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by **Leren** » Mon Jun 14, 2021 10:33 am

Code: Select all: *-----------* |...|.4.|..7| |...|512|...| |5.4|..8|...| |---+---+---| |...|.3.|..5| |...|...|298| |.87|...|3..| |---+---+---| |...|.8.|..1| |.73|2..|4..| |8.9|..4|.6.| *-----------* ....4...7...512...5.4..8.......3...5......298.87...3......8...1.732..4..8.9..4.6.

by **RSW** » Mon Jun 14, 2021 11:04 am

Code: Select all: +---------------+-----------+-------------+ | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369 68 | 5 1 2 | 89 b34 346 | | 5 36 4 | 7 9 8 | 16 123 236 | +---------------+-----------+-------------+ | 2469 2469 26 | 8 3 19 | 16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 |*9-1 2 5 | 3 a14 46 | +---------------+-----------+-------------+ | 246 2456 256 | 369 8 369 | 7 c23 1 | | 16 7 3 | 2 5 16 | 4 8 9 | | 8 12 9 |e13 7 4 | 5 6 d23 | +---------------+-----------+-------------+

(1=4)r6c8-(4=3)r2c8-(3=2)r7c8-(2=3)r9c9-(3=1)r9c4 => -1r6c4; ste

by **jco** » Mon Jun 14, 2021 12:36 pm

Code: Select all: .-----------------------------------------------. | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369 68 | 5 1 2 | 89 34 346 | | 5 36 4 | 7 9 8 | 16 e23-1 d236 | |-----------------+-------------+---------------| | 2469 2469 26 | 8 3 19 | 16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 |b19 2 5 | 3 a14 46 | |-----------------+-------------+---------------| | 246 2456 256 | 369 8 369 | 7 23 1 | | 16 7 3 | 2 5 16 | 4 8 9 | | 8 12 9 |c13 7 4 | 5 6 c23 | '-----------------------------------------------'

ALS S-wing (1)r6c8 = r6c4 - (1=32)r9c49 - r3c9 = (2)r3c8 => -1 r3c8; ste

by **Ngisa** » Mon Jun 14, 2021 1:46 pm

Code: Select all: +---------------------+-----------------+------------------+ | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369 68 | 5 1 2 | 89 34 346 | | 5 36 4 | 7 9 8 |e16 f13-2 236 | +---------------------+-----------------+------------------+ | 2469 2469 26 | 8 3 c19 |d16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 | 19 2 5 | 3 14 46 | +---------------------+-----------------+------------------+ | 246 2456 256 |a369 8 a369 | 7 a23 1 | | 16 7 3 | 2 5 b16 | 4 8 9 | | 8 12 9 | 13 7 4 | 5 6 23 | +---------------------+-----------------+------------------+

(2=6)r7c864 - (6=1)r8c6 - r4c6 = r4c7 - r3c7 = (1)r3c8 => - 2r3c8; stte

Clement

by **pjb** » Mon Jun 14, 2021 11:42 pm

Code: Select all: 129 129 128 | 36 4 36 | 89 5 7 7 369 68 | 5 1 2 | 89 34 346 5 36 4 | 7 9 8 | 16 b123 a26-3 ------------------------+----------------------+--------------------- 2469 2469 26 | 8 3 19 | 16 7 5 3 15 15 | 4 6 7 | 2 9 8 69 8 7 |d19 2 5 | 3 c14 46 ------------------------+----------------------+--------------------- 246 2456 256 | 369 8 369 | 7 23 1 16 7 3 | 2 5 16 | 4 8 9 8 12 9 |e13 7 4 | 5 6 f3-2

(2)r3c9 = (2-1)r3c8 = (1)r6c8 - (1)r6c4 = (1-3)r9c4 = (3-2)r9c9 => -2 r9c9, -3 r3c9; stte

Phil

by **storm_norm22** » Tue Jun 15, 2021 12:07 am

Code: Select all: +-----------------+-------------+--------------+ | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369 68 | 5 1 2 | 89 34 346 | | 5 36 4 | 7 9 8 | 16 123 236 | +-----------------+-------------+--------------+ | 2469 2469 26 | 8 3 19 | 16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 | 19 2 5 | 3 14 46 | +-----------------+-------------+--------------+ | 246 2456 256 | 369 8 369 | 7 23 1 | | 16 7 3 | 2 5 16 | 4 8 9 | | 8 12 9 | 13 7 4 | 5 6 23 | +-----------------+-------------+--------------+

(4=3)r2c8 - (3)r7c8 = (3)r9c9 - (3=1)r9c4 - (1)r6c4 = (1)r6c8; r6c8 <> 4

Website · by **denis_berthier** » Tue Jun 15, 2021 3:32 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 129 129 128 ! 36 4 36 ! 189 5 7 ! ! 7 369 68 ! 5 1 2 ! 689 34 346 ! ! 5 136 4 ! 7 9 8 ! 16 123 236 ! +----------------+----------------+----------------+ ! 2469 2469 26 ! 8 3 19 ! 16 7 5 ! ! 3 15 15 ! 4 6 7 ! 2 9 8 ! ! 69 8 7 ! 19 2 5 ! 3 14 46 ! +----------------+----------------+----------------+ ! 246 2456 256 ! 369 8 369 ! 7 23 1 ! ! 16 7 3 ! 2 5 16 ! 4 8 9 ! ! 8 12 9 ! 13 7 4 ! 5 6 23 ! +----------------+----------------+----------------+

