The New Sudoku Players' Forum

by **Leren** » Wed Sep 29, 2021 10:01 am

Code: Select all: *-----------* |.1.|...|..8| |...|4..|..3| |6.5|.18|...| |---+---+---| |92.|.7.|...| |..8|...|6.9| |4..|59.|8..| |---+---+---| |..9|6.5|...| |.82|..3|.9.| |...|.8.|.54| *-----------* .1......8...4....36.5.18...92..7......8...6.94..59.8....96.5....82..3.9.....8..54

by **P.O.** » Wed Sep 29, 2021 10:58 am

Code: Select all: after singles: 2 1 4 3 56 679 579 67 8 8 9 7 4 56 26 15 126 3 6 3 5 d-279 1 8 479 247 c+27 9 2 h13+6 8 7 g14-6 14 134 5 17 5 8 e1+2 3 124 6 1247 9 4 67 136 5 9 f-(12)+6 8 1237 b+127 ×17 4 9 6 2 5 3 8 a-17 5 8 2 17 4 3 17 9 6 3 67 i+16 179 8 179 2 5 4

c9n1{r7r6} - c9n2{r6r3} - c4n2{r3r5} - r6c6{n2n6} - r4n6{c6c3} - r9c3{n6n1} => r7c1 <> 1
ste.

by **marek stefanik** » Wed Sep 29, 2021 11:25 am

This should maybe count as two steps:

Code: Select all: .-------------.--------------.----------------. | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 27 | :-------------+--------------+----------------: | 9 2 136 | 8 7 16–4|a14 134 5 | |e17 5 8 | 2 3 f14 | 6 7–14 9 | | 4 67 36–1| 5 9 16 | 8 1237 b127 | :-------------+--------------+----------------: |d17 4 9 | 6 2 5 | 3 8 c17 | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | '-------------'--------------'----------------'

(4=1)r4c7 – 1r6c9* = r7c9 – r7c1 = 1r5c1* – (1=4)r5c6 => –4r4c6, –4r5c8, –1r5c8*, –1r6c3, stte

Marek

by **jco** » Wed Sep 29, 2021 11:40 am

Code: Select all: .---------------------------------------------. | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 27 | |-------------+--------------+----------------| | 9 2 136 | 8 7 146 | 14 134 5 | |c17 5 8 | 2 3 14 | 6 147 9 | | 4 b67 136 | 5 9 a16 | 8 1237 27-1| |-------------+--------------+----------------| |d17 4 9 | 6 2 5 | 3 8 e17 | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | '---------------------------------------------'

(1=6)r6c6 - (6=7)r6c2 - r5c1 = r7c1 - (7=1)r7c9 => -1 r6c9; ste

Website · by **denis_berthier** » Wed Sep 29, 2021 12:47 pm

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 2 1 4 ! 3 56 79 ! 579 67 8 ! ! 8 9 7 ! 4 56 2 ! 15 16 3 ! ! 6 3 5 ! 79 1 8 ! 479 247 27 ! +----------------+----------------+----------------+ ! 9 2 136 ! 8 7 146 ! 14 134 5 ! ! 17 5 8 ! 2 3 14 ! 6 147 9 ! ! 4 67 136 ! 5 9 16 ! 8 1237 127 ! +----------------+----------------+----------------+ ! 17 4 9 ! 6 2 5 ! 3 8 17 ! ! 5 8 2 ! 17 4 3 ! 17 9 6 ! ! 3 67 16 ! 179 8 79 ! 2 5 4 ! +----------------+----------------+----------------+

===> There are 18 W1-anti-backdoors:
n4r3c8 n2r3c9 n6r4c3 n4r4c7 n3r4c8 n7r5c1 n6r6c2 n3r6c3 n6r6c6 n2r6c8 n1r6c9 n1r7c1 n7r7c9 n7r8c4 n1r8c7 n7r9c2 n6r9c3 n1r9c4

Here are a few associated solutions, in increasing order of complexity. There are also step whip solutions, but I'll skip them as they are not necessary

Code: Select all: biv-chain[4]: r6c2{n7 n6} - r6c6{n6 n1} - c9n1{r6 r7} - r7n7{c9 c1} ==> r5c1≠7, r9c2≠7 stte

Code: Select all: biv-chain[4]: r6c6{n6 n1} - c9n1{r6 r7} - r7n7{c9 c1} - b4n7{r5c1 r6c2} ==> r6c2≠6 stte

Code: Select all: biv-chain[4]: r6c6{n1 n6} - c2n6{r6 r9} - b7n7{r9c2 r7c1} - r7n1{c1 c9} ==> r6c9≠1 stte

jco's solution

Code: Select all: biv-chain[4]: r5c1{n1 n7} - r6c2{n7 n6} - r6c6{n6 n1} - c9n1{r6 r7} ==> r7c1≠1 stte

A slight variant of the previous chain, with one more elimination:

Code: Select all: biv-chain[4]: c1n7{r7 r5} - r6c2{n7 n6} - r6c6{n6 n1} - c9n1{r6 r7} ==> r7c9≠7, r7c1≠1 stte

Code: Select all: biv-chain[4]: r4n6{c3 c6} - r6c6{n6 n1} - c9n1{r6 r7} - b7n1{r7c1 r9c3} ==> r9c3≠6, r4c3≠1 stte

