The New Sudoku Players' Forum

by **Leren** » Sun May 23, 2021 10:40 am

Code: Select all: *-----------* |.5.|.8.|1..| |3..|..9|64.| |..6|...|...| |---+---+---| |...|...|...| |4..|..7|.3.| |.1.|.6.|5..| |---+---+---| |7..|..3|4..| |.6.|.1.|8.7| |...|9..|...| *-----------* .5..8.1..3....964...6...............4....7.3..1..6.5..7....34...6..1.8.7...9.....

by **jco** » Sun May 23, 2021 1:37 pm

Code: Select all: .-----------------------------------------. | 29 5 249 | 467 8 46 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 79 257 259 | |-------------+------------+--------------| | 6 3 27 |b28 4 5 | 79 c178 19 | | 4 8 5 | 1 9 7 | 2 3 6 | | 29 1 279 | 3 6 28 | 5 78 4 | |-------------+------------+--------------| | 7 9 28 |a68 5 3 | 4 c12-6 12 | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 68 | 3 d256 25 | '-----------------------------------------'

AHS M-Wing (6=8)r7c4-(8)r4c4=(8-16)r47c8=(6)r9c8 => -6 r7c8; ste

by **rjamil** » Sun May 23, 2021 3:27 pm

Code: Select all: +--------------+------------+----------------+ | 29 5 249 | 467 8 46 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 79 257 259 | +--------------+------------+----------------+ | 6 3 (27) | 28 4 5 | (79) 178 (19) | | 4 8 5 | 1 9 7 | 2 3 6 | | 29 1 279 | 3 6 28 | 5 78 4 | +--------------+------------+----------------+ | 7 9 8-2 | 68 5 3 | 4 126 (12) | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 68 | 3 256 25 | +--------------+------------+----------------+

WXYZ-Wing: 1279 @ r4c379 r7c9 => -2 @ r7c3; stte

::: OR :::

Code: Select all: +-------------+-------------+----------------+ | 29 5 249 | 467 8 46 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 79 257 259 | +-------------+-------------+----------------+ | 6 3 27 | (8)-2 4 5 | 79 7(1-8) 19 | | 4 8 5 | 1 9 7 | 2 3 6 | | 29 1 279 | 3 6 28 | 5 78 4 | +-------------+-------------+----------------+ | 7 9 28 | (6-8) 5 3 | 4 (16)2 12 | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 68 | 3 256 25 | +-------------+-------------+----------------+

Strong Wing: SL 6 @ r7c48 1 @ r47c8 8 @ r47c4 r4c48 => -2 @ r4c4 => -8 @ r7c4 r4c8; stte

R. Jamil

by **eleven** » Sun May 23, 2021 6:07 pm

Code: Select all: +----------------+----------------+----------------+ |#29 5 #29+4 | 467 8 6-4 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 79 257 259 | +----------------+----------------+----------------+ | 6 3 27 | 28 4 5 | 79 178 19 | | 4 8 5 | 1 9 7 | 2 3 6 | |#29 1 #29+7 | 3 6 *28 | 5 78 4 | +----------------+----------------+----------------+ | 7 9 28 | 68 5 3 | 4 126 12 | | 5 6 3 | 24 1 a24 | 8 9 7 | | 1 24 248 | 9 7 68 | 3 256 25 | +----------------+----------------+----------------+

UR 29r16c13: 4r1c3 == 2r6c6 - (2=4)r8c6 => -4r1c6, stte

by **SteveG48** » Sun May 23, 2021 7:24 pm

Code: Select all: *--------------------------------------------------* |a29 5 249 | 467 8 46 | 1 ad27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 9-7 d257 259 | *----------------+----------------+----------------| | 6 3 27 | 28 4 5 | 79 18-7 19 | | 4 8 5 | 1 9 7 | 2 3 6 | |b29 1 279 | 3 6 b28 | 5 8-7 4 | *----------------+----------------+----------------| | 7 9 28 | 68 5 3 | 4 126 12 | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 c68 | 3 d256 25 | *--------------------------------------------------*

