The New Sudoku Players' Forum

by **shye** » Fri Sep 03, 2021 10:01 pm

Code: Select all: +-------+-------+-------+ | 6 1 8 | . . . | 5 9 . | | 4 . . | . . 9 | 8 . 1 | | 5 . . | . . . | . 2 4 | +-------+-------+-------+ | . . . | 7 6 . | . . 8 | | . . . | 3 . . | . . . | | . 8 . | . . . | 4 . . | +-------+-------+-------+ | 8 9 . | . . 5 | . 4 . | | 1 . 4 | . . . | 9 . 5 | | . 5 2 | 9 . . | . 8 . | +-------+-------+-------+ 618...59.4....98.15......24...76...8...3......8....4..89...5.4.1.4...9.5.529...8.

estimated rating: 9.0
this thing took a long time to make ｡•́ < •̀｡ its not as perfect as i wanted it but i think it came out good enough! my own path is 3 steps, offering a cookie for those who get fewer

Website · by **denis_berthier** » Sat Sep 04, 2021 7:00 am

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Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 6 1 8 ! 4 237 237 ! 5 9 37 ! ! 4 2 37 ! 56 357 9 ! 8 367 1 ! ! 5 37 9 ! 168 1378 13678 ! 367 2 4 ! +----------------------+----------------------+----------------------+ ! 9 34 135 ! 7 6 124 ! 23 135 8 ! ! 27 467 1567 ! 3 124589 1248 ! 267 1567 2679 ! ! 237 8 13567 ! 125 1259 12 ! 4 13567 23679 ! +----------------------+----------------------+----------------------+ ! 8 9 367 ! 16 137 5 ! 12367 4 2367 ! ! 1 367 4 ! 268 2378 23678 ! 9 367 5 ! ! 37 5 2 ! 9 1347 13467 ! 1367 8 367 ! +----------------------+----------------------+----------------------+

FIRST STEP:
FORCING[3]-T&E(W1) applied to trivalue candidates n1r6c4, n2r6c4 and n5r6c4 :
===> 0 values decided in the three cases:
===> 13 candidates eliminated in the three cases: n3r2c5 n6r3c4 n8r3c6 n7r3c7 n5r6c3 n5r6c5 n1r7c5 n6r7c7 n6r8c4 n2r8c5 n1r9c5 n3r9c7 n6r9c7

Code: Select all: CURRENT RESOLUTION STATE: 6 1 8 4 237 237 5 9 37 4 2 37 56 57 9 8 367 1 5 37 9 18 1378 1367 36 2 4 9 34 135 7 6 124 23 135 8 27 467 1567 3 124589 1248 267 1567 2679 237 8 1367 125 129 12 4 13567 23679 8 9 367 16 37 5 1237 4 2367 1 367 4 28 378 23678 9 367 5 37 5 2 9 347 13467 17 8 367

SECOND STEP:
FORCING[3]-T&E(W1) applied to trivalue candidates n3r2c8, n6r2c8 and n7r2c8 :
===> 8 values decided in the three cases: n8r3c4 n2r8c4 n4r9c5 n6r8c2 n1r3c5 n2r7c9 n2r1c5 n5r4c3
===> 57 candidates eliminated in the three cases: n3r1c5 n7r1c5 n2r1c6 n1r3c4 n3r3c5 n7r3c5 n8r3c5 n1r3c6 n1r4c3 n3r4c3 n1r4c6 n3r4c8 n5r4c8 n7r5c1 n6r5c2 n5r5c3 n7r5c3 n1r5c5 n2r5c5 n4r5c5 n9r5c5 n2r5c6 n1r5c8 n6r5c8 n2r5c9 n6r5c9 n7r5c9 n3r6c1 n1r6c3 n3r6c3 n7r6c3 n2r6c4 n1r6c5 n2r6c5 n3r6c8 n7r6c8 n2r6c9 n7r6c9 n6r7c3 n2r7c7 n3r7c7 n7r7c7 n3r7c9 n6r7c9 n7r7c9 n3r8c2 n7r8c2 n8r8c4 n2r8c6 n3r8c6 n6r8c6 n6r8c8 n3r9c5 n7r9c5 n3r9c6 n4r9c6 n7r9c6

