The New Sudoku Players' Forum

Website · by **denis_berthier** » Sun Jan 19, 2025 5:25 am

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Code: Select all: +-------+-------+-------+ ! 1 2 . ! . . 6 ! 7 . 9 ! ! 4 . . ! . . 9 ! . . 6 ! ! . . . ! . . . ! 4 . . ! +-------+-------+-------+ ! . . . ! 5 . . ! . . . ! ! . . . ! 8 3 . ! . . 1 ! ! 7 1 . ! . . 2 ! . . . ! +-------+-------+-------+ ! . 4 1 ! 7 . . ! . 6 . ! ! 6 7 . ! . . . ! . 4 2 ! ! 9 . . ! . . . ! 1 . 7 ! +-------+-------+-------+ 12...67.94....9..6......4.....5........83...171...2....417...6.67.....429.....1.7

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 3578 ! 123 12578 9 ! 2358 12358 6 ! ! 358 35689 356789 ! 123 12578 13578 ! 4 12358 358 ! +----------------------+----------------------+----------------------+ ! 238 3689 234689 ! 5 14679 147 ! 2368 23789 348 ! ! 25 569 24569 ! 8 3 47 ! 256 2579 1 ! ! 7 1 345689 ! 469 469 2 ! 3568 3589 3458 ! +----------------------+----------------------+----------------------+ ! 2358 4 1 ! 7 2589 358 ! 3589 6 358 ! ! 6 7 358 ! 139 1589 1358 ! 3589 4 2 ! ! 9 358 2358 ! 2346 24568 3458 ! 1 358 7 ! +----------------------+----------------------+----------------------+ 205 candidates.

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by **DEFISE** » Mon Jan 20, 2025 9:39 pm

I don't have a short path even with chains of length <= 12

Website · by **denis_berthier** » Tue Jan 21, 2025 3:35 am

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Having a short path isn't the goal of these puzzles. I just want to show rare puzzles where the use of ORk-chains with both impossible and deadly patterns allows to reduce the rating.
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by **Cenoman** » Tue Jan 21, 2025 10:04 pm

My three first steps:
After lcls, including NT(358)b1p357). Rating 10.8 (skfr)

Code: Select all: +-------------------------+-------------------------+------------------------+ | 1 2 358* | 34 458 6 | 7 358* 9 | | 4 358* 7 | 123 1258 9 | a2358* 12358 6 | | 358* 69 69 | 123 12578 13578 | 4 12358 358* | +-------------------------+-------------------------+------------------------+ | 238 3689 234689 | 5 14679 17-4 | b2368 c23789 348 | | 25 569 24569 | 8 3 7-4 | b256 c2579 1 | | 7 1 345689 | e469 e469 2 | 3568 d3589 3458 | +-------------------------+-------------------------+------------------------+ | A2358* 4 1 | 7 yB2589 358 | x3589 6 358* | | 6 7 358* | 139 1589 1358 | w3589* 4 2 | | 9 358* 2358 |zC2346 yC24568 zD3458 | 1 358* 7 | +-------------------------+-------------------------+------------------------+

1. Tridagon(358)b1379 (*) having three guardians (2r2c7, 2r7c1, 9r8c7)
(2)r2c7 - r45c7 = (27-9)r45c8 = r6c8 - (9=64)r6c45
(2)r7c1 - r7c5 = (26-4)r9c45 = (4)r9c6
(9)r8c7 - r7c7 = (926-4)b8p278 = (4)r9c6
=> -4 r45c6; 6 placements, NT(358)r3c169; rating 9.2

Hidden Text: Show

Code: Select all: +------------------------+---------------------+------------------------+ | 1 2 358* | 34 458 6 | 7 358* 9 | | 4 358* 7 | 123 1258 9 | a2358* 12358 6 | | 358* 69 69 | 12 7 358 | 4 12 358* | +------------------------+---------------------+------------------------+ | 238 3689 zC2368-9 | 5 469 1 | b2368 7 348 | | 5-2 c569 4 | 8 3 7 | b256 c259 1 | | 7 1 35689 | 469 469 2 | 3568 3589 3458 | +------------------------+---------------------+------------------------+ |xA2358* 4 1 | 7 x2589 358 | w3589 6 358* | | 6 7 358* | 139 1589 358 | v3589* 4 2 | | 9 358* yB2358 | 236 2568 4 | 1 358* 7 | +------------------------+---------------------+------------------------+