(7=29)r1c18 - (9=28)r6c16 - (8=6)r9c6 - (6=257)r139c8 => -7 r3c7,r46c8 ; stte

by **RSW** » Sun May 23, 2021 8:22 pm

Code: Select all: +-----------+----------+-------------+ | 29 5 249 | 467 8 46 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 24 6 | 47 3 1 | 79 257 259 | +-----------+----------+-------------+ | 6 3 a27 | 28 4 5 |b79 178 c19 | | 4 8 5 | 1 9 7 | 2 3 6 | | 29 1 279 | 3 6 28 | 5 78 4 | +-----------+----------+-------------+ | 7 9 8-2 | 68 5 3 | 4 126 d12 | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 68 | 3 256 25 | +-----------+----------+-------------+

(2=7)r4c3-(7=9)r4c7-(9=1)r4c9-(1=2)r7c9 => -2r7c3; stte
Edit: I see that this is the same solution as Rjamil's, so here's a different one:
(2=7)r4c3-(7=9)r4c7-(9=7)r3c7-(7=4)r3c4-(4=2)r8c4 => -2r4c4; stte

by **Cenoman** » Sun May 23, 2021 8:54 pm

Code: Select all: +------------------+------------------+-------------------+ | 29 5 249 | 467 8 e6-4 | 1 27 3 | | 3 7 1 | 5 2 9 | 6 4 8 | | 8 b24 6 | a47 3 1 | 79 257* 259* | +------------------+------------------+-------------------+ | 6 3 27 | 28 4 5 | 79 178 19 | | 4 8 5 | 1 9 7 | 2 3 6 | | 29 1 279 | 3 6 28 | 5 78 4 | +------------------+------------------+-------------------+ | 7 9 28 | 68 5 3 | 4 126 12 | | 5 6 3 | 24 1 24 | 8 9 7 | | 1 24 248 | 9 7 d68 | 3 c256* 25* | +------------------+------------------+-------------------+

UR(25)r39c89 using mixed internal-external
(4)r3c4 = (4-2)r3c2 == (6)r9c8 - r9c6 = (6)r1c6 => -4 r1c6; ste

...or (for fun) BUG+9

Hidden Text: Show

by **pjb** » Sun May 23, 2021 10:10 pm

Code: Select all: 29 5 a249 | 467 8 d6-4 | 1 27 3 3 7 1 | 5 2 9 | 6 4 8 8 24 6 | 47 3 1 | 79 257 259 ------------------------+----------------------+--------------------- 6 3 27 | 28 4 5 | 79 178 19 4 8 5 | 1 9 7 | 2 3 6 29 1 279 | 3 6 28 | 5 78 4 ------------------------+----------------------+--------------------- 7 9 28 | 68 5 3 | 4 126 12 5 6 3 | 24 1 24 | 8 9 7 1 24 b248 | 9 7 c68 | 3 256 25

(4)r1c3 = (4-8)r9c3 = (8-6)r9c6 = (6-4)r1c6 => -4 r1c6; stte

Phil

Website · by **denis_berthier** » Tue May 25, 2021 4:45 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------+-------------+-------------+ ! 29 5 249 ! 467 8 46 ! 1 27 3 ! ! 3 7 1 ! 5 2 9 ! 6 4 8 ! ! 8 24 6 ! 47 3 1 ! 79 257 259 ! +-------------+-------------+-------------+ ! 6 3 27 ! 28 4 5 ! 79 178 19 ! ! 4 8 5 ! 1 9 7 ! 2 3 6 ! ! 29 1 279 ! 3 6 28 ! 5 78 4 ! +-------------+-------------+-------------+ ! 7 9 28 ! 68 5 3 ! 4 126 12 ! ! 5 6 3 ! 24 1 24 ! 8 9 7 ! ! 1 24 248 ! 9 7 68 ! 3 256 25 ! +-------------+-------------+-------------+

1) Simplest-first solution:
finned-x-wing-in-columns: n2{c2 c9}{r3 r9} ==> r9c8 ≠ 2
biv-chain[3]: r1c6{n6 n4} - c3n4{r1 r9} - r9n8{c3 c6} ==> r9c6 ≠ 6
stte

