Why Not? (Sukaku)

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Why Not? (Sukaku)

Postby mith » Sun Dec 13, 2020 7:04 pm

Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 24        123456789 35        | 123456789 69        123456789 | 47        123456789 28        |
| 123456789 579       123456789 | 47        123456789 37        | 123456789 579       123456789 |
| 45        123456789 49        | 123456789 134       123456789 | 56        123456789 17        |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 15        123456789 | 24        123456789 79        | 123456789 69        12346789  |
| 48        123456789 123       | 123456789 57        123456789 | 136       123456789 79        |
| 12346789  29        123456789 | 38        123456789 15        | 123456789 35        123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 37        123456789 25        | 123456789 138       123456789 | 89        123456789 58        |
| 123456789 579       123456789 | 17        123456789 78        | 123456789 579       123456789 |
| 68        123456789 58        | 123456789 27        123456789 | 15        123456789 46        |
+-------------------------------+-------------------------------+-------------------------------+
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Re: Why Not? (Sukaku)

Postby 1to9only » Sun Dec 13, 2020 10:00 pm

The 729-chars version:
Code: Select all
.2.4.....123456789..3.5....123456789.....6..9123456789...4..7..123456789.2.....8.123456789....5.7.9123456789...4..7..123456789..3...7..123456789....5.7.9123456789...45....123456789...4....91234567891.34.....123456789....56...1234567891.....7..1234567891...5....123456789.2.4.....123456789......7.9123456789.....6..91234.6789...4...8.123456789123......123456789....5.7..1234567891.3..6...123456789......7.91234.6789.2......9123456789..3....8.1234567891...5....123456789..3.5....123456789..3...7..123456789.2..5....1234567891.3....8.123456789.......89123456789....5..8.123456789....5.7.91234567891.....7..123456789......78.123456789....5.7.9123456789.....6.8.123456789....5..8.123456789.2....7..1234567891...5....123456789...4.6...
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Re: Why Not? (Sukaku)

Postby m_b_metcalf » Sun Dec 13, 2020 10:23 pm

And the solution:
Hidden Text: Show
Code: Select all
  2  6  3  7  9  5  4  1  8
  1  7  8  4  6  3  5  9  2
  5  4  9  8  1  2  6  3  7
  3  5  7  2  4  9  8  6  1
  4  8  1  5  7  6  3  2  9
  9  2  6  3  8  1  7  5  4
  7  1  2  6  3  4  9  8  5
  6  9  4  1  5  8  2  7  3
  8  3  5  9  2  7  1  4  6
User avatar
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Re: Why Not? (Sukaku)

Postby yzfwsf » Mon Dec 14, 2020 2:09 am

Death Blossom: r5c3,1-{r248c2},2-{r268c2},3-{r3c13,r1c3,r2c2} => -5r13c2,-7r13579c2,-9r13c2;lclste
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Re: Why Not? (Sukaku)

Postby denis_berthier » Mon Dec 14, 2020 12:39 pm

Why "why not" ?

Code: Select all
(solve-sukaku-grid
   +-------------------------------+-------------------------------+-------------------------------+
   ! 24        123456789 35        ! 123456789 69        123456789 ! 47        123456789 28        !
   ! 123456789 579       123456789 ! 47        123456789 37        ! 123456789 579       123456789 !
   ! 45        123456789 49        ! 123456789 134       123456789 ! 56        123456789 17        !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 15        123456789 ! 24        123456789 79        ! 123456789 69        12346789  !
   ! 48        123456789 123       ! 123456789 57        123456789 ! 136       123456789 79        !
   ! 12346789  29        123456789 ! 38        123456789 15        ! 123456789 35        123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 37        123456789 25        ! 123456789 138       123456789 ! 89        123456789 58        !
   ! 123456789 579       123456789 ! 17        123456789 78        ! 123456789 579       123456789 !
   ! 68        123456789 58        ! 123456789 27        123456789 ! 15        123456789 46        !
   +-------------------------------+-------------------------------+-------------------------------+
)


Solved in W7:

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
448 candidates, 4639 csp-links and 4639 links. Density = 4.63%
z-chain-rc[5]: r1c7{n4 n7} - r3c9{n7 n1} - r3c5{n1 n3} - r2c6{n3 n7} - r2c4{n7 .} ==> r1c4 ≠ 4
z-chain-rc[5]: r1c7{n4 n7} - r3c9{n7 n1} - r3c5{n1 n3} - r2c6{n3 n7} - r2c4{n7 .} ==> r1c6 ≠ 4
z-chain-rc[5]: r6c6{n1 n5} - r6c8{n5 n3} - r5c7{n3 n6} - r3c7{n6 n5} - r9c7{n5 .} ==> r6c7 ≠ 1
t-whip-rc[5]: r9c7{n1 n5} - r7c9{n5 n8} - r7c7{n8 n9} - r8c8{n9 n7} - r8c4{n7 .} ==> r9c4 ≠ 1, r9c6 ≠ 1, r8c7 ≠ 1, r8c9 ≠ 1
t-whip-rc[5]: r1c3{n3 n5} - r3c1{n5 n4} - r3c3{n4 n9} - r2c2{n9 n7} - r2c6{n7 .} ==> r1c4 ≠ 3, r1c6 ≠ 3, r2c1 ≠ 3, r2c3 ≠ 3
whip-rc[5]: r2c6{n3 n7} - r8c6{n7 n8} - r7c5{n8 n1} - r3c5{n1 n4} - r2c4{n4 .} ==> r2c5 ≠ 3
whip-rc[5]: r8c4{n1 n7} - r2c4{n7 n4} - r3c5{n4 n3} - r7c5{n3 n8} - r8c6{n8 .} ==> r8c5 ≠ 1
biv-chain-rc[6]: r3c9{n1 n7} - r1c7{n7 n4} - r1c1{n4 n2} - r1c9{n2 n8} - r7c9{n8 n5} - r9c7{n5 n1} ==> r2c7 ≠ 1
z-chain-rc[6]: r6c6{n1 n5} - r6c8{n5 n3} - r5c7{n3 n6} - r4c8{n6 n9} - r5c9{n9 n7} - r3c9{n7 .} ==> r6c9 ≠ 1
whip-rc[6]: r6c6{n1 n5} - r6c8{n5 n3} - r5c7{n3 n6} - r4c8{n6 n9} - r4c6{n9 n7} - r5c5{n7 .} ==> r5c4 ≠ 1
whip-rc[6]: r6c6{n1 n5} - r6c8{n5 n3} - r5c7{n3 n6} - r4c8{n6 n9} - r4c6{n9 n7} - r5c5{n7 .} ==> r5c6 ≠ 1
whip[7]: r4c8{n6 n9} - r4c6{n9 n7} - r2c6{n7 n3} - b3n3{r2c9 r3c8} - r6c8{n3 n5} - r2c8{n5 n7} - r8c8{n7 .} ==> r1c8 ≠ 6
whip[7]: r4c8{n6 n9} - r4c6{n9 n7} - r2c6{n7 n3} - b3n3{r2c9 r1c8} - r6c8{n3 n5} - r2c8{n5 n7} - r8c8{n7 .} ==> r3c8 ≠ 6
whip[7]: r3c7{n6 n5} - r3c1{n5 n4} - r5c1{n4 n8} - r9c1{n8 n6} - c8n6{r9 r7} - b8n6{r7c4 r8c5} - b5n6{r4c5 .} ==> r5c7 ≠ 6
biv-chain-rc[3]: r9c7{n5 n1} - r5c7{n1 n3} - r6c8{n3 n5} ==> r7c8 ≠ 5, r8c8 ≠ 5, r9c8 ≠ 5, r4c7 ≠ 5, r6c7 ≠ 5
biv-chain-rc[3]: r8c6{n8 n7} - r8c8{n7 n9} - r7c7{n9 n8} ==> r7c4 ≠ 8, r7c5 ≠ 8, r7c6 ≠ 8, r8c7 ≠ 8, r8c9 ≠ 8
biv-chain-rc[3]: r8c4{n7 n1} - r7c5{n1 n3} - r7c1{n3 n7} ==> r7c4 ≠ 7, r7c6 ≠ 7, r8c1 ≠ 7, r8c2 ≠ 7, r8c3 ≠ 7
biv-chain-rc[3]: r7c3{n2 n5} - r8c2{n5 n9} - r6c2{n9 n2} ==> r7c2 ≠ 2, r9c2 ≠ 2, r4c3 ≠ 2, r5c3 ≠ 2, r6c3 ≠ 2
naked-pairs-in-a-row: r5{c3 c7}{n1 n3} ==> r5c8 ≠ 3, r5c8 ≠ 1, r5c6 ≠ 3, r5c4 ≠ 3, r5c2 ≠ 3, r5c2 ≠ 1
biv-chain-rc[3]: r4c2{n5 n1} - r5c3{n1 n3} - r1c3{n3 n5} ==> r4c3 ≠ 5, r6c3 ≠ 5, r1c2 ≠ 5, r2c2 ≠ 5, r3c2 ≠ 5
biv-chain-rc[3]: r2c4{n4 n7} - r2c2{n7 n9} - r3c3{n9 n4} ==> r3c4 ≠ 4, r3c5 ≠ 4, r3c6 ≠ 4, r2c1 ≠ 4, r2c3 ≠ 4
whip[1]: b2n4{r2c5 .} ==> r2c7 ≠ 4, r2c9 ≠ 4
naked-pairs-in-a-column: c5{r3 r7}{n1 n3} ==> r8c5 ≠ 3, r6c5 ≠ 3, r6c5 ≠ 1, r4c5 ≠ 3, r4c5 ≠ 1, r2c5 ≠ 1
singles ==> r6c6 = 1, r6c4 = 3, r6c8 = 5
naked-pairs-in-a-column: c8{r2 r8}{n7 n9} ==> r9c8 ≠ 9, r9c8 ≠ 7, r7c8 ≠ 9, r7c8 ≠ 7, r5c8 ≠ 9, r5c8 ≠ 7, r4c8 ≠ 9, r3c8 ≠ 9, r3c8 ≠ 7, r1c8 ≠ 9, r1c8 ≠ 7
naked-single ==> r4c8 = 6
whip[1]: b3n9{r2c9 .} ==> r2c1 ≠ 9, r2c2 ≠ 9, r2c3 ≠ 9, r2c5 ≠ 9
stte
Last edited by denis_berthier on Mon Dec 14, 2020 4:46 pm, edited 1 time in total.
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Re: Why Not? (Sukaku)