2. Tridagon(358)b1379 (*) having three guardians (2r2c7, 2r7c1, 9r8c7)
(2)r2c7 - r45c7 = (29)r5c28
(2)r7c1 - r9c3 = (2)r4c3
(9)r8c7 - r7c7 = (92)r7c15 - r9c3 = (2)r4c3
=> -2 r5c1, -9 r4c3; lcls 6 placements; rating 8.4

Code: Select all: +---------------------+----------------------+-----------------------+ | 1 2 358 | 34 458 6 | 7 358 9 | | 4 358 7 | c13-2* b258 9 | a258-3 1358-2* 6 | | 38 69 69 | c12* 7 358 | 4 12* 358 | +---------------------+----------------------+-----------------------+ | 238 38 2368 | 5 9 1 | 368 7 4 | | 5 69 4 | 8 3 7 | 26 29 1 | | 7 1 389 | 46 46 2 | 358 3589 358 | +---------------------+----------------------+-----------------------+ | 238 4 1 | 7 258 358 | 9 6 358 | | 6 7 358 | 9 1 358 | 358 4 2 | | 9 358 2358 | 236 2568 4 | 1 358 7 | +---------------------+----------------------+-----------------------+

3. UR(12)r23c48 using externals (2r2c5, 2r2c7)
(2)r2c7 == r2c5* - (2=13)r23c4 => -3 r2c7, -2 r2c28*; rating 8.4

EDIT Replaced flawed step 2 (and a half) with two steps (tridagon again and UR), yielding same eliminations. Thanks yzfwsf.
Edit2,3, corrected typos

by **yzfwsf** » Wed Jan 22, 2025 2:06 am

Hi, Cenoman
I think your second step did not include the guardian of 1 in UR12.

BTW:

Code: Select all: ,-------------------,----------------,-------------------, | 1 2 358 | 34 458 6 | 7 358 9 | | 4 358 7 | 123 1258 9 | 2358 12358 6 | | 358 69 69 | 12 7 358 | 4 12 358 | :-------------------+----------------+-------------------: | 238 3689 23689 | 5 469 1 | 2368 7 348 | | 25 569 4 | 8 3 7 | 256 259 1 | | 7 1 35689 | 469 469 2 | 3568 3589 3458 | :-------------------+----------------+-------------------: | 2358 4 1 | 7 2589 358 | 3589 6 358 | | 6 7 358 | 139 1589 358 | 3589 4 2 | | 9 358 2358 | 236 2568 4 | 1 358 7 | '-------------------'----------------'-------------------'

Uniqueness Test 7: 12 in r23c48; 2*biCell + 1*conjugate pairs(1c8) => r2c4 <> 2
Prior to this step, the SKFR rating is 9.2/9.0/9.0
After this step, the SKFR rating is 10.2/9.0/9.0
SukakuExplainer also has the same result(After elimination, the rating will be higher).

by **Cenoman** » Wed Jan 22, 2025 3:50 pm

yzfwsf wrote:Hi, Cenoman
I think your second step did not include the guardian of 1 in UR12. [...]
Uniqueness Test 7: 12 in r23c48; 2*biCell + 1*conjugate pairs(1c8) => r2c4 <> 2
Prior to this step, the SKFR rating is 9.2/9.0/9.0
After this step, the SKFR rating is 10.2/9.0/9.0 ...