Code: Select all: CURRENT RESOLUTION STATE: 6 1 8 4 2 37 5 9 37 4 2 37 56 57 9 8 367 1 5 37 9 8 1 367 36 2 4 9 34 5 7 6 24 23 1 8 2 47 16 3 58 148 267 57 9 27 8 6 15 9 12 4 156 369 8 9 37 16 37 5 1 4 2 1 6 4 2 378 78 9 37 5 37 5 2 9 4 16 17 8 367

stte

shye wrote: my own path is 3 steps, offering a cookie for those who get fewer

You didn't say which kinds of steps.
I'll send you my shipping address by PM

by **totuan** » Sat Sep 04, 2021 7:18 am

shye wrote:estimated rating: 9.0
this thing took a long time to make ｡•́ < •̀｡ its not as perfect as i wanted it but i think it came out good enough! my own path is 3 steps, offering a cookie for those who get fewer

My path 3 steps too

!

The first step eliminates 1’s on r4c6 (present as diagram is quite complex), I’ll study more and post my path later.

Thanks for the puzzle.
totuan

by **marek stefanik** » Sat Sep 04, 2021 9:18 am

The puzzle has the three-digit oddagon we've discussed in the hardest thread (*), but there is also a powerful uniqueness pattern (#). Together they give stte.

Code: Select all: +------------------------+------------------------+------------------------+ |*6 1 8 | 4 237 237 | 5 9 *37 | | 4 2 *37 | 56 357 9 | 8 *367 1 | | 5 *37 9 | 168 1378 13678 |*367 2 4 | +------------------------+------------------------+------------------------+ | 9 #34 #135 | 7 6 124 |#23 #135 8 | | 2–#7 #467 #1567 | 3 124589 1248 |#267 #1567 29–#67 | | 237 8 13567 | 125 1259 12 | 4 13567 23679 | +------------------------+------------------------+------------------------+ | 8 9 *367 | 16 137 5 | 1–#2–*367 4 2367 | | 1 *367 4 | 268 2378 23678 | 9 *367 5 | |*37 5 2 | 9 1347 13467 | 1367 8 *367 | +------------------------+------------------------+------------------------+

(3=15)r4c38 – (15=6|7)r5c38 – (67=2|4)r5c27 – (24=3)r4c27 – Loop

Xsudo input: Show

Marek

by **shye** » Sat Sep 04, 2021 11:51 pm

denis_berthier wrote:You didn't say which kinds of steps.
I'll send you my shipping address by PM

cheeky but clever! well done, you definitely get a cookie :lol:

totuan wrote:My path 3 steps too !

The first step eliminates 1’s on r4c6 (present as diagram is quite complex), I’ll study more and post my path later.

looking forward to it! the last time you solved one of puzzles was fascinating (っ◔◡◔)っ

marek_stefanik wrote:The puzzle has the three-digit oddagon we've discussed in the hardest thread (*), but there is also a powerful uniqueness pattern (#). Together they give stte.

oh wow! i had no idea there was a uniqueness deduction like that in here, its in the same sort of area to the UR i got for my third step, and yay you found the trivalue oddagon ヽ(´▽`)/ big fan of this solution path, also gets a cookie

i'll share mine then!