Postby mith » Mon Dec 14, 2020 3:57 pm

denis_berthier wrote:Why "why not" ?


My intended path:

Hidden Text: Show
WXYZ-Wing: 1347 in r2c46,r3c59,Pivot Cell Is r3c5 => r2c789,r3c46<>7
XY-Wing: 569 in r2c8 r4c8 r3c7 => r456c7,r13c8 <> 6
XY-Wing: 135 in r5c7 r9c7 r6c8 => r789c8,r46c7 <> 5
XY-Wing: 789 in r8c8 r8c6 r7c7 => r7c456,r8c79 <> 8
XY-Wing: 137 in r7c5 r7c1 r8c4 => r8c123,r7c46 <> 7
XY-Wing: 259 in r8c2 r6c2 r7c3 => r456c3,r79c2 <> 2
Naked Pair: in r5c3,r5c7 => r5c2<>13,r5c4<>3,r5c6<>3,r5c8<>13
XY-Wing: 135 in r5c3 r1c3 r4c2 => r123c2,r46c3 <> 5
XY-Wing: 479 in r2c2 r2c4 r3c3 => r3c456,r2c13 <> 4
Naked Pair: in r3c5,r7c5 => r2c5<>13,r4c5<>13,r6c5<>13,r8c5<>13
stte

"Y Knot"
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Re: Why Not? (Sukaku)

Postby 1to9only » Mon Dec 14, 2020 4:54 pm

I think that's about the same as SukakuExplainer's solving path.
The SudokuExplainer that has Hodoku solving methods starts off differently:
Hidden Text: Show
Code: Select all
ALS-XZ: in box 1 and box 2 on 7 and 3,4: -3r1c46, -34r2c13
ALS-XZ: in box 1 and col 4 on 7 and 2: -2r1c4, -2r4c1
ALS-XZ: in box 1 and box 2 on 7 and 4: -4r3c456
followed by a number of XY-Wings
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Re: Why Not? (Sukaku)

Postby mith » Mon Dec 14, 2020 6:16 pm

Yeah, I was checking it against SE and YZF's solver as I narrowed in on a unique solution, no surprises there.

Here's a harder version with 12 (plus a slew of other stuff), though I suspect the non-thematic ones are redundant. I'm going to attempt to get this as close to just the thematic technique + basics as I can.

Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 26        123456789 | 456       123456789 123456789 | 59        123456789 123456789 |
| 123456789 123456789 123       | 123456789 16        123456789 | 34        123456789 28        |
| 36        57        123456789 | 123456789 123456789 49        | 123456789 789       123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 123456789 35        | 26        123456789 28        | 123456789 123456789 123       |
| 123456789 24        123456789 | 123456789 123456789 123456789 | 123456789 27        123456789 |
| 456       123456789 123456789 | 46        123456789 48        | 35        123456789 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 123       123456789 | 19        123456789 123456789 | 123456789 29        15        |
| 34        123456789 59        | 123456789 68        123456789 | 456       123456789 123456789 |
| 123456789 123456789 17        | 123456789 123456789 789       | 123456789 48        123456789 |
+-------------------------------+-------------------------------+-------------------------------+
123456789.2...6...123456789...456...123456789123456789....5...9123456789123456789123456789123456789123......1234567891....6...123456789..34.....123456789.2.....8...3..6.......5.7..123456789123456789123456789...4....9123456789......789123456789123456789123456789..3.5.....2...6...123456789.2.....8.123456789123456789123......123456789.2.4.....123456789123456789123456789123456789123456789.2....7..123456789...456...123456789123456789...4.6...123456789...4...8...3.5....123456789123456789123456789123......1234567891.......9123456789123456789123456789.2......91...5......34.....123456789....5...9123456789.....6.8.123456789...456...1234567891234567891234567891234567891.....7..123456789123456789......789123456789...4...8.123456789
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Re: Why Not? (Sukaku)

Postby m_b_metcalf » Mon Dec 14, 2020 6:29 pm

For this new one, my program reports : 'Backdoor value 2r1c1'
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Re: Why Not? (Sukaku)

Postby mith » Mon Dec 14, 2020 6:53 pm

Oh, nice, I didn't think to check backdoors given how complicated the solution path was. That gives an easy way to simplify it:

Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 24        26        123456789 | 456       123456789 123456789 | 59        123456789 38        |
| 123456789 123456789 123       | 123456789 16        123456789 | 34        123456789 28        |
| 36        57        123456789 | 123456789 123456789 49        | 123456789 789       123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 123456789 35        | 26        123456789 28        | 123456789 123456789 123       |
| 123456789 24        123456789 | 123456789 123456789 123456789 | 123456789 27        123456789 |
| 456       123456789 123456789 | 46        123456789 48        | 35        123456789 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 123       123456789 | 19        123456789 123456789 | 123456789 29        15        |
| 34        123456789 59        | 123456789 68        123456789 | 456       123456789 123456789 |
| 69        123456789 17        | 123456789 123456789 789       | 123456789 48        47        |
+-------------------------------+-------------------------------+-------------------------------+
.2.4......2...6...123456789...456...123456789123456789....5...9123456789..3....8.123456789123456789123......1234567891....6...123456789..34.....123456789.2.....8...3..6.......5.7..123456789123456789123456789...4....9123456789......789123456789123456789123456789..3.5.....2...6...123456789.2.....8.123456789123456789123......123456789.2.4.....123456789123456789123456789123456789123456789.2....7..123456789...456...123456789123456789...4.6...123456789...4...8...3.5....123456789123456789123456789123......1234567891.......9123456789123456789123456789.2......91...5......34.....123456789....5...9123456789.....6.8.123456789...456...123456789123456789.....6..91234567891.....7..123456789123456789......789123456789...4...8....4..7..


(SE now finds
Hidden Text: Show
13 XY-Wings
)

But this version definitely reduces the number actually needed to solve it. (You can do it with 2.)
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Re: Why Not? (Sukaku)

Postby denis_berthier » Mon Dec 14, 2020 7:11 pm

Code: Select all
(solve-sukaku-grid
   +-------------------------------+-------------------------------+-------------------------------+
   ! 24        26        123456789 ! 456       123456789 123456789 ! 59        123456789 38        !
   ! 123456789 123456789 123       ! 123456789 16        123456789 ! 34        123456789 28        !
   ! 36        57        123456789 ! 123456789 123456789 49        ! 123456789 789       123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123456789 35        ! 26        123456789 28        ! 123456789 123456789 123       !
   ! 123456789 24        123456789 ! 123456789 123456789 123456789 ! 123456789 27        123456789 !
   ! 456       123456789 123456789 ! 46        123456789 48        ! 35        123456789 123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 123       123456789 ! 19        123456789 123456789 ! 123456789 29        15        !
   ! 34        123456789 59        ! 9         68        123456789 ! 456       123456789 123456789 !
   ! 69        123456789 17        ! 123456789 123456789 789       ! 123456789 48        47        !
   +-------------------------------+-------------------------------+-------------------------------+
)


