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by **Leren** » Sun Jul 11, 2021 10:01 am

Code: Select all: *-----------* |...|...|148| |...|.47|...| |82.|...|...| |---+---+---| |.1.|5..|9.4| |4.2|...|.3.| |7..|1..|...| |---+---+---| |...|6.1|7..| |..7|.2.|.89| |..5|..9|...| *-----------* ......148....47...82........1.5..9.44.2....3.7..1........6.17....7.2..89..5..9...

by **jco** » Sun Jul 11, 2021 1:15 pm

Code: Select all: .---------------------------------------------. | 369 7 369 | 2 5 36 | 1 4 8 | | 5 c36 1 | 8 4 7 |d236 9 d236 | | 8 2 4 | 9 1 36 |e36-5 56 7 | |--------------+-------------+----------------| | 36 1 8 | 5 36 2 | 9 7 4 | | 4 59 2 | 7 69 8 |a56 3 1 | | 7 59 36 | 1 369 4 | 8 256 256 | |--------------+-------------+----------------| | 239 4 39 | 6 8 1 | 7 25 235 | | 1 c36 7 | 34 2 5 |b346 8 9 | | 236 8 5 | 34 7 9 | 2346 1 236 | '---------------------------------------------'

(5=6)r5c7 - r8c7 = (63)r28c2 - (3)r2c79 = (3)r3c7 => -5 r3c7; ste

by **Ngisa** » Sun Jul 11, 2021 3:06 pm

Code: Select all: +--------------------+-------------------+----------------------+ | 369 7 369 | 2 5 36 | 1 4 8 | | 5 36 1 | 8 4 7 | 236 9 236 | | 8 2 4 | 9 1 36 | 356 56 7 | +--------------------+-------------------+----------------------+ |a36 1 8 | 5 b36 2 | 9 7 4 | | 4 59 2 | 7 c69 8 |d56 3 1 | | 7 59 36 | 1 369 4 | 8 256 256 | +--------------------+-------------------+----------------------+ | 239 4 39 | 6 8 1 | 7 25 235 | | 1 36 7 | 34 2 5 |e346 8 9 | | 23-6 8 5 | 34 7 9 |e2346 1 f236 | +--------------------+-------------------+----------------------+

(6)r4c1 = r4c5 – r5c5 = r5c7 – r89c7 = (6)r9c9 => - 6r9c1; stte

Clement

by **Cenoman** » Sun Jul 11, 2021 5:33 pm

Code: Select all: +-------------------+------------------+---------------------+ | 369 7 369 | 2 5 36 | 1 4 8 | | 5 d36 1 | 8 4 7 | c236 9 236 | | 8 2 4 | 9 1 36 | b356 56 7 | +-------------------+------------------+---------------------+ | 36 1 8 | 5 36 2 | 9 7 4 | | 4 59 2 | 7 69 8 | a5-6 3 1 | | 7 59 36 | 1 369 4 | 8 256 256 | +-------------------+------------------+---------------------+ | 239 4 39 | 6 8 1 | 7 25 235 | | 1 e36 7 | 34* 2 5 | f346* 8 9 | | 236 8 5 | 34* 7 9 | 2346* 1 236 | +-------------------+------------------+---------------------+

UR(34)r89c47 using externals
(5)r5c7 = (5-3)r3c7 == (3)r2c7 - (3=6)r2c2 - r8c2 = (6)r8c7 => -6 r5c7; ste

by **P.O.** » Sun Jul 11, 2021 6:01 pm

Code: Select all: after singles: 369 7 a3-69 2 5 36 1 4 8 5 3×6 1 8 4 7 236 9 236 8 2 4 9 1 36 356 56 7 36 1 8 5 36 2 9 7 4 4 569 2 7 69 8 d5+6 3 1 7 3569 b3+69 1 369 4 8 c25-6 c25-6 239 4 39 6 8 1 7 25 235 1 f3+6 7 34 2 5 e34-6 8 9 236 8 5 34 7 9 2346 1 236 depth: 2 candidate: 6 from cell (((2 2 1) (3 6))) ((6 0) (1 3 1) (3 6 9)) if R1C3 is not 6 ((6 0) (6 3 4) (3 6 9)) R6C3 is 6 ((6 1 3) (5 7 6) (5 6)) R5C7 is 6 ((6 2 1) (8 2 7) (3 6)) R8C2 is 6 ste.