Hidden Text: Show

Code: Select all: .-----------------.--------------------.---------------------. |#6 1 8 | 4 237 237 | 5 9 #37 | | 4 2 #37 | 56 357 9 | 8 #367 1 | | 5 #37 9 | 168 1378 13678 |#367 2 4 | :-----------------+--------------------+---------------------: | 9 34 135 | 7 6 124 | 23 135 8 | | 27 467 1567 | 3 124589 1248 | 267 1567 2679 | | 237 8 13567 | 125 1259 12 | 4 13567 23679 | :-----------------+--------------------+---------------------: | 8 9 #367 | 16 137 5 |#12-367 4 2367 | | 1 #367 4 | 268 2378 23678 | 9 #367 5 | |#37 5 2 | 9 1347 13467 | 1367 8 #367 | '-----------------'--------------------'---------------------'

trivalue oddagon
guardians 1r7c7 & 2r7c7
=> -367r7c7

Code: Select all: .-----------------.--------------------.--------------------. | 6 1 8 | 4 237 237 | 5 9 37 | | 4 2 37 |#56 357 9 | 8 367 1 | | 5 37 9 | 18-6 1378 13678 | 367 2 4 | :-----------------+--------------------+--------------------: | 9 #34 15-3 | 7 6 #124 |#23 15-3 8 | | 27 467 1567 | 3 4589-12 48-12 | 67-2 1567 2679 | | 237 8 13567 |#125 59-12 #12 | 4 13567 23679 | :-----------------+--------------------+--------------------: | 8 9 367 |#16 37-1 5 |#12 4 2367 | | 1 367 4 | 28-6 2378 23678 | 9 367 5 | | 37 5 2 | 9 1347 13467 | 1367 8 367 | '-----------------'--------------------'--------------------'

ALS CNL
(1=2)r7c7 - (2=3)r4c7 - (3=4)r4c2 - (4=125)b5p379 - (5=6)r2c4 - (6=1)r7c4 - 1r7c7 loop
all weak links become strong
=> -12b5p568 -1r7c5 -2r5c7 -3r4c38 -6r38c4

Code: Select all: .-----------------.------------------.--------------------. | 6 1 8 | 4 237 237 | 5 9 37 | | 4 2 37 | 56 357 9 | 8 367 1 | | 5 37 9 | 18 1378 13678 | 367 2 4 | :-----------------+------------------+--------------------: | 9 34 *15 | 7 6 124 | 23 *15 8 | | 27 467 *167-5 | 3 4589 48 | 67 *167-5 2679 | | 237 8 13567 | 125 59 12 | 4 13567 23679 | :-----------------+------------------+--------------------: | 8 9 367 | 16 37 5 | 12 4 2367 | | 1 367 4 | 28 2378 23678 | 9 367 5 | | 37 5 2 | 9 1347 13467 | 1367 8 367 | '-----------------'------------------'--------------------'

UR type 4
15UR in r45c38 => -5r5c38

stte

by **totuan** » Sun Sep 05, 2021 11:25 am

Hi shye & marek,
Nice path!
I’m not familiar with oddagons, my ugly path based on AUR(15)r45c38. To reduce complexity of the AUR and the number of steps, I try to eliminate 1r4c6 first

.

Code: Select all: *-----------------------------------------------------------------------------* | 6 1 8 | 4 237 237 | 5 9 37 | | 4 2 37 | 56 357 9 | 8 367 1 | | 5 37 9 | 168 1378 13678 | 367 2 4 | |-------------------------+-------------------------+-------------------------| | 9 34 135 | 7 6 124 | 23 135 8 | | 27 467 1567 | 3 124589 1248 | 267 1567 2679 | | 237 8 13567 | 125 1259 12 | 4 13567 23679 | |-------------------------+-------------------------+-------------------------| | 8 9 367 | 16 137 5 | 12367 4 2367 | | 1 367 4 | 268 2378 23678 | 9 367 5 | | 37 5 2 | 9 1347 13467 | 1367 8 367 | *-----------------------------------------------------------------------------*

