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by **Leren** » Sat Jul 17, 2021 8:20 am

Code: Select all: *-----------* |.6.|...|...| |...|.28|..5| |...|.3.|.28| |---+---+---| |...|1..|3..| |.83|.9.|.4.| |54.|..7|...| |---+---+---| |45.|..2|..1| |...|8..|7..| |.29|...|.6.| *-----------* .6...........28..5....3..28...1..3...83.9..4.54...7...45...2..1...8..7...29....6.

Website · by **denis_berthier** » Sat Jul 17, 2021 9:14 am

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Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 12789 6 124578 ! 4579 157 159 ! 149 179 3 ! ! 1379 1379 147 ! 4679 2 8 ! 1469 179 5 ! ! 179 179 1457 ! 45679 3 1569 ! 1469 2 8 ! +----------------------+----------------------+----------------------+ ! 2679 79 267 ! 1 4568 456 ! 3 58 67 ! ! 167 8 3 ! 2 9 56 ! 15 4 67 ! ! 5 4 16 ! 3 68 7 ! 2 18 9 ! +----------------------+----------------------+----------------------+ ! 4 5 678 ! 679 67 2 ! 89 3 1 ! ! 136 13 16 ! 8 1456 134569 ! 7 59 2 ! ! 1378 2 9 ! 57 157 135 ! 58 6 4 ! +----------------------+----------------------+----------------------+

1) Simplest-first solution:
naked-pairs-in-a-column: c3{r6 r8}{n1 n6} ==> r7c3 ≠ 6, r4c3 ≠ 6, r3c3 ≠ 1, r2c3 ≠ 1, r1c3 ≠ 1
whip[1]: r7n6{c5 .} ==> r8c5 ≠ 6, r8c6 ≠ 6
hidden-pairs-in-a-block: b7{n7 n8}{r7c3 r9c1} ==> r9c1 ≠ 3, r9c1 ≠ 1
singles ==> r9c6 = 3, r9c5 = 1
hidden-pairs-in-a-row: r1{n2 n8}{c1 c3} ==> r1c3 ≠ 7, r1c3 ≠ 5, r1c3 ≠ 4, r1c1 ≠ 9, r1c1 ≠ 7, r1c1 ≠ 1
singles ==> r3c3 = 5, r2c3 = 4
finned-x-wing-in-rows: n7{r9 r3}{c4 c1} ==> r2c1 ≠ 7
finned-x-wing-in-rows: n5{r5 r9}{c7 c6} ==> r8c6 ≠ 5
hidden-triplets-in-a-row: r4{n4 n5 n8}{c5 c6 c8} ==> r4c6 ≠ 6, r4c5 ≠ 6
biv-chain[3]: r4c8{n8 n5} - r8n5{c8 c5} - c5n4{r8 r4} ==> r4c5 ≠ 8
stte

2) 1-step solutions
===> There are 19 W1-anti-backdoors:
n2r1c1 n8r1c3 n2r4c3 n8r4c5 n5r4c8 n5r5c6 n1r5c7 n1r6c3 n6r6c5 n8r6c8 n7r7c3 n9r7c4 n7r7c5 n8r7c7 n6r8c3 n9r8c8 n8r9c1 n7r9c4 n5r9c7

The simplest 1-step solution (with no undeclared Subsets) is:

Code: Select all: biv-chain[4]: r5c6{n6 n5} - c7n5{r5 r9} - r9c4{n5 n7} - r7c5{n7 n6} ==> r6c5 ≠ 6, r4c5 ≠ 6, r8c6 ≠ 6 stte

There's also a z-chain[4]:

Code: Select all: z-chain[4]: r4n8{c8 c5} - c5n4{r4 r8} - r8n5{c5 c6} - r5n5{c6 .} ==> r4c8 ≠ 5 stte

by **RSW** » Sat Jul 17, 2021 9:55 am

Code: Select all: +--------------+---------------+-------------+ | 28 6 28 | 4579 57 159 | 149 179 3 | | 1379 1379 4 | 679 2 8 | 169 179 5 | | 179 179 5 | 4679 3 169 | 1469 2 8 | +--------------+---------------+-------------+ | 2679 79 27 | 1 458 45 | 3 58 67 | | 167 8 3 | 2 9 e56 |d15 4 67 | | 5 4 16 | 3 *8-6 7 | 2 18 9 | +--------------+---------------+-------------+ | 4 5 78 | 679 a67 2 | 89 3 1 | | 136 13 16 | 8 45 459 | 7 59 2 | | 78 2 9 |b57 1 3 |c58 6 4 | +--------------+---------------+-------------+

