The New Sudoku Players' Forum

by **Leren** » Fri Jul 09, 2021 8:36 am

Code: Select all: *-----------* |...|..1|4.3| |..2|49.|.68| |...|6.2|1..| |---+---+---| |..6|.4.|.1.| |1.7|2..|..4| |24.|...|...| |---+---+---| |.79|1..|..6| |..1|.7.|.9.| |85.|...|...| *-----------* .....14.3..249..68...6.21....6.4..1.1.72....424........791....6..1.7..9.85.......

by **pjb** » Fri Jul 09, 2021 9:47 am

Code: Select all: 9 6 58 | 7 58 1 | 4 2 3 357 1 2 | 4 9 35 | 57 6 8 b3457 38 3458 | 6 358 2 | 1 a57 9 ------------------------+----------------------+--------------------- 35 389 6 | 3589 4 7 | 389 1 2 1 389 7 | 2 36 3689 | 35689 358 4 2 4 358 | 3589 1 3689 | 3689 38 7 ------------------------+----------------------+--------------------- c34 7 9 | 1 235 358 | 238 d348 6 6 2 1 | 38 7 4 | 38 9 5 8 5 34 | 39 236 369 | 237 e34-7 1

(7)r3c8 = (7-4)r3c1 = (4)r7c1 - (4)r7c8 = (4-7)r9c8 => -7 r9c8; stte

Phil

by **Cenoman** » Fri Jul 09, 2021 9:56 am

Code: Select all: +----------------------+----------------------+---------------------+ | 9 6 58 | 7 58 1 | 4 2 3 | | a357 1 2 | 4 9 35 | 5-7 6 8 | | 345-7 38 3458 | 6 358 2 | 1 c57 9 | +----------------------+----------------------+---------------------+ | a35 389 6 | 3589 4 7 | 389 1 2 | | 1 389 7 | 2 36 3689 | 35689 c358 4 | | 2 4 358 | 3589 1 3689 | 3689 c38 7 | +----------------------+----------------------+---------------------+ | a34 7 9 | 1 235 358 | 238 b348 6 | | 6 2 1 | 38 7 4 | 38 9 5 | | 8 5 34 | 39 236 369 | 237 347 1 | +----------------------+----------------------+---------------------+

(7=354)r247c1 - (4=3|8)r7c7 - (385=7)r356c8 => -7 r2c8, r3c1; ste

by **P.O.** » Fri Jul 09, 2021 3:45 pm

Code: Select all: after singles: 9 6 58 7 58 1 4 2 3 357 1 2 4 9 35 57 6 8 3457 d38 d3-458 6 d358 2 1 a×5-7 9 35 389 6 3589 4 7 3589 1 2 1 389 7 2 3568 35689 35689 358 4 2 4 358 3589 1 35689 35689 358 7 34 7 9 1 2358 358 238 348 6 6 2 1 38 7 4 38 9 5 8 5 c3+4 39 236 369 237 b3-4+7 1 depth: 2 candidate: 5 from start ((7 0) (3 8 3) (5 7)) if R3C8 is not 7 ((7 0) (9 8 9) (3 4 7)) R9C8 is 7 ((4 1 10) (9 3 7) (3 4)) R9C3 is 4 ((5 2 1 221) ((3 2 1) (3 8)) ((3 3 1) (3 4 5 8)) ((3 5 2) (3 5 8))) a triplet: one is 5 ste.

by **Sudtyro2** » Fri Jul 09, 2021 8:38 pm

Code: Select all: +-------------------+---------------+----------------+ | 9 6 58 | 7 58 1 | 4 2 3 | | 357 1 2 | 4 9 35 | 5-7 6 8 | | b3457# 38 c3458 | 6 358 2 | 1 a57 9 | +-------------------+---------------+----------------+ | 35 389 6 | 3589 4 7 | 389 1 2 | | 1 389 7 | 2 36 3689 | 35689 358 4 | | 2 4 358 | 3589 1 3689 | 3689 38 7 | +-------------------+---------------+----------------+ | 34 7 9 | 1 235 358 | 238 348 6 | | 6 2 1 | 38 7 4 | 38 9 5 | | 8 5 d34 | 39 236 369 | f237 e34-7 1 | +-------------------+---------------+----------------+

Kraken (7)r3:
(7)r3c8 = (7-4)r3c1 = r3c3 - r9c3 = (4-7)r9c8 = (7)r9c7 => -7 r2c7,r9c8; stte
Or, simply drop the first term in the Kraken chain to get the same two eliminations from the Siamese Kraken Franken 1x1 Fish(7)r3\(b3,c8) + rfr3c1(#). [Edited 7/3/21 to correct the 1-Fish base/cover notation]
Note similarity to Phil's chain.