My path for this one:
01: Present as diagram: r4c6<>1
Look at 7’s: if 7r5c7 => (7)r5c7-r5c2/r56c8=[7’s:r3c2=r8c2-r8c8=r2c8]-r2c3/r8c2=[7’s:r2c5=r2c8-r8c8=r8c56]-(7)r7c5
Set: {[7’s:r3c2=r8c2-r8c8=r2c8]-r2c3/r8c2=[7’s:r2c5=r2c8-r8c8=r8c56]}= {pattern 7’s}

Code: Select all: (2)r5c7-r4c7=r4c6* (7-2)r7c9=r7c7-r4c7=r4c6* || || (7)r5c7--r5c2/r56c8={pattern 7’s}-(7)r7c5 || | || || |--------------------------(7)r7c7 (4)r5c2-r4c2=r4c6* || | || || || | (7-6)r7c3=r8c2-(6)r5c2 || | || || -----------------------------------------(7)r5c2 || (6)r5c7-r3c7=r2c8-(6=5)r2c4-(5=12)r6c46*

02: UR(15)r45c38 => r5c56<>249, some singles
03: XY-wing: (367)r19c9/r3c7 => r79c7<>6, stte

totuan

by **marek stefanik** » Sun Sep 05, 2021 1:05 pm

shye wrote:i'll share mine then!

Interesting, my solution path was almost identical before I started looking for a way to skip step two.

totuan wrote:To reduce complexity of the AUR and the number of steps, I try to eliminate 1r4c6 first .

I would say it's easier to use the UR directly to reduce the complexity of the net.

It's even simpler with externals – you need 1 or 5 in r6c38, resulting in a triple with c46 => 9r6c5, 2r6c46.
The 7r5c7 – r7c5 deduction is really cool, there is also an oddagon (Broken Wing) for it:

Code: Select all: +---------+---------+---------+ | . . . | . . . | . . . | | . . # | . G . | . # . | | . # . | . . . | . . . | +---------+---------+---------+ | . . . | . . . | . . . | | . G . | . . . | a G . | | . . . | . . . | . G . | +---------+---------+---------+ | . . . | . b . | . . . | | . # . | . G G | . # . | | . . . | . . . | . . . | +---------+---------+---------+

In r28c28b1 7 has to appear outside #, but ab see all the guardians => a – b

BTW with the trivalue oddagon, there are usually eliminations in the rest of the grid as well.
I was curious about this one – and it turns out that 6s only have one pattern which doesn't break the 367 template.
This is enough to get btte, the effective elimination is 6r2c4.
Maybe someone can use this to get a one-stepper.

Marek

by **totuan** » Mon Sep 06, 2021 6:39 am

marek stefanik wrote:
totuan wrote:To reduce complexity of the AUR and the number of steps, I try to eliminate 1r4c6 first .
I would say it's easier to use the UR directly to reduce the complexity of the net. It's even simpler with externals – you need 1 or 5 in r6c38, resulting in a triple with c46 => 9r6c5, 2r6c46.

Thanks and yes, I known. At first I found:
AUR(15)r45c38: (1)r4c6=(1|5&8)r5c56-(4)r5c56=r4c6 => loop: r4c6<>2, r5c56<>29
That was the same result as your loop, but at that times - without oddagons, the puzzles far from 3 steps. So I try to attack 1r4c6 first

totuan

by **shye** » Mon Sep 06, 2021 8:50 am

got the urge to look for an alternate way through that ignores the tri-odd, and found something i thought was nice!

Code: Select all: .-----------------.--------------------.---------------------. | 6 1 8 | 4 237 237 | 5 9 #37 | | 4 2 #37 | 56 357 9 | 8 #367 1 | | 5 #37 9 | 168 1378 13678 | 367 2 4 | :-----------------+--------------------+---------------------: | 9 34 135 | 7 6 124 | 23 135 8 | | 27 467 1567 | 3 124589 1248 | 267 1567 2679 | | 237 8 13567 | 125 1259 12 | 4 13567 23679 | :-----------------+--------------------+---------------------: | 8 9 367 | 16 137 5 | 12367 4 2367 | | 1 #367 4 | 268 2378 23678 | 9 37-6 5 | |#37 5 2 | 9 1347 13467 | 1367 8 #367 | '-----------------'--------------------'---------------------'

