a dual then more of the same then more work

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a dual then more of the same then more work

Postby ghfick » Thu Oct 08, 2020 12:13 am

.8.9.3...4....2.9.....1.8.3.9.....282..7.8..584.....1.3.4.2.....1.5....9...1.7.4.
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Re: a dual then more of the same then more work

Postby denis_berthier » Thu Oct 08, 2020 4:34 am

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = BC+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
lots of singles
127 candidates, 527 csp-links and 527 links. Density = 6.59%
whip[1]: b7n5{r9c2 .} ==> r2c2 ≠ 5
naked-pairs-in-a-row: r5{c2 c8}{n3 n6} ==> r5c7 ≠ 6, r5c7 ≠ 3, r5c5 ≠ 6
finned-x-wing-in-columns: n5{c6 c1}{r3 r6} ==> r6c3 ≠ 5
whip[1]: r6n5{c6 .} ==> r4c5 ≠ 5
finned-x-wing-in-rows: n7{r3 r8}{c1 c8} ==> r7c8 ≠ 7
biv-chain[3]: r6c9{n7 n6} - r5n6{c8 c2} - b4n3{r5c2 r6c3} ==> r6c3 ≠ 7
whip[1]: r6n7{c9 .} ==> r4c7 ≠ 7
naked-pairs-in-a-row: r4{c5 c7}{n4 n6} ==> r4c3 ≠ 6, r4c1 ≠ 6
finned-x-wing-in-columns: n6{c6 c3}{r6 r3} ==> r3c1 ≠ 6
singles ==> r8c1 = 6, r9c2 = 5, r7c2 = 7
hidden-pairs-in-a-column: c7{n1 n5}{r2 r7} ==> r7c7 ≠ 6, r2c7 ≠ 7, r2c7 ≠ 6
x-wing-in-rows: n6{r4 r9}{c5 c7} ==> r6c7 ≠ 6, r6c5 ≠ 6, r2c5 ≠ 6, r1c5 ≠ 6
finned-x-wing-in-rows: n6{r1 r5}{c8 c3} ==> r6c3 ≠ 6
singles ==> r6c3 = 3, r5c2 = 6, r2c2 = 3, r5c8 = 3
finned-x-wing-in-columns: n6{c4 c8}{r7 r2} ==> r2c9 ≠ 6
whip[1]: b3n6{r3c8 .} ==> r7c8 ≠ 6
biv-chain[3]: r3n7{c1 c8} - r3n6{c8 c6} - r2n6{c4 c3} ==> r2c3 ≠ 7
biv-chain[3]: r2n7{c9 c5} - c5n8{r2 r8} - r8c8{n8 n7} ==> r1c8 ≠ 7, r3c8 ≠ 7
stte
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Re: a dual then more of the same then more work

Postby ghfick » Fri Oct 09, 2020 12:01 am

Hi Denis,
SudoRules path is interesting. My cryptic title was for another path that uses the somewhat rare Dual Empty Rectangle followed by 3! more Empty Rectangles. Maybe this combo is even more rare? I think you still need an XY Chain. Sure there are 'quicker' paths but I had not seen so many ERs [in my memory].
Gordon
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Re: a dual then more of the same then more work

Postby denis_berthier » Fri Oct 09, 2020 5:58 am

ghfick wrote:Hi Denis,
SudoRules path is interesting. My cryptic title was for another path that uses the somewhat rare Dual Empty Rectangle followed by 3! more Empty Rectangles. Maybe this combo is even more rare? I think you still need an XY Chain. Sure there are 'quicker' paths but I had not seen so many ERs [in my memory].
Gordon

Hi Gordon,
I see. I misunderstood "dual" as referring to some symmetry, but I couldn't find any. And, anyway, symmetries can rarely be exploited for eliminations.
ERs are not (directly) coded in SudoRules. I keep them and all the exotic fish patterns as good exercises for people trying to expand the existing rules.
ER eliminations may be obtained by chains.
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Re: a dual then more of the same then more work

Postby Cenoman » Fri Oct 09, 2020 5:10 pm

Code: Select all
 +---------------------+-------------------+----------------------+
 |  1     8    w567*   |  9   x567    3    |  2     w567*   4     |
 |  4     367   3567   |  68   5678   2    |  1567   9      167   |
 | c567   2     9      |  4    1    yb56   |  8      567    3     |
 +---------------------+-------------------+----------------------+
 | d567   9     567    |  3    46-5   1    |  467    2      8     |
 |  2   wC36*   1      |  7    49     8    |  49   wB36*    5     |
 |  8     4    D3-567  |  2    569  za56   |  3679   1     A67    |
 +---------------------+-------------------+----------------------+
 |  3     567   4      |  68   2      9    |  1567   5678   167   |
 |  67    1     2      |  5    368    4    |  367    3678   9     |
 |  9     56    8      |  1    36     7    |  356    4      2     |
 +---------------------+-------------------+----------------------+

1. Kite (5)r6c6 = r3c6 - r3c1 = (5)r4c1 => -5 r4c5, r6c3
2. H-Wing (7=6)r6c9 - (6=3)r5c8 - r5c2 = (3)r6c3 => -7 r6c3
3. Almost kite (6)
[(6)r1c3 = r1c8 - r5c8 = r5c2] = r1c5 - r3c6 = r6c6 => -6r6c3; 7 placements and basics

Code: Select all
 +------------------+-------------------+--------------------+
 |  1    8    567   |  9    567    3    |  2    c567*  4     |
 |  4    3   f567   | h68  e567-8  2    |  15    9    d167*  |
 | g57   2    9     |  4    1     h56   |  8    c567*  3     |
 +------------------+-------------------+--------------------+
 |  57   9    57    |  3    46     1    |  46    2     8     |
 |  2    6    1     |  7    49     8    |  49    3     5     |
 |  8    4    3     |  2    569    56   |  679   1     67    |
 +------------------+-------------------+--------------------+
 |  3    7    4     |  68   2      9    |  15    568   16    |
 |  6    1    2     |  5   a38*    4    |  37   a78*   9     |
 |  9    5    8     |  1    36     7    |  36    4     2     |
 +------------------+-------------------+--------------------+

4. Almost grouped L2-Wing:
[(8)r8c5 = (8-7)r8c8 = r13c8 - r2c9 = (7)r2c5] = (7)r2c3 - (7=5)r3c1 - (5=68)b2p49 => -8 r2c5; ste
(embedded wing tagged a to e, spoiler chain f to h)
Last edited by Cenoman on Fri Oct 09, 2020 8:40 pm, edited 1 time in total.
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Re: a dual then more of the same then more work

Postby ghfick » Fri Oct 09, 2020 5:47 pm

DER.png
DER.png (119.46 KiB) Viewed 443 times

Here is the Dual ER with HoDoKu
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Re: a dual then more of the same then more work

Postby yzfwsf » Sat Oct 10, 2020 12:43 am

Dual ER.png
Dual ER.png (31.36 KiB) Viewed 427 times

Dual Empty Rectangle : 6 in b3 connected by r5,c4 = > r7c28,r2c2 <> 6

Dual ER2.png
Dual ER2.png (30.34 KiB) Viewed 426 times

Dual Empty Rectangle : 6 in b5 connected by r3,c2 = > r78c3 <> 6
Hodoku can't catch it.
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