(6=7)r7c5 - (7=5)r9c4 - (5)r9c7 = r5c7 - (5=6)r5c6 => -6r6c5; ste

by **pjb** » Sat Jul 17, 2021 11:54 am

Code: Select all: 28 6 28 | 4579 57 159 | 149 179 3 1379 1379 4 | 679 2 8 | 169 179 5 179 179 5 | 4679 3 169 | 1469 2 8 ------------------------+----------------------+--------------------- 2679 79 27 | 1 458 45 | 3 58 67 167 8 3 | 2 9 56 |a15 4 67 5 4 16 | 3 c68 7 | 2 b18 9 ------------------------+----------------------+--------------------- 4 5 78 | 679 d67 2 | 89 3 1 136 13 16 | 8 45 459 | 7 59 2 78 2 9 |e57 1 3 | 8-5 6 4

(5=1)r5c7 - (1=8)r6c8 - (8=6)r6c5 - (6=7)r7c5 - (7=5)r9c4 => -5 r9c7; stte

Phil

by **jco** » Sat Jul 17, 2021 12:12 pm

Not the simplest,

Hidden Text: Show

but the very first move I considered.

Code: Select all: .--------------------------------------------------. | 28 6 28 | 4579 57 159 | 149 179 3 | | 1379 1379 4 | 679 2 8 | 169 179 5 | | 179 179 5 | 4679 3 169 | 1469 2 8 | |----------------+-----------------+---------------| | 2679 79 27 | 1 b(45)8 (45)| 3 58 67 | | 167 8 3 | 2 9 56 | 15 4 67 | | 5 4 16 | 3 a68 7 | 2 18 9 | |----------------+-----------------+---------------| | 4 5 78 |d679 da67 2 | 89 3 1 | | 136 13 16 | 8 (45) c(45)9| 7 59 2 | | 78 2 9 | 5-7 1 3 | 58 6 4 | '--------------------------------------------------'

UR(45) r48c56 using internals

(7=68)r67c5 - (8)r4c5 == (9)r8c6 - (9=67)r7c45 => -7 r9c4; ste

Edit: added hidden part.

by **SteveG48** » Sat Jul 17, 2021 2:09 pm

Code: Select all: *-----------------------------------------------------------* | 28 6 28 | 4579 57 159 | 149 b179 3 | | 1379 1379 4 | 679 2 8 | 169 b179 5 | | 179 179 5 | 4679 3 169 | 1469 2 8 | *-------------------+-------------------+-------------------| | 2679 79 27 | 1 458 45 | 3 58 67 | | 167 8 3 | 2 9 56 | 15 4 67 | | 5 4 16 | 3 c68 7 | 2 b18 9 | *-------------------+-------------------+-------------------| | 4 5 8-7 | 679 c67 2 | 89 3 1 | | 136 13 16 | 8 45 459 | 7 b59 2 | |a78 2 9 | 5-7 1 3 |a58 6 4 | *-----------------------------------------------------------*

(7=85)r9c17 - (5=1798)r1268c8 - (8=67)r67c5 => -7 r7c3,r9c4 ; stte

by **P.O.** » Sat Jul 17, 2021 6:05 pm

Code: Select all: after singles: 12789 6 124578 4579 1457 1459 149 d(179) 3 1379 1379 147 4679 2 8 1469 d(179) 5 179 179 1457 45679 3 14569 1469 2 8 2679 79 267 1 4568 456 3 5789 679 167 8 3 2 9 56 156 4 67 5 4 16 3 c-6+8 7 2 d(1-89) 69 4 5 b6+78 679 c+6-7 2 89 3 1 136 13 16 8 1456 134569 7 e+5-9 2 a13-7×8 2 9 57 157 135 e-5+8 6 4 depth: 3 candidate: 8 from start ((7 0) (9 1 7) (1 3 7 8)) if R9C1 is not 7 ((7 0) (7 3 7) (6 7 8)) R7C3 is 7 ((8 1 102) (6 5 5) (6 8)) R6C5 is 8 from a pair ((9 2 2 222) ((1 8 3) (1 7 9)) ((2 8 3) (1 7 9)) ((6 8 6) (1 8 9))) a triplet one is 9 ((8 3 143) (9 7 9) (5 8)) R9C7 is 8 from a pair ste.

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