bivalue oddagon
guardians 6r2c8 & 6r8c2 & 6r9c9
=> -6r8c8

Code: Select all: .-----------------.--------------------.---------------------. | 6 1 8 | 4 237 237 | 5 9 37 | | 4 2 #37 | 56 357 9 | 8 #37+6 1 | | 5 #37 9 | 168 1378 13678 | 367 2 4 | :-----------------+--------------------+---------------------: | 9 34 *135 | 7 6 124 | 23 *135 8 | | 27 467 *1567 | 3 124589 1248 | 267 *1567 2679 | | 237 8 *13567 | 125 1259 12 | 4 *13567 23679 | :-----------------+--------------------+---------------------: | 8 9 367 | 16 137 5 | 12367 4 2367 | | 1 #367 4 | 268 2378 23678 | 9 #37 5 | | 37 5 2 | 9 1347 13467 | 1367 8 367 | '-----------------'--------------------'---------------------'

bivalue oddagon (#) & extended UR (*) combination
BO guardians 6r2c8 & 6r8c2
ER guardians 6r2c8 & 6r7c3
if no 6 in r2c8, repeat 6s in b7

=> +6r2c8
solves with a locked pair

also, ttt, i just spent some time following your solution path and mapping it out on the grid, its crazy cool!

by **shye** » Thu Sep 16, 2021 4:10 pm

shye wrote:bivalue oddagon (#) & extended UR (*) combination
BO guardians 6r2c8 & 6r8c2
ER guardians 6r2c8 & 6r7c3
if no 6 in r2c8, repeat 6s in b7

=> +6r2c8

i learned how to work aurs in xsudo so naturally here i am to post the t&l for this hehe >ᴗ>

11 Truths = {156C3 156C8 38N2 2N3 28N8}
11 Links = {3r28 7r28 3c28 7c28 37b1 6b7}
1 Permiable XUG =>
AUR points {aur 1r4c3 5r4c3 1r4c8 5r4c8 1r5c3 5r5c3 6r5c3 1r5c8 5r5c8 6r5c8 1r6c3 5r6c3 6r6c3 1r6c8 5r6c8 6r6c8 }

side note, what the hell is a permiable xug :lol:

by **marek stefanik** » Sat Sep 18, 2021 10:14 am

Nice solution!

Also, I think you've found a bug in Xsudo regarding the 6r56c8 eliminations:

If there is no 6 in c8, the eliminations apply (obviously).
If there is exactly one 6 in c8, the eliminations apply (your pattern).
If there is more than one 6 in c8, the eliminations don't apply (since you can have both a guardian of the oddagon and one of the eliminations).

This is a typical behaviour of links, yet if you delete (truth) 6C8 and use (link) 6c8 instead, it doesn't find the eliminations.

The reason for it is that Xsudo doesn't check for eliminations within the MUG (or XUG, as it called it, never heard that term either), only for its presence in the solutions of the pattern.
You can see it with this logic set (after you delete 6r7c3):
5 Truths = {156C3 15C8}
1 Permiable XUG =>
AUR points {aur 1r4c3 5r4c3 1r4c8 5r4c8 1r5c3 5r5c3 6r5c3 1r5c8 5r5c8 6r5c8 1r6c3 5r6c3 6r6c3 1r6c8 5r6c8 6r6c8 }
(Xsudo only realises the eliminations after you add (truth) 6C8, but the number of 6s you allow in c8 is irrelevant for the MUG)

