The New Sudoku Players' Forum

[ghfick]

.8.9.3...4....2.9.....1.8.3.9.....282..7.8..584.....1.3.4.2.....1.5....9...1.7.4.

[denis_berthier]

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

[ghfick]

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

[denis_berthier]

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.

[Cenoman]

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)

[ghfick]

DER.png (119.46 KiB) Viewed 649 times

Here is the Dual ER with HoDoKu

[yzfwsf]

Dual ER.png (31.36 KiB) Viewed 633 times

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

Dual ER2.png (30.34 KiB) Viewed 632 times

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