Thanks, yzfwsf, for spotting the flaw :oops:

I have edited my post above, replacing old step #2a by new step #2, resulting in the same eliminations (-2r5c1, -9r4c3), from tridagon kraken instead of UR(12).
Then old step #2b can be kept as step#3 (guardian 1r2c5 eliminated) and the rating is kept at 8.4 [eliminating 2r2c8 makes the difference with what you have rated]

by **eleven** » Wed Jan 22, 2025 5:28 pm

yzfwsf wrote:Uniqueness Test 7: 12 in r23c48; 2*biCell + 1*conjugate pairs(1c8) => r2c4 <> 2
Prior to this step, the SKFR rating is 9.2/9.0/9.0
After this step, the SKFR rating is 10.2/9.0/9.0
SukakuExplainer also has the same result(After elimination, the rating will be higher).

The reason is, that the Explainers don't find "destroyed" UR eliminations.

Code: Select all: +-------------------+--------------------+-------------------+ | 1 2 358 | 34 458 6 | 7 358 9 | | 4 58-3 7 | *1+3 1258 9 | 258-3 *12+3 6 | | 358 69 69 | *12 7 358 | 4 *12 358 | +-------------------+--------------------+-------------------+ | 238 3689 23689 | 5 469 1 | 2368 7 348 | | 25 569 4 | 8 3 7 | 256 259 1 | | 7 1 35689 | 469 469 2 | 3568 3589 3458 | +-------------------+--------------------+-------------------+ | 2358 4 1 | 7 258 358 | 9 6 358 | | 6 7 358 | 19 19 358 | 358 4 2 | | 9 358 2358 | 236 2568 4 | 1 358 7 | +-------------------+--------------------+-------------------+

With 123r2c4 you have a UR 12 with internals 3r2c48.
So one way is to add (reinsert) a 2 in the non-given cell.
Or you just see, that without the 3's in 3r2c48 the deadly 1212 pattern is forced:
1r2c4-> 2r3c4, 1r3c8, 2r2c8.

by **eleven** » Wed Jan 22, 2025 8:43 pm

After Cenoman's 2nd step you can use another impossible pattern (#):

Code: Select all: +----------------------+----------------------+----------------------+ | 1 2 #358 | 34 458 6 | 7 #358 9 | | 4 #358 7 | 123 258 9 |#358+2 12358 6 | |#38 69 69 | 12 7 #358 | 4 12 #358 | +----------------------+----------------------+----------------------+ | 238 38 2368 | 5 9 1 | 368 7 4 | | 5 69 4 | 8 3 7 | 26 29 1 | | 7 1 389 | 46 46 2 | 358 3589 358 | +----------------------+----------------------+----------------------+ |#238 4 1 | 7 258 #358 | 9 6 #358 | | 6 7 #358 | 9 1 #358 |#358 4 2 | | 9 358 #2358 | 236 2568 4 | 1 #358 7 | +----------------------+----------------------+----------------------+

It is a combination of two 14 cell impossible 3-digit patterns, which you get without one of the 2's b7 => 2r2c7 (proof e.g. by fixing c6 to 3 numbers)

Hidden Text: Show

Code: Select all: +----------------+----------------+----------------+ | 1 2 358 | 34 458 6 | 7 358 9 | | 4 358 7 | 1 58 9 | 2 358 6 | | 38 6 9 | 2 7 358 | 4 1 358 | +----------------+----------------+----------------+ | 2 *38 6 | 5 9 1 |*38 7 4 | | 5 9 4 | 8 3 7 | 6 2 1 | | 7 1 38 | 46 46 2 | 358 9 358 | +----------------+----------------+----------------+ | 38 4 1 | 7 2 358 | 9 6 358 | | 6 7 38+5 | 9 1 358 |*38+5 4 2 | | 9 *38+5 2 | 36 568 4 | 1 *38+5 7 | +----------------+----------------+----------------+

oddagon 35 (*):
5r9c2 = r8c3 - r8c7 == 5r9c28 => -5r9c5, bte

by **totuan** » Fri Jan 24, 2025 11:19 am

Quite buzy before TET holiday in Vietnam… Many "year end party"