by **pjb** » Mon Jul 12, 2021 3:10 am

Code: Select all: 369 7 369 | 2 5 36 | 1 4 8 5 36 1 | 8 4 7 | 236 9 236 8 2 4 | 9 1 36 | 356 56 7 ------------------------+----------------------+--------------------- a36 1 8 | 5 b36 2 | 9 7 4 4 59 2 | 7 c69 8 |d56 3 1 7 59 36 | 1 369 4 | 8 256 256 ------------------------+----------------------+--------------------- 239 4 39 | 6 8 1 | 7 25 235 1 f36 7 | 34 2 5 |e346 8 9 23-6 8 5 | 34 7 9 | 2346 1 236

(6)r4c1 = r4c5 - r5c5 = r5c7 - r8c7 = (6)r8c2 => -6 r9c1; stte
(Same cells constitute a sashimi SF)
Phil

by **Sudtyro2** » Mon Jul 12, 2021 4:13 pm

Code: Select all: +----------------+------------+------------------+ | 369 7 369 | 2 5 36 | 1 4 8 | | 5 36* 1 | 8 4 7 | 236# 9 236* | | 8 2 4 | 9 1 36 | 356 56 7 | +----------------+------------+------------------+ | 36 1 8 | 5 36 2 | 9 7 4 | | 4 59 2 | 7 69 8 | 5-6 3 1 | | 7 59 36 | 1 369 4 | 8 256 256# | +----------------+------------+------------------+ | 239 4 39 | 6 8 1 | 7 25 235 | | 1 36* 7 | 34 2 5 | 346 8 9 | | 236* 8 5 | 34 7 9 | 2346# 1 236* | +----------------+------------+------------------+

In 6s, a 5-link oddagon(*) with three [ORed] guardians(#):
(6)r6c9,r29c7 => -6 r5c7; stte

SteveC

by **Cenoman** » Tue Jul 13, 2021 7:44 am

Sudtyro2 wrote:In 6s, a 5-link oddagon(*) with three [ORed] guardians(#):
(6)r6c9,r29c7 => -6 r5c7; stte

Applause !

Website · by **denis_berthier** » Fri Jul 16, 2021 5:48 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 369 7 369 ! 2 5 36 ! 1 4 8 ! ! 5 36 1 ! 8 4 7 ! 236 9 236 ! ! 8 2 4 ! 9 1 36 ! 356 56 7 ! +----------------+----------------+----------------+ ! 36 1 8 ! 5 36 2 ! 9 7 4 ! ! 4 569 2 ! 7 69 8 ! 56 3 1 ! ! 7 3569 36 ! 1 369 4 ! 8 256 256 ! +----------------+----------------+----------------+ ! 239 4 39 ! 6 8 1 ! 7 25 235 ! ! 1 36 7 ! 34 2 5 ! 346 8 9 ! ! 236 8 5 ! 34 7 9 ! 2346 1 236 ! +----------------+----------------+----------------+

===> There are 25 W1-anti-backdoors:
n6r1c6 n6r2c2 n3r3c6 n5r3c7 n6r3c8 n3r4c1 n6r4c5 n5r5c2 n9r5c5 n6r5c7 n9r6c2 n6r6c3 n3r6c5 n2r6c8 n5r6c9 n2r7c1 n5r7c8 n3r7c9 n3r8c2 n4r8c4 n6r8c7 n6r9c1 n3r9c4 n4r9c7 n6r9c9

The simplest two 1-step solutions are:

Code: Select all: z-chain[3]: b7n6{r8c2 r9c1} - c9n6{r9 r6} - c3n6{r6 .} ==> r2c2 ≠ 6 stte

Code: Select all: z-chain[3]: r8n6{c7 c2} - r2n6{c2 c9} - b9n6{r9c9 .} ==> r5c7 ≠ 6 stte

Upon seeing Sudtyro2's solution, I tried to activate only oddagons, but starting from the PM after whips[1], I need 2 oddagons:

Code: Select all: oddagon[5]: r4c1{n3 n6},b4n6{r4c1 r6c2},r6n6{c2 c3},r6c3{n6 n3},b4n3{r6c3 r4c1} ==> r6c2 ≠ 6 oddagon[5]: r2n6{c2 c9},c9n6{r2 r9},r9n6{c9 c1},b7n6{r9c1 r8c2},c2n6{r8 r2} ==> r5c7 ≠ 6 stte

The first eliminates a candidate that is already supposed to be eliminated in Studtyro2's starting point; he second is (unsurprisingly) the same as Sudtyro2's.

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