Marek

by **yzfwsf** » Mon Apr 10, 2023 6:10 am

After singles and Lcs, my solver found a two-step solution path.
Triplet Oddagon Type 1: 367r19c19,r2c38,r3c27,r7c37,r8c28 => r7c7<>367
Uniqueness External Test 3: 15 in r45c38 => r6c5<>1,r4c6<>2,r5c5<>2,r5c6<>2,r6c1<>2,r6c5<>2,r6c9<>2,r6c5<>5
stte

by **P.O.** » Wed Apr 12, 2023 9:31 am

i'm currently experimenting with the following strategy that i read about on Phil's site: if a candidate is false in the contexts of all the branches of a relationship OR then it can be eliminated.
http://www.philsfolly.net.au/contra_help.htm
the context of a chain are its links and their eliminations, then a loop sets the resulting naked singles and their eliminations, nothing else neither HS nor intersections nor subsets etc.
so here a tentative resolution of this puzzle using this strategy, the two eliminations are found on the first resolution state after basics:
r2c8 <> 3
r1c9 <> 3
ste.

Code: Select all: basics: ( n2r2c2 n4r1c4 n9r3c3 n9r4c1 ) intersections: ((((2 0) (7 7 9) (1 2 3 6 7)) ((2 0) (7 9 9) (2 3 6 7))) (((1 0) (7 7 9) (1 2 3 6 7)) ((1 0) (9 7 9) (1 3 6 7)))) 6 1 8 4 237 237 5 9 37 4 2 37 56 357 9 8 367 1 5 37 9 168 1378 13678 367 2 4 9 34 135 7 6 124 23 135 8 27 467 1567 3 124589 1248 267 1567 2679 237 8 13567 125 1259 12 4 13567 23679 8 9 367 16 137 5 12367 4 2367 1 367 4 268 2378 23678 9 367 5 37 5 2 9 1347 13467 1367 8 367

FIRST ELIMINATION r2c8 <> 3
relationship OR between n3r6c1 - n3r9c1
first chain context:

Hidden Text: Show

Code: Select all: 6 1 8 4 237 237 5 9 37 4 2 37 56 357 9 8 367 1 5 37 9 168 1378 13678 367 2 4 9 4 15 7 6 12 23 135 8 2 67 1567 3 14589 148 67 1567 679 3 8 1567 125 1259 12 4 1567 2679 8 9 36 16 137 5 12367 4 2367 1 36 4 268 2378 23678 9 367 5 7 5 2 9 134 1346 136 8 36 3r2c8 => r5c2 <> 6,7 r2c8=3 - c3n3{r2 r7} - r8c2{n3 n6} r2c8=3 - r1c9{n3 n7} - r3c7{n37 n6} - r5c7{n6 n7} => r2c8 <> 3

second chain context:

Hidden Text: Show

Code: Select all: 6 1 8 4 237 237 5 9 37 4 2 37 56 357 9 8 367 1 5 37 9 168 1378 13678 367 2 4 9 34 135 7 6 124 23 135 8 27 46 156 3 124589 1248 267 1567 2679 27 8 1356 125 1259 12 4 13567 23679 8 9 67 16 137 5 12367 4 2367 1 67 4 268 2378 23678 9 367 5 3 5 2 9 147 1467 167 8 67 3r2c8 => r9c9 <> 6,7 r2c8=3 - r2c3{n3 n7} - b7n7{r7c3 r8c2} - r8c8{n37 n6} r2c8=3 - r1c9{n3 n7} => r2c8 <> 3

SECOND ELIMINATION r1c9 <> 3
relationship OR between n4r4c2 - n4r4c6
first chain context:

Hidden Text: Show

Code: Select all: 6 1 8 4 2 37 5 9 37 4 2 37 6 357 9 8 37 1 5 37 9 8 137 37 367 2 4 9 4 135 7 6 12 23 135 8 27 67 1567 3 48 48 267 1567 2679 237 8 1367 5 9 12 4 1367 2367 8 9 367 1 37 5 2367 4 2367 1 367 4 2 378 3678 9 367 5 37 5 2 9 347 3467 1367 8 367 3r1c9 => r2c8 <> 3,7 r1c9=3 - r1c6{n3 n7} - r3c6{n7 n3} - c2n3{r3 r8} - r9c1{n3 n7} - r9c9{n37 n6} - r8c8{n36 n7} => r1c9 <> 3

second chain context:

Hidden Text: Show

Code: Select all: ((4 0) (4 6 5) (1 2 4)) r4c6=4 ((2 1 10) (4 7 6) (2 3)) n2r4c7 ((4 1 5) (5 2 4) (4 6 7)) n4r5c2 ((4 1 1) (9 5 8) (1 3 4 7)) n4r9c5 ((2 1 10) (4 7 6) (2 3)) n2r4c7 ((2 2 1) (7 9 9) (2 3 6 7)) n2r7c9 ((4 1 5) (5 2 4) (4 6 7)) n4r5c2 (((6 2 10) (8 2 7) (3 6 7)) n6r8c2 ((3 2 9) (4 2 4) (3 4)) n3r4c2 ((6 2 2 11) ((5 3 4) (1 5 6 7)) ((6 3 4) (1 3 5 6 7)))) n6r56c3 ((6 2 10) (8 2 7) (3 6 7)) n6r8c2 ((7 3 10) (3 2 1) (3 7)) n7r3c2 ((6 3 2 2) ((5 3 4) (1 5 6 7)) ((6 3 4) (1 3 5 6 7)))) n6r56c3 ((3 2 9) (4 2 4) (3 4)) n3r4c2 ((2 3 9) (4 7 6) (2 3)) n2r4c7 ((7 3 9) (3 2 1) (3 7)) n7r3c2 ((3 3 1) (9 1 7) (3 7)) n3r9c1 ((3 3 1) (2 3 1) (3 7)) n3r2c3 ((7 3 2 32) ((5 1 4) (2 7)) ((6 1 4) (2 3 7))) n7r56c1 ((2 3 2 32) ((5 1 4) (2 7)) ((6 1 4) (2 3 7))) n2r56c1 ((3 3 1 2) ((6 8 6) (1 3 5 6 7)) ((6 9 6) (2 3 6 7 9))) n3r6c89 ((7 3 9) (3 2 1) (3 7)) n7r3c2 ((6 4 76) (8 2 7) (3 6 7)) n6r8c2 ((3 4 9) (2 3 1) (3 7))) n3r2c3 ((3 3 1) (9 1 7) (3 7)) n3r9c1 ((3 4 1) (2 3 1) (3 7)) n3r2c3 ((7 4 2 11) ((5 1 4) (2 7)) ((6 1 4) (2 3 7))) n7r56c1 ((7 3 2 32) ((5 1 4) (2 7)) ((6 1 4) (2 3 7))) n7r56c1 ((6 4 2 62) ((5 3 4) (1 5 6 7)) ((6 3 4) (1 3 5 6 7))) n6r56c3 ((5 4 2 62) ((4 3 4) (1 3 5)) ((5 3 4) (1 5 6 7)) ((6 3 4) (1 3 5 6 7))) n5r456c3 ((1 4 2 62) ((4 3 4) (1 3 5)) ((5 3 4) (1 5 6 7)) ((6 3 4) (1 3 5 6 7))) n1r456c3

Code: Select all: 6 1 8 4 237 237 5 9 37 4 2 3 56 57 9 8 67 1 5 7 9 168 138 1368 36 2 4 9 3 15 7 6 4 2 15 8 27 4 156 3 12589 128 67 1567 679 27 8 156 125 1259 12 4 13567 3679 8 9 7 16 13 5 136 4 2 1 6 4 28 2378 2378 9 37 5 3 5 2 9 4 167 167 8 67 3r1c9 => r7c4 <> 1,6 r1c9=3 - c7n3{r3 r7} - r7c5{n3 n1} r1c9=3 - r3c7{n3 n6} - c6n6{r3 r9} => r1c9 <> 3

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