Code: Select all: *-----------------------------------------------------------------------------* | 1 2 #358 | 34 458 6 | 7 #358 9 | | 4 #358 7 | 123 1258 9 |#358+2 12358 6 | |#358 69 69 | 123 12578 13578 | 4 12358 #358 | |-------------------------+-------------------------+-------------------------| | 238 3689 234689 | 5 14679 17-4 | 2368 23789 348 | | 25 569 24569 | 8 3 7-4 | 256 2579 1 | | 7 1 345689 | 469 469 2 | 3568 3589 3458 | |-------------------------+-------------------------+-------------------------| |#358+2 4 1 | 7 2589 358 | 3589 6 # 358 | | 6 7 #358 | 139 1589 1358 |#358+9 4 2 | | 9 #358 2358 | 2346 24568 3458 | 1 #358 7 | *-----------------------------------------------------------------------------*

My path for this one: Tridagon(358) #-marked cells => (2)r2c7=(2)r7c1=(9)r8c7
01: Present as diagram: r45c6<>4, some singles

Code: Select all: (2)r2c7-r45c7=(27-9)r45c8=r6c8-(9=46)r6c45* || (2)r7c1------------------(2=358)r9c238-(358=4)r9c6* || | (9)r8c7-(3589=2)r7c1679-

Code: Select all: *---------------------------------------------------------------------* | 1 2 358 | 34 458 6 | 7 358 9 | | 4 358 7 | 123 1258 9 | 2358 12358 6 | | 358 d69 69 | 12 7 358 | 4 12 358 | |-----------------------+----------------------+----------------------| | 238 3689 d23689 | 5 e469 1 | 2368 7 348 | |cd25 d569 4 | 8 3 7 | 256 259 1 | | 7 1 35689 | 469 469 2 | 3568 3589 3458 | |-----------------------+----------------------+----------------------| | b2358 4 1 | 7 a2589 358 | 3589 6 358 | | 6 7 358 | 139 1589 358 | 3589 4 2 | | 9 358 c2358 | 236 2568 4 | 1 358 7 | *---------------------------------------------------------------------*

02: (2)r7c5=r7c1-(2)r5c1,r9c3=(2569)r3c2,r5c12,r4c3-(9)r4c23=r4c5 => r7c5<>9, r7c8=9

Code: Select all: *----------------------------------------------------------------------* | 1 2 *#358 | 34 458 6 | 7 *#358 9 | | 4 *#358 7 | 123 1258 9 |*#358+2 12358 6 | |*#358 69 69 | 12 7 #358 | 4 12 *#358 | |-----------------------+----------------------+-----------------------| | 238 3689 23689 | 5 469 1 | 2368 7 348 | | 25 569 4 | 8 3 7 | 256 259 1 | | 7 1 35689 | 469 469 2 | 3568 3589 3458 | |-----------------------+----------------------+-----------------------| | *358+2 4 1 | 7 258 358 | 9 6 *#358 | | 6 7 *#358 | 19 19 #358A |*#358 4 2 | | 9 *#358 #358+2 | 236 2568 4 | 1 *#358 7 | *----------------------------------------------------------------------*

Tridagon(358) *-marked cells => (2)r2c7=(2)r7c1
Impossible pattern(358) #-marked cells => (2)r9c3=(2)r2c7
03: (2)r2c7==(2)r7c1-(2)r9c3==(2)r2c7 => r2c7=2, some singles and easy to finish.

Prove for Impossible pattern:

Hidden Text: Show

Code: Select all: A=(3|5|8) *----------------------------------------------* | . . 358 | . . . | . 358 . | | . 358 . | . . . | 358 . . | | 358 . . | . . 358 | . . 358 | |----------------+------------+----------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |----------------+------------+----------------| | . . . | . . . | . . 358 | | . . 358 | . . 358A | 358 . . | | . 358 358 | . . . | . 358 . | *----------------------------------------------* Let A=3 => r8c3<>3 => r9c23=3 => r9c8<>3 => r7c9=3 => r3c1=3 => r9c3=3 *----------------------------------------------* | . . 58 | . . . | . 358 . | | . e58 . | . . . |a58+3 . . | | 3 . . | . . 58 | . . 58 | |----------------+------------+----------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |----------------+------------+----------------| | . . . | . . . | . . 3 | | . . 58 | . . 3 |b58 . . | | . d58 3 | . . . | . c58 . | *----------------------------------------------* Oddagon(58) abcde => r2c7=3 *----------------------------------------------* | . . e58 | . . . | . a58 . | | . d58 . | . . . | 3 . . | | 3 . . | . . 58 | . . 58 | |----------------+------------+----------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |----------------+------------+----------------| | . . . | . . . | . . 3 | | . . 58 | . . 3 | 58 . . | | . c58 3 | . . . | . b58 . | *----------------------------------------------* Oddagon(58) abcde => impossble. The same for A=(5|8)

Another view for third step, using RT’s properties for tridagon puzzles contains 2 guardians with one guardian at rectangle.

Hidden Text: Show

P/s: I don’t see powerful moves on using UR/DPs for this one.

Thanks for the puzzle!
totuan

Website · by **denis_berthier** » Sun Jan 26, 2025 3:19 am

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Thanks for your solutions.
Mine is similar to the previous puzzle, with a mix of ORk-whips based on a tridagon and 2 DPs, but easier.

whip[2]: r3n9{c3 c2} - r3n6{c2 .} ==> r3c3≠8, r3c3≠3, r3c3≠5, r3c3≠7
hidden-single-in-a-block ==> r2c3=7
whip[2]: r3n9{c2 c3} - r3n6{c3 .} ==> r3c2≠8, r3c2≠3, r3c2≠5

The 3 ORk-relations used:

Code: Select all: DP4-2-1s-OR4-relation for digits: 69 in cells (marked #): (r5c3 r5c2 r3c3 r3c2) with 4 guardians (in cells marked @) : n2r5c3 n4r5c3 n5r5c3 n5r5c2 +-------------------------+-------------------------+-------------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 7 ! 123 1258 9 ! 2358 12358 6 ! ! 358 69# 69# ! 123 12578 13578 ! 4 12358 358 ! +-------------------------+-------------------------+-------------------------+ ! 238 3689 234689 ! 5 14679 147 ! 2368 23789 348 ! ! 25 569#@ 24569#@ ! 8 3 47 ! 256 2579 1 ! ! 7 1 345689 ! 469 469 2 ! 3568 3589 3458 ! +-------------------------+-------------------------+-------------------------+ ! 2358 4 1 ! 7 2589 358 ! 3589 6 358 ! ! 6 7 358 ! 139 1589 1358 ! 3589 4 2 ! ! 9 358 2358 ! 2346 24568 3458 ! 1 358 7 ! +-------------------------+-------------------------+-------------------------+ DP4-2-1-OR8-relation for digits: 12 in cells (marked #): (r3c8 r3c4 r2c8 r2c4) with 8 guardians (in cells marked @) : n3r3c8 n5r3c8 n8r3c8 n3r3c4 n3r2c8 n5r2c8 n8r2c8 n3r2c4 +-------------------------+-------------------------+-------------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 7 ! 123#@ 1258 9 ! 2358 12358#@ 6 ! ! 358 69 69 ! 123#@ 12578 13578 ! 4 12358#@ 358 ! +-------------------------+-------------------------+-------------------------+ ! 238 3689 234689 ! 5 14679 147 ! 2368 23789 348 ! ! 25 569 24569 ! 8 3 47 ! 256 2579 1 ! ! 7 1 345689 ! 469 469 2 ! 3568 3589 3458 ! +-------------------------+-------------------------+-------------------------+ ! 2358 4 1 ! 7 2589 358 ! 3589 6 358 ! ! 6 7 358 ! 139 1589 1358 ! 3589 4 2 ! ! 9 358 2358 ! 2346 24568 3458 ! 1 358 7 ! +-------------------------+-------------------------+-------------------------+ Trid-OR3-relation for digits 3, 5 and 8 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b3, with cells (marked #): r1c8, r2c7, r3c9 b7, with cells (marked #): r8c3, r9c2, r7c1 b9, with cells (marked #): r8c7, r9c8, r7c9 with 3 guardians (in cells marked @): n2r2c7 n2r7c1 n9r8c7 +----------------------+----------------------+----------------------+ ! 1 2 358# ! 34 458 6 ! 7 358# 9 ! ! 4 358# 7 ! 123 1258 9 ! 2358#@ 12358 6 ! ! 358# 69 69 ! 123 12578 13578 ! 4 12358 358# ! +----------------------+----------------------+----------------------+ ! 238 3689 234689 ! 5 14679 147 ! 2368 23789 348 ! ! 25 569 24569 ! 8 3 47 ! 256 2579 1 ! ! 7 1 345689 ! 469 469 2 ! 3568 3589 3458 ! +----------------------+----------------------+----------------------+ ! 2358#@ 4 1 ! 7 2589 358 ! 3589 6 358# ! ! 6 7 358# ! 139 1589 1358 ! 3589#@ 4 2 ! ! 9 358# 2358 ! 2346 24568 3458 ! 1 358# 7 ! +----------------------+----------------------+----------------------+