2) 1-step solutions:
There are 29 W1-anti-backdoors: n9r1c1 n4r1c3 n6r1c4 n7r1c4 n4r1c6 n2r1c8 n2r3c2 n4r3c4 n7r3c7 n9r3c9 n7r4c3 n2r4c4 n9r4c7 n8r4c8 n1r4c9 n2r6c1 n9r6c3 n8r6c6 n7r6c8 n2r7c3 n8r7c4 n1r7c8 n6r7c8 n2r7c9 n4r8c4 n2r8c6 n4r9c2 n8r9c3 n6r9c6

all of which lead to a single-step solution with whips[≤7]

The simplest 6 require only a bivalue-chain[3]:

Code: Select all: biv-chain[3]: c3n4{r1 r9} - r9n8{c3 c6} - c6n6{r9 r1} ==> r1c6 ≠ 4 stte

Code: Select all: biv-chain[3]: r7c4{n6 n8} - r4n8{c4 c8} - c8n1{r4 r7} ==> r7c8 ≠ 6 stte

Code: Select all: biv-chain[3]: r4n8{c4 c8} - c8n1{r4 r7} - r7n6{c8 c4} ==> r7c4 ≠ 8 stte

Code: Select all: biv-chain[3]: r9c6{n8 n6} - r1c6{n6 n4} - c3n4{r1 r9} ==> r9c3 ≠ 8 stte

Code: Select all: biv-chain[3]: r1c6{n6 n4} - c3n4{r1 r9} - r9n8{c3 c6} ==> r9c6 ≠ 6 stte

Code: Select all: biv-chain[3]: c4n8{r4 r7} - r7n6{c4 c8} - c8n1{r7 r4} ==> r4c8 ≠ 8 stte

Next comes a bivalue-chain[4] in rc-space (xy-chain[4]):

Code: Select all: biv-chain-rc[4]: r4c3{n2 n7} - r4c7{n7 n9} - r4c9{n9 n1} - r7c9{n1 n2} ==> r7c3 ≠ 2 stte

There are also 10 1-step solutions with a bivalue-chain[4]
biv-chain[4]: r3c2{n4 n2} - c1n2{r1 r6} - c6n2{r6 r8} - c6n4{r8 r1} ==> r1c3 ≠ 4, r3c4 ≠ 4
stte

biv-chain[4]: r1c6{n6 n4} - c3n4{r1 r9} - b7n8{r9c3 r7c3} - r7c4{n8 n6} ==> r1c4 ≠ 6, r9c6 ≠ 6
stte

biv-chain[4]: r3n4{c2 c4} - b8n4{r8c4 r8c6} - c6n2{r8 r6} - c1n2{r6 r1} ==> r3c2 ≠ 2
stte

biv-chain[4]: r3c2{n4 n2} - c1n2{r1 r6} - b5n2{r6c6 r4c4} - r8c4{n2 n4} ==> r3c4 ≠ 4
stte

biv-chain[4]: r4n2{c3 c4} - r8c4{n2 n4} - r3c4{n4 n7} - c7n7{r3 r4} ==> r4c3 ≠ 7
stte

biv-chain[4]: r4c3{n2 n7} - c7n7{r4 r3} - r3c4{n7 n4} - r8c4{n4 n2} ==> r4c4 ≠ 2
stte

biv-chain[4]: r6c8{n8 n7} - r1n7{c8 c4} - b2n6{r1c4 r1c6} - r9c6{n6 n8} ==> r6c6 ≠ 8
stte

biv-chain[4]: r1n7{c8 c4} - b2n6{r1c4 r1c6} - r9c6{n6 n8} - r6n8{c6 c8} ==> r6c8 ≠ 7
stte

biv-chain[4]: r3c4{n4 n7} - c7n7{r3 r4} - r4c3{n7 n2} - c4n2{r4 r8} ==> r8c4 ≠ 4
stte

biv-chain[4]: r6c6{n2 n8} - r9n8{c6 c3} - c3n4{r9 r1} - c6n4{r1 r8} ==> r8c6 ≠ 2
stte

The New Sudoku Players' Forum

Leren's Puzzles 19

Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19

Re: Leren's Puzzles 19