===> There are 23 W1-anti-backdoors:
n1r1c1 n3r2c8 n4r2c9 n3r3c2 n6r3c7 n1r3c8 n2r3c8 n9r4c6 n1r4c7 n5r5c2 n1r5c3 n9r6c1 n1r6c4 n4r6c8 n6r6c9 n5r7c3 n9r7c4 n3r7c8 n6r8c1 n1r8c6 n1r9c2 n3r9c4 n2r9c9
19 of which give rise to a 1-step solution with of whip of length ≤ 5

The simplest few require only a bivalue-chain[4], and one even requires only a bivalue-chain[4] in rn-space:

Code: Select all: biv-chain-rn[4]: r3n2{c8 c9} - r9n2{c9 c2} - r9n1{c2 c4} - r6n1{c4 c8} ==> r3c8 ≠ 1 stte

Code: Select all: biv-chain[4]: r7c8{n2 n3} - r9n3{c9 c4} - c4n1{r9 r6} - c8n1{r6 r3} ==> r3c8 ≠ 2 stte

Code: Select all: biv-chain[4]: c8n4{r2 r6} - r6n1{c8 c4} - r9c4{n1 n3} - b9n3{r9c9 r7c8} ==> r2c8 ≠ 3 stte

Code: Select all: biv-chain[4]: r6c8{n1 n4} - r2c8{n4 n3} - b9n3{r7c8 r9c9} - r9c4{n3 n1} ==> r6c4 ≠ 1 stte

Code: Select all: biv-chain[4]: r2c8{n4 n3} - b9n3{r7c8 r9c9} - r9c4{n3 n1} - r6n1{c4 c8} ==> r6c8 ≠ 4 stte

Code: Select all: biv-chain[4]: r2c8{n3 n4} - r6c8{n4 n1} - c4n1{r6 r9} - r9n3{c4 c9} ==> r7c8 ≠ 3, r2c9 ≠ 3, r3c9 ≠ 3 stte

Code: Select all: biv-chain[4]: r9n2{c2 c9} - b3n2{r3c9 r3c8} - c8n1{r3 r6} - c4n1{r6 r9} ==> r9c2 ≠ 1 stte

Code: Select all: biv-chain[4]: r9c9{n3 n2} - b3n2{r3c9 r3c8} - c8n1{r3 r6} - c4n1{r6 r9} ==> r9c4 ≠ 3 stte

Code: Select all: biv-chain[4]: r9c2{n2 n1} - c4n1{r9 r6} - c8n1{r6 r3} - b3n2{r3c8 r3c9} ==> r9c9 ≠ 2 stte

by **Cenoman** » Tue Jun 15, 2021 4:06 pm

Code: Select all: +----------------------+-------------------+-------------------+ | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369* 68 | 5 1 2 | 89 34 346* | | 5 36* 4 | 7 9 8 | c16 c13-2 236* | +----------------------+-------------------+-------------------+ | 2469 a2469 26 | 8 3 19 | b16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 | 19 2 5 | 3 14 a46 | +----------------------+-------------------+-------------------+ | 246 A2456 256 | B369 8 B369 | 7 zB23 1 | | 16 7 3 | 2 5 16 | 4 8 9 | | 8 12 9 | 13 7 4 | 5 6 y23 | +----------------------+-------------------+-------------------+

UR(36)r23c29 using externals
(6)r4c2|r6c9 - r4c6 = (61)r3c78
(6)r7c2 - (6=392)r7c468
(3)r9c9 - (3=2)r7c8
=> -2 r3c8; ste

by **Sudtyro2** » Wed Jun 16, 2021 12:24 pm

Code: Select all: +----------------+----------------+-----------------+ | 129 129 128 | 36 4 36 | 89 5 7 | | 7 369 68 | 5 1 2 | 89 a34 346 | | 5 36 4 | 7 9 8 | 16 123 c236 | +----------------+----------------+-----------------+ | 2469 2469 26 | 8 3 19 | 16 7 5 | | 3 15 15 | 4 6 7 | 2 9 8 | | 69 8 7 | 9-1 2 5 | 3 ab14 b46 | +----------------+----------------+-----------------+ | 246 2456 256 | 369 8 369 | 7 23 1 | | 16 7 3 | 2 5 16 | 4 8 9 | | 8 12 9 | d13 7 4 | 5 6 d23 | +----------------+----------------+-----------------+

Myth's CoALS rule applied to the two overlapping ALS tagged (a&b).
The digits in the overlap cell(r6c8) are strongly linked to the digits in the non-overlap cells(r2c8,r6c9) not found in the overlap cell.
(14=36)r26c8,r6c9 - (3|6=2)r3c9 - (2=31)r9c49 => -1 r6c4; stte.

SteveC

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