DP4-2-1s-OR4-whip[3]: OR4{{n5r5c3 n2r5c3 n4r5c3 | n5r5c2}} - r5c7{n5 n2} - r5c1{n2 .} ==> r5c3≠6

whip[5]: c4n2{r3 r9} - r9n6{c4 c5} - r9n4{c5 c6} - r5c6{n4 n7} - r3n7{c6 .} ==> r3c5≠2
whip[5]: c8n7{r4 r5} - c8n9{r5 r6} - b5n9{r6c5 r4c5} - r4n7{c5 c6} - r4n1{c6 .} ==> r4c8≠8
whip[5]: c8n7{r4 r5} - c8n9{r5 r6} - b5n9{r6c5 r4c5} - r4n7{c5 c6} - r4n1{c6 .} ==> r4c8≠3
whip[5]: c8n7{r4 r5} - c8n9{r5 r6} - b5n9{r6c5 r4c5} - r4n7{c5 c6} - r4n1{c6 .} ==> r4c8≠2

Trid-OR3-whip[4]: r7n2{c1 c5} - r7n9{c5 c7} - OR3{{n9r8c7 n2r7c1 | n2r2c7}} - b6n2{r5c7 .} ==> r5c1≠2
naked-single ==> r5c1=5

Code: Select all: +----------------------+----------------------+----------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 7 ! 123 1258 9 ! 2358 12358 6 ! ! 38 69 69 ! 123 1578 13578 ! 4 12358 358 ! +----------------------+----------------------+----------------------+ ! 238 3689 234689 ! 5 14679 147 ! 2368 79 348 ! ! 5 69 249 ! 8 3 47 ! 26 279 1 ! ! 7 1 34689 ! 469 469 2 ! 3568 3589 3458 ! +----------------------+----------------------+----------------------+ ! 238 4 1 ! 7 2589 358 ! 3589 6 358 ! ! 6 7 358 ! 139 1589 1358 ! 3589 4 2 ! ! 9 358 2358 ! 2346 24568 3458 ! 1 358 7 ! +----------------------+----------------------+----------------------+

At least one candidate of a previous DP4-2-1s-OR4-relation between candidates n2r5c3 n4r5c3 n5r5c3 n5r5c2 has just been eliminated.
There remains a DP4-2-1s-OR2-relation between candidates: n2r5c3 n4r5c3

DP4-2-1s-OR2-whip[1]: OR2{{n4r5c3 n2r5c3 | .}} ==> r5c3≠9

whip[2]: r3c2{n6 n9} - r5c2{n9 .} ==> r4c2≠6
whip[2]: r3c2{n9 n6} - r5c2{n6 .} ==> r4c2≠9
whip[5]: b5n6{r6c5 r4c5} - r4n1{c5 c6} - r4n7{c6 c8} - r4n9{c8 c3} - r3c3{n9 .} ==> r6c3≠6
whip[3]: r5c3{n4 n2} - r5c7{n2 n6} - b4n6{r5c2 .} ==> r4c3≠4