SteveC
PS. Seems that P.O.'s opening grid shows different eliminations among the 4,5&7 digits in c9.
Am I reading that matrix correctly?

by **jco** » Fri Jul 09, 2021 10:00 pm

Sudtyro2 wrote:(...)
PS. Seems that P.O.'s opening grid shows different eliminations among the 4,5&7 digits in c9.
Am I reading that matrix correctly?

This is an AIC version of P.O.'s move:

(7)r3c8=(7-4)r9c8=r9c3-(4=385)r3c235 => -5 r3c8; ste

The elimination in P.O.'s board is marked with an "x". In the cells the digits with +/- are the ones selected for the chain (cells' sequence ordered with letters as usual).

Regards,

by **SteveG48** » Sat Jul 10, 2021 11:56 pm

Code: Select all: *--------------------------------------------------------------------* | 9 6 58 | 7 58 1 | 4 2 3 | | 357 1 2 | 4 9 35 | 57 6 8 | | 3457 a38 a3458 | 6 a358 2 | 1 7-5 9 | *----------------------+----------------------+----------------------| | 35 389 6 | 3589 4 7 | 389 1 2 | | 1 389 7 | 2 36 3689 | 35689 c358 4 | | 2 4 358 | 3589 1 3689 | 3689 c38 7 | *----------------------+----------------------+----------------------| | 34 7 9 | 1 235 358 | 238 c348 6 | | 6 2 1 | 38 7 4 | 38 9 5 | | 8 5 b34 | 39 236 369 | 237 c347 1 | *--------------------------------------------------------------------*

(5=384)r3c235 - 4r9c3 = (3485)r5679c8 => -5 r3c8 ; stte

Website · by **denis_berthier** » Sun Jul 11, 2021 4:58 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 9 6 58 ! 7 58 1 ! 4 2 3 ! ! 357 1 2 ! 4 9 35 ! 57 6 8 ! ! 3457 38 3458 ! 6 358 2 ! 1 57 9 ! +-------------------+-------------------+-------------------+ ! 35 389 6 ! 3589 4 7 ! 389 1 2 ! ! 1 389 7 ! 2 36 3689 ! 35689 358 4 ! ! 2 4 358 ! 3589 1 3689 ! 3689 38 7 ! +-------------------+-------------------+-------------------+ ! 34 7 9 ! 1 235 358 ! 238 348 6 ! ! 6 2 1 ! 38 7 4 ! 38 9 5 ! ! 8 5 34 ! 39 236 369 ! 237 347 1 ! +-------------------+-------------------+-------------------+

There are 9 W1-anti-backdoors:
n7r2c7 n4r3c1 n7r3c1 n5r3c8 n5r5c7 n3r7c1 n4r7c8 n4r9c3 n7r9c8
all of which give rise to a solution with whips[≤7]
The simplest four are:

Code: Select all: biv-chain-cn[3]: c1n4{r3 r7} - c8n4{r7 r9} - c8n7{r9 r3} ==> r3c1 ≠ 7 stte

Code: Select all: biv-chain-rn[3]: r3n7{c8 c1} - r3n4{c1 c3} - r9n4{c3 c8} ==> r9c8 ≠ 7 stte

Code: Select all: biv-chain-rn[4]: r3n7{c8 c1} - r3n4{c1 c3} - r9n4{c3 c8} - r9n7{c8 c7} ==> r2c7 ≠ 7, r9c8 ≠ 7 stte

Code: Select all: z-chain[4]: c8n7{r3 r9} - c8n4{r9 r7} - c1n4{r7 r3} - r3n7{c1 .} ==> r3c8 ≠ 5 stte

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