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by **Leren** » Thu Jun 03, 2021 6:36 am

Code: Select all: *-----------* |...|..4|6..| |..8|...|..2| |...|...|...| |---+---+---| |..5|2..|..8| |.6.|..1|...| |7..|3..|..5| |---+---+---| |6..|..8|4..| |4..|9..|1..| |..2|.5.|...| *-----------* .....46....8.....2...........52....8.6...1...7..3....56....84..4..9..1....2.5....

Website · by **denis_berthier** » Thu Jun 03, 2021 9:19 am

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Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 5 12379 1379 ! 178 12379 4 ! 6 3789 1379 ! ! 139 13479 8 ! 6 1379 3579 ! 3579 3479 2 ! ! 1239 123479 6 ! 178 12379 23579 ! 35789 34789 13479 ! +----------------------+----------------------+----------------------+ ! 139 139 5 ! 2 4679 679 ! 379 134679 8 ! ! 2389 6 349 ! 5 4789 1 ! 2379 3479 3479 ! ! 7 1289 149 ! 3 4689 69 ! 29 1469 5 ! +----------------------+----------------------+----------------------+ ! 6 3579 379 ! 17 1237 8 ! 4 23579 379 ! ! 4 3578 37 ! 9 2367 2367 ! 1 23578 367 ! ! 1389 13789 2 ! 4 5 367 ! 3789 3789 3679 ! +----------------------+----------------------+----------------------+

There is an easy solution with swordfish and bivalue-chains[3}

Apart from allowing hidden Subsets, there is no 1-step solution with chains of reasonable length. (There's only 1 W1-anti-backdoor: n8r9c7.)

As for 2-step solutions (with no undeclared Subset steps), there are lots of them. Here is the simplest:

Code: Select all: biv-chain-rn[2]: r8n5{c8 c2} - r8n8{c2 c8} ==> r8c8 ≠ 2, r8c8 ≠ 3, r8c8 ≠ 7 singles and whips[1] z-chain[4]: r5n9{c3 c5} - c5n7{r5 r7} - r7n3{c5 c9} - r8n3{c9 .} ==> r5c3 ≠ 3 stte

The first eliminations can also be done by:
biv-chain-cn[2]: c8n2{r8 r7} - c8n5{r7 r8} ==> r8c8 ≠ 8, r8c8 ≠ 3, r8c8 ≠ 7

Notice that the first version is also hidden pairs in a row and the second hidden pairs in a column - so that

Code: Select all: z-chain[4]: r5n9{c3 c5} - c5n7{r5 r7} - r7n3{c5 c9} - r8n3{c9 .} ==> r5c3 ≠ 3 is a 1-step solution modulo Pairs

by **pjb** » Thu Jun 03, 2021 12:52 pm

Code: Select all: 5 379 1 | 78 2 4 | 6 3789 379 39 3479 8 | 6 1 359 | 357 3479 2 2 3479 6 | 78 39 359 | 3578 34789 1 ------------------------+----------------------+--------------------- 139 139 5 | 2 4 79 | 37 6 8 8 6 9-3 | 5 b79 1 | 2 c37 4 7 2 4 | 3 8 6 | 9 1 5 ------------------------+----------------------+--------------------- 6 5 *379 | 1 a37 8 | 4 2 *379 4 8 *37 | 9 6 2 | 1 5 *37 139 139 2 | 4 5 37 | 378 3789 6

Kraken X-wing of 3's at r78c39, fin at r7c5 linked via (7)r7c5 = r5c5 - (7=3)r5c8 => -3 r5c3; stte

Phil

by **jco** » Thu Jun 03, 2021 9:16 pm

Code: Select all: .-------------------------------------------------------. | 5 379 1 | 78 2 4 | 6 3789 379 | | 39 3479 8 | 6 1 359 | 357 3479 2 | | 2 3479 6 | 78 39 359 | 3578 34789 1 | |--------------------+---------------+------------------| | 13-9 13-9 5 | 2 4 a79 | 37 6 8 | | 8 6 d39 | 5 7-9 1 | 2 37 4 | | 7 2 4 | 3 8 6 | 9 1 5 | |--------------------+---------------+------------------| | 6 5 c379 | 1 37 8 | 4 2 379 | | 4 8 c37 | 9 6 2 | 1 5 37 | | b139 b139 2 | 4 5 a37 | 378 3789 6 | '-------------------------------------------------------'

ALS W-wing (9=73)r49c6-(3)r9c12=(3)r78c3-(3=9)r5c3 => -9 r4c12,r5c5

by **Cenoman** » Fri Jun 04, 2021 4:19 pm

Code: Select all: +---------------------+------------------+-----------------------+ | 5 379 1 | 78 2 4 | 6 3789 379 | | 39 3479 8 | 6 1 359 | 357 3479 2 | | 2 3479 6 | 78 39 359 | 3578 34789 1 | +---------------------+------------------+-----------------------+ | 139* 139* 5 | 2 4 a9-7 | 37 6 8 | | 8 6 39 | 5 79 1 | 2 37 4 | | 7 2 4 | 3 8 6 | 9 1 5 | +---------------------+------------------+-----------------------+ | 6 5 379 | 1 37 8 | 4 2 379 | | 4 8 37 | 9 6 2 | 1 5 37 | | b139* b139* 2 | 4 5 c37 | 378 3789 6 | +---------------------+------------------+-----------------------+

UR (19)r49c12 using mixed external-internals
(9)r4c6 == (3)r9c12 - (3=7)r9c6 => -7 r4c6; ste

by **SteveG48** » Fri Jun 04, 2021 4:48 pm

Code: Select all: *--------------------------------------------------------------------* | 5 379 1 | 78 2 4 | 6 3789 379 | | 39 3479 8 | 6 1 359 | 357 3479 2 | | 2 3479 6 | 78 a39 359 | 3578 34789 1 | *----------------------+----------------------+----------------------| | 139 139 5 | 2 4 79 | 37 6 8 | | 8 6 e39 | 5 7-9 1 | 2 37 4 | | 7 2 4 | 3 8 6 | 9 1 5 | *----------------------+----------------------+----------------------| | 6 5 d379 | 1 a37 8 | 4 2 bc379 | | 4 8 de37 | 9 6 2 | 1 5 c37 | | 139 139 2 | 4 5 37 | 378 3789 6 | *--------------------------------------------------------------------*

(9=37)r37c5 - 7r7c9 = 9r7c9|7r8c9 - (79)r78c3 = 9r58c3 => -9 r5c5 ; stte

by **jco** » Fri Jun 04, 2021 9:00 pm

Cenoman wrote:
Code: Select all
+---------------------+------------------+-----------------------+ | 5 379 1 | 78 2 4 | 6 3789 379 | | 39 3479 8 | 6 1 359 | 357 3479 2 | | 2 3479 6 | 78 39 359 | 3578 34789 1 | +---------------------+------------------+-----------------------+ | 139* 139* 5 | 2 4 a9-7 | 37 6 8 | | 8 6 39 | 5 79 1 | 2 37 4 | | 7 2 4 | 3 8 6 | 9 1 5 | +---------------------+------------------+-----------------------+ | 6 5 379 | 1 37 8 | 4 2 379 | | 4 8 37 | 9 6 2 | 1 5 37 | | b139* b139* 2 | 4 5 c37 | 378 3789 6 | +---------------------+------------------+-----------------------+

UR (19)r49c12 using mixed external-internals
(9)r4c6 == (3)r9c12 - (3=7)r9c6 => -7 r4c6; ste

Very nice !!

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