Trid-OR3-ctr-whip[6]: b4n6{r4c3 r5c2} - r5c7{n6 n2} - c3n2{r5 r9} - b8n2{r9c4 r7c5} - r7n9{c5 c7} - OR3{{n9r8c7 n2r7c1 n2r2c7 | .}} ==> r4c3≠3, r4c3≠8
Trid-OR3-ctr-whip[6]: r5c2{n9 n6} - r5c7{n6 n2} - c3n2{r5 r9} - b8n2{r9c4 r7c5} - r7n9{c5 c7} - OR3{{n9r8c7 n2r7c1 n2r2c7 | .}} ==> r4c3≠9

whip[3]: r5c6{n4 n7} - r4n7{c6 c8} - r4n9{c8 .} ==> r4c5≠4
whip[3]: r4n1{c6 c5} - r4n7{c5 c8} - r4n9{c8 .} ==> r4c6≠4
hidden-single-in-a-row ==> r4c9=4
whip[3]: r4n1{c5 c6} - r4n7{c6 c8} - r4n9{c8 .} ==> r4c5≠6
whip[1]: b5n6{r6c5 .} ==> r6c7≠6
whip[4]: r9n6{c4 c5} - r9n2{c5 c3} - r5c3{n2 n4} - c6n4{r5 .} ==> r9c4≠4
whip[4]: r9n6{c5 c4} - r9n2{c4 c3} - r5c3{n2 n4} - c6n4{r5 .} ==> r9c5≠4
hidden-single-in-a-block ==> r9c6=4
singles ==> r5c6=7, r4c6=1, r4c5=9, r4c8=7, r8c4=9, r8c5=1, r7c7=9, r3c5=7, r5c3=4
whip[1]: r5n2{c8 .} ==> r4c7≠2
whip[2]: r3n2{c4 c8} - r3n1{c8 .} ==> r3c4≠3

Code: Select all: +-------------------+-------------------+-------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 7 ! 123 258 9 ! 2358 12358 6 ! ! 38 69 69 ! 12 7 358 ! 4 12358 358 ! +-------------------+-------------------+-------------------+ ! 238 38 26 ! 5 9 1 ! 368 7 4 ! ! 5 69 4 ! 8 3 7 ! 26 29 1 ! ! 7 1 389 ! 46 46 2 ! 358 3589 358 ! +-------------------+-------------------+-------------------+ ! 238 4 1 ! 7 258 358 ! 9 6 358 ! ! 6 7 358 ! 9 1 358 ! 358 4 2 ! ! 9 358 2358 ! 236 2568 4 ! 1 358 7 ! +-------------------+-------------------+-------------------+

At least one candidate of a previous DP4-2-1-OR8-relation between candidates n3r3c8 n5r3c8 n8r3c8 n3r3c4 n3r2c8 n5r2c8 n8r2c8 n3r2c4 has just been eliminated.
There remains a DP4-2-1-OR7-relation between candidates: n3r3c8 n5r3c8 n8r3c8 n3r2c8 n5r2c8 n8r2c8 n3r2c4

whip[2]: r3n2{c8 c4} - r3n1{c4 .} ==> r3c8≠3, r3c8≠5, r3c8≠8

Code: Select all: +-------------------+-------------------+-------------------+ ! 1 2 358 ! 34 458 6 ! 7 358 9 ! ! 4 358 7 ! 123 258 9 ! 2358 12358 6 ! ! 38 69 69 ! 12 7 358 ! 4 12 358 ! +-------------------+-------------------+-------------------+ ! 238 38 26 ! 5 9 1 ! 368 7 4 ! ! 5 69 4 ! 8 3 7 ! 26 29 1 ! ! 7 1 389 ! 46 46 2 ! 358 3589 358 ! +-------------------+-------------------+-------------------+ ! 238 4 1 ! 7 258 358 ! 9 6 358 ! ! 6 7 358 ! 9 1 358 ! 358 4 2 ! ! 9 358 2358 ! 236 2568 4 ! 1 358 7 ! +-------------------+-------------------+-------------------+

