The New Sudoku Players' Forum

by **P.O.** » Sat Oct 16, 2021 4:28 pm

Code: Select all: . . 1 . . . . . . . . . . 9 2 . 7 6 . . . 8 . . 2 1 9 7 5 8 . . 9 . 2 . . . . 2 4 5 . . . . . . . . 6 . 9 . 3 . . . . 1 . 8 . . 7 2 4 . . . . . . 1 9 . . . . . . ..1..........92.76...8..219758..9.2....245........6.9.3....1.8..724......19......

by **shye** » Sat Oct 16, 2021 7:13 pm

Code: Select all: .----------------.---------------.----------------. | 9 2 1 | 56 3567 347 | 3458 45 38 | |~45~ 8 #345 | 1 9 2 |#345 7 6 | | 456 36-4 7 | 8 35 34 | 2 1 9 | :----------------+---------------+----------------: | 7 5 8 | 3 1 9 | 6 2 4 | | 1 9 6 | 2 4 5 | 78 3 78 | | 2 #34 #34 | 7 8 6 | 1 9 5 | :----------------+---------------+----------------: | 3 #46 #45 | 9 2567 1 |#457 8 27 | | 568 7 2 | 4 356 38 | 9 56 1 | | 4568 1 9 | 56 2567 78 | 3457 456 237 | '----------------'---------------'----------------'

finned swordfish
4 in r267 covered by c237, fin in r2c1
=> -4r3c2

Code: Select all: .---------------.---------------.----------------. | 9 2 1 | 56 3567 347 |[3458]#45 [38] | |#45 8 #345 | 1 9 2 | 35-4 7 6 | | 456 #36 7 | 8 35 34 | 2 1 9 | :---------------+---------------+----------------: | 7 5 8 | 3 1 9 | 6 2 4 | | 1 9 6 | 2 4 5 |[78] 3 [78] | | 2 34 34 | 7 8 6 | 1 9 5 | :---------------+---------------+----------------: | 3 *46 45 | 9 *2567 1 | 457 8 *27 | | 568 7 2 | 4 356 38 | 9 56 1 | | 4568 1 9 |#56 2567 78 |[3457] 456 [237]| '---------------'---------------'----------------' 4r1c7 || 5r1c7 - (5=4)r1c8 || 4r9c7 || 5r9c7 - (5=6)r9c4 - 6r7c5 = 6r7c2 - (6=354)b1p468 || / 2r9c9 - 2r7c9 = 2r7c5

extended rectangle chain
internal guardians: 45r19c7, 2r9c9
=> -4r2c7

locked candidates and a single

Code: Select all: .---------------.--------------.----------------. | 9 2 1 | 56 *3567 *7-3| 3458 45 *38 | | 45 8 345 | 1 9 2 | 35 7 6 | | 56 *36 7 | 8 #35 4 | 2 1 9 | :---------------+--------------+----------------: | 7 5 8 | 3 1 9 | 6 2 4 | | 1 9 6 | 2 4 5 | 78 3 78 | | 2 34 34 | 7 8 6 | 1 9 5 | :---------------+--------------+----------------: | 3 *46 45 | 9 #2567# 1 | 457 8 *27 | | 568 7 2 | 4 356 38 | 9 56 1 | | 4568 1 9 | 56 2567 78 | 3457 456 *237 | '---------------'--------------'----------------' 2r7c5 - 2r7c9 = (2-3)r9c9 = 3r1c9 || 5r7c5 - (5=3)r3c5 || 6r5c7 - 6r7c2 = (6-3)r3c2 = 3r3c5 || 7r5c7 - 7r1c5 = 7r1c6

kraken cell r7c5
-3r1c6
solves with a naked pair

it wasnt until after my solve that i noticed there was an ALS w-wing that wouldve made things simpler >_> but i like some of these steps so its worth sharing at least

by **Cenoman** » Sat Oct 16, 2021 10:13 pm

Two W-Wings:

Code: Select all: +---------------------+--------------------+---------------------+ | 9 2 1 | 56 3567 347 | 3458 45 38 | | 45 8 345 | 1 9 2 | 345 7 6 | | 456 a346 7 | 8 5-3 a34 | 2 1 9 | +---------------------+--------------------+---------------------+ | 7 5 8 | 3 1 9 | 6 2 4 | | 1 9 6 | 2 4 5 | 78 3 78 | | 2 34 34 | 7 8 6 | 1 9 5 | +---------------------+--------------------+---------------------+ | 3 b46 45 | 9 c2567 1 | 457 8 27 | | 568 7 2 | 4 d356 38 | 9 56 1 | | 4568 1 9 | d56 2567 78 | 3457 456 237 | +---------------------+--------------------+---------------------+