Code: Select all: biv-chain[5]: c9n1{r7 r6} - r6c6{n1 n6} - c2n6{r6 r9} - b7n7{r9c2 r7c1} - b9n7{r7c9 r8c7} ==> r8c7≠1, r7c9≠7 stte

Code: Select all: biv-chain[5]: r9c3{n1 n6} - r4n6{c3 c6} - r6c6{n6 n1} - c9n1{r6 r7} - r8n1{c7 c4} ==> r9c4≠1 stte

Code: Select all: z-chain[5]: b9n7{r8c7 r7c9} - c9n1{r7 r6} - r6c6{n1 n6} - c2n6{r6 r9} - r9n7{c2 .} ==> r8c4≠7 stte

There's also a harder, exotic solution:

Code: Select all: oddagon[7]: r5c1{n1 n7},r5n7{c1 c8},b6n7{r5c8 r6c9},r6c9{n7 n1},c9n1{r6 r7},r7n1{c9 c1},c1n1{r7 r5} ==> r6c8≠2 stte

by **Cenoman** » Wed Sep 29, 2021 12:53 pm

Code: Select all: +------------------+-------------------+---------------------+ | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 27 | +------------------+-------------------+---------------------+ | 9 2 136 | 8 7 146 | c14 134 5 | | a17* 5 8 | 2 3 14 | 6 ba147* 9 | | 4 67 136 | 5 9 16 | 8 1237 27-1 | +------------------+-------------------+---------------------+ | a17* 4 9 | 6 2 5 | 3 8 a17* | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | +------------------+-------------------+---------------------+

Almost RP:
[RP(17)r5c18, r7c19] = (4)r5c8 - (4=1)r4c7 => -1 r6c9; ste

by **yzfwsf** » Wed Sep 29, 2021 1:55 pm

Code: Select all: .-------------.--------------.----------------. | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 2*7 | :-------------+--------------+----------------: | 9 2 136 | 8 7 146 | 14 134 5 | | #17 5 8 | 2 3 14 | 6 #147 9 | | 4 67 136 | 5 9 16 | 8 123*7 #127| :-------------+--------------+----------------: | #17 4 9 | 6 2 5 | 3 8 #17 | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | '-------------'--------------'----------------'

Oddagon Forcing Chain: Each true guardian of Oddagon 7r5c18,r7c19,r6c9 will lead r3c8=2
(7-2)r3c9 = 2r3c8
(7-2)r6c8 = 2r3c8

by **shye** » Wed Sep 29, 2021 2:26 pm

got a fun solution for this one

looks perhaps similar to yzfs?

Code: Select all: .-------------.--------------.----------------. | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 *27 | :-------------+--------------+----------------: | 9 2 136 | 8 7 146 |*14 134 5 | |#17 5 8 | 2 3 14 | 6 #147 9 | | 4 67 136 | 5 9 16 | 8 1237 #127 | :-------------+--------------+----------------: |#17 4 9 | 6 2 5 | 3 8 #1-7 | | 5 8 2 | 17 4 3 |*17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | '-------------'--------------'----------------'

bivalue oddagon chain
(7=2)r3c9 - 2r6c9 = 4r5c8 - (4=17)r48c7
=> -7r7c9 stte

by **RSW** » Wed Sep 29, 2021 8:07 pm

Code: Select all: +-------------+------------+---------------+ | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 27 | +-------------+------------+---------------+ | 9 2 136 | 8 7 146 | 14 134 5 | |*1-7 5 8 | 2 3 14 | 6 147 9 | | 4 e67 136 | 5 9 d16 | 8 1237 c127 | +-------------+------------+---------------+ |a17 4 9 | 6 2 5 | 3 8 b17 | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 *6-7 16 | 179 8 79 | 2 5 4 | +-------------+------------+---------------+

(7)r7c1=(7-1)r7c9=(1)r6c9-(1=6)r6c6-(6=7)r6c2 => -7r5c1, -7r9c2; stte

by **SteveG48** » Thu Sep 30, 2021 5:17 pm

Code: Select all: *------------------------------------------------------------* | 2 1 4 | 3 56 79 | 579 67 8 | | 8 9 7 | 4 56 2 | 15 16 3 | | 6 3 5 | 79 1 8 | 479 247 27 | *-------------------+-------------------+--------------------| | 9 2 c136 | 8 7 146 |c14 134 5 | | 17* 5 8 | 2 3 14 | 6 b147 9 | | 4 b67 d136 | 5 9 16 | 8 e137-2 a127* | *-------------------+-------------------+--------------------| | 17* 4 9 | 6 2 5 | 3 8 17* | | 5 8 2 | 17 4 3 | 17 9 6 | | 3 67 16 | 179 8 79 | 2 5 4 | *------------------------------------------------------------*

2r6c9 =(RP1/7r57c1,r67c9)= (46)r5c8,r6c2 - (4|6=13)r4c37 - 3r6c3 = 3r6c8 => -2 r6c8 ; stte

Or,

(4=792)r3c479 - 2r6c9 =RP= 4r5c8 => -4 r3c8,r4c7 ; stte

But still pretty much the same as Cenoman and others.

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