At least one candidate of a previous DP4-2-1-OR7-relation between candidates n3r3c8 n5r3c8 n8r3c8 n3r2c8 n5r2c8 n8r2c8 n3r2c4 has just been eliminated.
There remains a DP4-2-1-OR4-relation between candidates: n3r2c8 n5r2c8 n8r2c8 n3r2c4

finned-x-wing-in-rows: n5{r3 r7}{c9 c6} ==> r8c6≠5
whip[2]: b1n5{r2c2 r1c3} - r8n5{c3 .} ==> r2c7≠5
DP4-2-1-OR4-whip[2]: OR4{{n8r2c8 n3r2c8 n5r2c8 | n3r2c4}} - r2n1{c4 .} ==> r2c8≠2
DP4-2-1-OR4-whip[3]: r2n1{c4 c8} - OR4{{n8r2c8 n3r2c4 n5r2c8 | n3r2c8}} - r2c8{n5 .} ==> r2c4≠2

end in W6:
whip[3]: b3n2{r2c7 r3c8} - r3n1{c8 c4} - r2c4{n1 .} ==> r2c7≠3
whip[4]: r2n2{c5 c7} - r5c7{n2 n6} - b4n6{r5c2 r4c3} - c3n2{r4 .} ==> r9c5≠2
whip[4]: c5n2{r7 r2} - r2c7{n2 n8} - r8n8{c7 c3} - r1n8{c3 .} ==> r7c5≠8
whip[6]: c1n2{r4 r7} - c5n2{r7 r2} - r2c7{n2 n8} - r3n8{c9 c6} - c6n5{r3 r7} - r7c5{n5 .} ==> r4c1≠8
whip[6]: b7n2{r9c3 r7c1} - b8n2{r7c5 r9c4} - r3c4{n2 n1} - r2c4{n1 n3} - c2n3{r2 r4} - r4c1{n3 .} ==> r9c3≠3
whip[6]: c1n8{r3 r7} - r7n2{c1 c5} - r2c5{n2 n5} - c2n5{r2 r9} - b7n3{r9c2 r8c3} - r8c6{n3 .} ==> r3c6≠8
whip[1]: c6n8{r8 .} ==> r9c5≠8
whip[4]: r2c7{n8 n2} - r2c5{n2 n5} - r3n5{c6 c9} - r3n8{c9 .} ==> r2c2≠8
whip[5]: r4n8{c7 c2} - r9n8{c2 c3} - b7n2{r9c3 r7c1} - c5n2{r7 r2} - r2c7{n2 .} ==> r8c7≠8
whip[5]: b8n8{r8c6 r7c6} - c1n8{r7 r3} - r3n3{c1 c9} - b9n3{r7c9 r9c8} - b9n8{r9c8 .} ==> r8c6≠3
naked-single ==> r8c6=8
finned-x-wing-in-rows: n3{r8 r4}{c7 c3} ==> r6c3≠3
whip[1]: r6n3{c9 .} ==> r4c7≠3
whip[2]: c7n5{r6 r8} - c7n3{r8 .} ==> r6c7≠8
whip[2]: r3n8{c9 c1} - r7n8{c1 .} ==> r6c9≠8
whip[2]: r6n9{c8 c3} - r6n8{c3 .} ==> r6c8≠3, r6c8≠5
whip[2]: c2n8{r9 r4} - r6n8{c3 .} ==> r9c8≠8
singles ==> r7c9=8, r3c1=8
whip[1]: r7n5{c6 .} ==> r9c5≠5
singles ==> r9c5=6, r6c5=4, r6c4=6, r1c4=4
finned-x-wing-in-rows: n3{r1 r8}{c3 c8} ==> r9c8≠3
stte

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