1. ALS W-Wing(3=46)r3c26 - r7c2 = r7c5 - (6=53)b8p57 => -3 r3c5; 3 placements & lcls

Code: Select all: +--------------------+-------------------+--------------------+ | 9 2 1 | 6 37 347 | 3458 a45 38 | | d45 8 345 | 1 9 2 | 3-4 7 6 | | 46 346 7 | 8 5 34 | 2 1 9 | +--------------------+-------------------+--------------------+ | 7 5 8 | 3 1 9 | 6 2 4 | | 1 9 6 | 2 4 5 | 78 3 78 | | 2 34 34 | 7 8 6 | 1 9 5 | +--------------------+-------------------+--------------------+ | 3 46 45 | 9 267 1 | 457 8 27 | | c568 7 2 | 4 36 38 | 9 b56 1 | | 468 1 9 | 5 267 78 | 347 46 237 | +--------------------+-------------------+--------------------+

2. W-Wing (4=5)r1c8 - r8c8 = r8c1 - (5=4)r2c1 => -4 r2c7; ste

by **P.O.** » Sun Oct 17, 2021 4:19 pm

my solution is 2 steps;

Code: Select all: after singles and intersections: 9 2 1 56 3567 347 3458 d+45 38 a±4+5 8 e3+45 1 9 2 e3×-45 7 6 b×4-56 3×46 7 8 b3+5 34 2 1 9 7 5 8 3 1 9 6 2 4 1 9 6 2 4 5 78 3 78 2 34 34 7 8 6 1 9 5 3 46 45 9 2567 1 457 8 27 568 7 2 4 c3-56 38 9 c+56 1 4568 1 9 56 2567 78 3457 456 237

r2c1{n4 n5} - r3n5{c1 c5} - r8n5{c5 c8} - r1c8{n5 n4} - r2n4{c7 c3} => r2c7 r3c1 r3c2 <> 4
single: ( r3c6b2 n4 )

Code: Select all: 9 2 1 56 3567 37 3458 45 38 45 8 345 1 9 2 35 7 6 56 a±36 7 8 a+35 4 2 1 9 7 5 8 3 1 9 6 2 4 1 9 6 2 4 5 78 3 78 2 d×3+4 34 7 8 6 1 9 5 3 c4+6 45 9 c25-67 1 457 8 27 568 7 2 4 b-3+(56) 38 9 56 1 4568 1 9 b+(56) 2567 78 3457 456 237

r3n3{c2 c5} - b8{r8c5r9c4}{n5n6} - r7n6{c5 c2} - c2n4{r7 r6} => r6c2 <> 3
ste.

Website · by **denis_berthier** » Mon Oct 18, 2021 6:17 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 9 2 1 ! 56 3567 347 ! 3458 45 38 ! ! 45 8 345 ! 1 9 2 ! 345 7 6 ! ! 456 346 7 ! 8 35 34 ! 2 1 9 ! +----------------+----------------+----------------+ ! 7 5 8 ! 3 1 9 ! 6 2 4 ! ! 1 9 6 ! 2 4 5 ! 78 3 78 ! ! 2 34 34 ! 7 8 6 ! 1 9 5 ! +----------------+----------------+----------------+ ! 3 46 45 ! 9 2567 1 ! 457 8 27 ! ! 568 7 2 ! 4 356 38 ! 9 56 1 ! ! 4568 1 9 ! 56 2567 78 ! 3457 456 237 ! +----------------+----------------+----------------+ 88 candidates

Can be solved in Z4

No 1-step solution with chains of reasonable length.

Three 2-step solution in W4:
Same 1st step for the 3 solutions:
whip[4]: r1c8{n4 n5} - b2n5{r1c5 r3c5} - r8n5{c5 c1} - r2c1{n5 .} ==> r2c7≠4
whip[1]: r2n4{c3 .} ==> r3c1≠4, r3c2≠4
hidden-single-in-a-row ==> r3c6=4

Second step can be:
z-chain[4]: r9c4{n6 n5} - r8c5{n5 n3} - r3n3{c5 c2} - c2n6{r3 .} ==> r7c5≠6
stte
OR:
whip[4]: r7n6{c2 c5} - r9c4{n6 n5} - r8c5{n5 n3} - r3n3{c5 .} ==> r3c2≠6
stte
OR:
whip[4]: r3c2{n3 n6} - r7n6{c2 c5} - r8c5{n6 n5} - r9c4{n5 .} ==> r3c5≠3
stte

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