This puzzle much simpler:
Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
485 candidates, 5446 csp-links and 5446 links. Density = 4.64%
naked-quads-in-a-block: b5{r4c4 r4c6 r6c6 r6c4}{n6 n2 n8 n4} ==> r6c5 ≠ 8, r6c5 ≠ 6, r6c5 ≠ 4, r6c5 ≠ 2, r5c6 ≠ 8, r5c6 ≠ 6, r5c6 ≠ 4, r5c6 ≠ 2, r5c5 ≠ 8, r5c5 ≠ 6, r5c5 ≠ 4, r5c5 ≠ 2, r5c4 ≠ 8, r5c4 ≠ 6, r5c4 ≠ 4, r5c4 ≠ 2, r4c5 ≠ 8, r4c5 ≠ 6, r4c5 ≠ 4, r4c5 ≠ 2
whip[1]: b5n2{r4c6 .} ==> r4c1 ≠ 2, r4c2 ≠ 2, r4c7 ≠ 2, r4c8 ≠ 2, r4c9 ≠ 2
whip[1]: b5n4{r6c6 .} ==> r6c1 ≠ 4, r6c2 ≠ 4, r6c3 ≠ 4, r6c8 ≠ 4, r6c9 ≠ 4
whip[1]: b5n6{r6c4 .} ==> r1c4 ≠ 6, r2c4 ≠ 6, r3c4 ≠ 6, r8c4 ≠ 6, r9c4 ≠ 6
whip[1]: b5n8{r6c6 .} ==> r1c6 ≠ 8, r2c6 ≠ 8, r7c6 ≠ 8, r8c6 ≠ 8, r9c6 ≠ 8
biv-chain-rc[3]: r9c3{n1 n7} - r9c6{n7 n9} - r7c4{n9 n1} ==> r7c1 ≠ 1, r7c2 ≠ 1, r7c3 ≠ 1, r9c4 ≠ 1, r9c5 ≠ 1
biv-chain-rc[3]: r5c2{n4 n2} - r7c2{n2 n3} - r8c1{n3 n4} ==> r4c1 ≠ 4, r5c1 ≠ 4, r8c2 ≠ 4, r9c2 ≠ 4
biv-chain-rc[3]: r7c2{n2 n3} - r8c1{n3 n4} - r1c1{n4 n2} ==> r7c1 ≠ 2, r1c2 ≠ 2, r2c2 ≠ 2
stte
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Re: Why Not? (Sukaku)

Postby denis_berthier » Tue Dec 15, 2020 12:56 am

mith wrote:My intended path:

Hidden Text: Show
WXYZ-Wing: 1347 in r2c46,r3c59,Pivot Cell Is r3c5 => r2c789,r3c46<>7
XY-Wing: 569 in r2c8 r4c8 r3c7 => r456c7,r13c8 <> 6
XY-Wing: 135 in r5c7 r9c7 r6c8 => r789c8,r46c7 <> 5
XY-Wing: 789 in r8c8 r8c6 r7c7 => r7c456,r8c79 <> 8
XY-Wing: 137 in r7c5 r7c1 r8c4 => r8c123,r7c46 <> 7
XY-Wing: 259 in r8c2 r6c2 r7c3 => r456c3,r79c2 <> 2
Naked Pair: in r5c3,r5c7 => r5c2<>13,r5c4<>3,r5c6<>3,r5c8<>13
XY-Wing: 135 in r5c3 r1c3 r4c2 => r123c2,r46c3 <> 5
XY-Wing: 479 in r2c2 r2c4 r3c3 => r3c456,r2c13 <> 4
Naked Pair: in r3c5,r7c5 => r2c5<>13,r4c5<>13,r6c5<>13,r8c5<>13
stte

"Y Knot"


On seeing the WXYZ-Wing in your solution, I tried to add braids. Instead of a solution in W7, I get one in B4. So, that's an interesting example of a very rare case where the B and W ratings are different.
Part of the eliminations done by your WXYZ-wings are done by braids[4] and the rest by simpler bivalue-chains[3]:

Code: Select all
(solve-sukaku-grid
   +-------------------------------+-------------------------------+-------------------------------+
   ! 24        123456789 35        ! 123456789 69        123456789 ! 47        123456789 28        !
   ! 123456789 579       123456789 ! 47        123456789 37        ! 123456789 579       123456789 !
   ! 45        123456789 49        ! 123456789 134       123456789 ! 56        123456789 17        !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 123456789 15        123456789 ! 24        123456789 79        ! 123456789 69        12346789  !
   ! 48        123456789 123       ! 123456789 57        123456789 ! 136       123456789 79        !
   ! 12346789  29        123456789 ! 38        123456789 15        ! 123456789 35        123456789 !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 37        123456789 25        ! 123456789 138       123456789 ! 89        1234567   58        !
   ! 123456789 579       123456789 ! 17        123456789 78        ! 123456789 579       123456789 !
   ! 68        123456789 58        ! 123456789 27        123456789 ! 15        123456789 46        !
   +-------------------------------+-------------------------------+-------------------------------+
)


***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = B+SFin
***  Using CLIPS 6.32-r779
***********************************************************************************************
448 candidates, 4639 csp-links and 4639 links. Density = 4.63%
braid[4]: r7c9{n8 n5} - r7c7{n8 n9} - r8c6{n8 n7} - r8c8{n9 .} ==> r8c9 ≠ 8
braid[4]: r7c9{n8 n5} - r7c7{n8 n9} - r8c6{n8 n7} - r8c8{n9 .} ==> r8c7 ≠ 8
braid[4]: r8c6{n8 n7} - r7c7{n8 n9} - r7c9{n8 n5} - r8c8{n9 .} ==> r7c6 ≠ 8
braid[4]: r8c6{n7 n8} - r7c1{n7 n3} - r7c5{n3 n1} - r8c4{n7 .} ==> r7c6 ≠ 7
braid[4]: r8c6{n8 n7} - r7c7{n8 n9} - r7c9{n8 n5} - r8c8{n9 .} ==> r7c5 ≠ 8
biv-chain-rc[3]: r8c4{n7 n1} - r7c5{n1 n3} - r7c1{n3 n7} ==> r7c4 ≠ 7, r8c1 ≠ 7, r8c2 ≠ 7, r8c3 ≠ 7
biv-chain-rc[3]: r7c3{n2 n5} - r8c2{n5 n9} - r6c2{n9 n2} ==> r7c2 ≠ 2, r9c2 ≠ 2, r4c3 ≠ 2, r5c3 ≠ 2, r6c3 ≠ 2
biv-chain-rc[3]: r4c2{n5 n1} - r5c3{n1 n3} - r1c3{n3 n5} ==> r4c3 ≠ 5, r6c3 ≠ 5, r1c2 ≠ 5, r2c2 ≠ 5, r3c2 ≠ 5
biv-chain-rc[3]: r2c4{n4 n7} - r2c2{n7 n9} - r3c3{n9 n4} ==> r3c4 ≠ 4, r3c5 ≠ 4, r3c6 ≠ 4, r2c1 ≠ 4, r2c3 ≠ 4
naked-pairs-in-a-column: c5{r3 r7}{n1 n3} ==> r8c5 ≠ 3, r8c5 ≠ 1, r6c5 ≠ 3, r6c5 ≠ 1, r4c5 ≠ 3, r4c5 ≠ 1, r2c5 ≠ 3, r2c5 ≠ 1
biv-chain-rc[3]: r3c9{n7 n1} - r3c5{n1 n3} - r2c6{n3 n7} ==> r2c7 ≠ 7, r2c8 ≠ 7, r2c9 ≠ 7, r3c4 ≠ 7, r3c6 ≠ 7
biv-chain-rc[3]: r3c7{n6 n5} - r2c8{n5 n9} - r4c8{n9 n6} ==> r1c8 ≠ 6, r3c8 ≠ 6, r4c7 ≠ 6, r5c7 ≠ 6, r6c7 ≠ 6
naked-pairs-in-a-row: r5{c3 c7}{n1 n3} ==> r5c8 ≠ 3, r5c8 ≠ 1, r5c6 ≠ 3, r5c6 ≠ 1, r5c4 ≠ 3, r5c4 ≠ 1, r5c2 ≠ 3, r5c2 ≠ 1
stte
denis_berthier
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