ≠ 9, r3c1 ≠ 8, r3c1 ≠ 7, r1c2 ≠ 9, r1c2 ≠ 8, r1c2 ≠ 7
hidden-pairs-in-a-block: b6{r4c7 r6c8}{n2 n3} ==> r6c8 ≠ 9, r6c8 ≠ 5, r6c8 ≠ 1, r4c7 ≠ 9, r4c7 ≠ 5
swordfish-in-rows: n5{r2 r5 r9}{c7 c1 c8} ==> r6c7 ≠ 5, r6c1 ≠ 5, r1c7 ≠ 5
naked-single ==> r6c7 = 9
hidden-triplets-in-a-column: c7{n4 n5 n6}{r5 r2 r9} ==> r9c7 ≠ 8, r9c7 ≠ 7, r2c7 ≠ 8, r2c7 ≠ 7
naked-triplets-in-a-row: r2{c1 c6 c7}{n5 n6 n4} ==> r2c8 ≠ 5
hidden-pairs-in-a-block: b3{r1c9 r2c7}{n4 n5} ==> r1c9 ≠ 9, r1c9 ≠ 7, r1c9 ≠ 1
hidden-triplets-in-a-column: c1{n4 n5 n6}{r9 r5 r2} ==> r5c1 ≠ 9, r5c1 ≠ 7, r5c1 ≠ 1
finned-x-wing-in-rows: n7{r2 r5}{c2 c5} ==> r6c5 ≠ 7
hidden-triplets-in-a-row: r6{n4 n5 n6}{c9 c3 c4} ==> r6c4 ≠ 8, r6c4 ≠ 7, r6c4 ≠ 1, r6c3 ≠ 8, r6c3 ≠ 7
naked-pairs-in-a-block: b4{r5c1 r6c3}{n4 n5} ==> r4c3 ≠ 5
finned-x-wing-in-columns: n7{c3 c7}{r8 r3} ==> r3c9 ≠ 7
whip[1]: c9n7{r8 .} ==> r8c7 ≠ 7
swordfish-in-columns: n7{c3 c4 c9}{r8 r3 r7} ==> r8c1 ≠ 7, r7c2 ≠ 7, r7c1 ≠ 7, r3c7 ≠ 7, r3c6 ≠ 7
hidden-single-in-a-block ==> r1c7 = 7
hidden-single-in-a-column ==> r6c1 = 7
naked-pairs-in-a-column: c1{r1 r7}{n8 n9} ==> r8c1 ≠ 9, r8c1 ≠ 8, r4c1 ≠ 9, r4c1 ≠ 8
hidden-triplets-in-a-column: c6{n4 n6 n7}{r9 r2 r5} ==> r9c6 ≠ 8, r9c6 ≠ 1, r5c6 ≠ 9, r5c6 ≠ 1
finned-x-wing-in-rows: n1{r9 r6}{c2 c5} ==> r5c5 ≠ 1
hidden-triplets-in-a-row: r7{n4 n6 n7}{c4 c3 c9} ==> r7c9 ≠ 9, r7c4 ≠ 8
naked-pairs-in-a-block: b8{r7c4 r9c6}{n4 n7} ==> r9c5 ≠ 7, r8c4 ≠ 7
hidden-pairs-in-a-row: r8{n7 n9}{c3 c9} ==> r8c3 ≠ 8
swordfish-in-columns: n8{c3 c4 c7}{r3 r4 r8} ==> r4c6 ≠ 8, r3c6 ≠ 8
swordfish-in-rows: n9{r3 r4 r8}{c9 c6 c3} ==> r1c6 ≠ 9
naked-pairs-in-a-column: c6{r1 r6}{n1 n8} ==> r4c6 ≠ 1, r3c6 ≠ 1


At this point, there (at least) two possibilities:

- several (3D) bivalue-chains[3]:

Code: Select all

biv-chain[3]: b7n2{r7c2 r8c1} - b7n1{r8c1 r9c2} - r5c2{n1 n9} ==> r7c2 ≠ 9
biv-chain[3]: r1n2{c8 c2} - r7c2{n2 n8} - c1n8{r7 r1} ==> r1c8 ≠ 8
biv-chain[3]: c1n8{r1 r7} - r7n9{c1 c8} - r2c8{n9 n8} ==> r2c2 ≠ 8
biv-chain[3]: r2n8{c5 c8} - c7n8{r3 r8} - b8n8{r8c4 r9c5} ==> r1c5 ≠ 8, r6c5 ≠ 8
biv-chain[3]: c6n1{r1 r6} - r6c5{n1 n2} - c8n2{r6 r1} ==> r1c8 ≠ 1
stte


- or a single xy-chain[4]:

Code: Select all

biv-chain-rc[4]: r5c8{n1 n5} - r9c8{n5 n8} - r2c8{n8 n9} - r3c9{n9 n1} ==> r4c9 ≠ 1, r1c8 ≠ 1
stte