The New Sudoku Players' Forum

Website · by **denis_berthier** » Sat Jan 28, 2023 6:21 am

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Code: Select all: +-------+-------+-------+ ! . . . ! 4 . 6 ! 7 8 . ! ! . . . ! 1 8 . ! . 6 3 ! ! 6 8 . ! . 3 7 ! . . . ! +-------+-------+-------+ ! 2 . 8 ! . . 3 ! . . . ! ! . 7 1 ! . . . ! 6 . 8 ! ! 9 6 . ! 8 . . ! . . . ! +-------+-------+-------+ ! . . . ! 3 . 8 ! . 4 6 ! ! . . 6 ! . 4 . ! . 1 . ! ! . . 4 ! . . 1 ! . . 7 ! +-------+-------+-------+ ...4.678....18..6368..37...2.8..3....71...6.896.8........3.8.46..6.4..1...4..1..7;1950;10679 SER = 11.7

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 135 12359 2359 ! 4 259 6 ! 7 8 259 ! ! 457 2459 2579 ! 1 8 259 ! 259 6 3 ! ! 6 8 259 ! 259 3 7 ! 12459 259 12459 ! +-------------------+-------------------+-------------------+ ! 2 45 8 ! 5679 15679 3 ! 1459 579 1459 ! ! 345 7 1 ! 259 259 2459 ! 6 2359 8 ! ! 9 6 35 ! 8 1257 245 ! 12345 2357 1245 ! +-------------------+-------------------+-------------------+ ! 157 1259 2579 ! 3 2579 8 ! 259 4 6 ! ! 3578 2359 6 ! 2579 4 259 ! 23589 1 259 ! ! 358 2359 4 ! 2569 2569 1 ! 23589 2359 7 ! +-------------------+-------------------+-------------------+ 180 candidates.

by **totuan** » Sun Jan 29, 2023 9:02 am

Code: Select all: *--------------------------------------------------------------------* | 135 12359 2359 | 4 *259 6 | 7 8 *259 | | 457 2459 2579 | 1 8 *259 |*259 6 3 | | 6 8 259 |*259 3 7 | 14 *259 14 | |----------------------+----------------------+----------------------| | 2 45 8 | 67 167 3 | 1459 579 1459 | | 345 7 1 | 259 259 2459 | 6 235 8 | | 9 6 35 | 8 17 245 | 12345 2357 1245 | |----------------------+----------------------+----------------------| | 157 1259 2579 | 3 *2579 8 |*259 4 6 | | 3578 2359 6 | 2579 4 *259 | 23589 1 *259 | | 358 2359 4 |*2569 2569 1 | 23589 *2359 7 | *--------------------------------------------------------------------*

My path for this one:
For this one, Tridagon (259)B2389 - * marked cells, with three guardians 7r7c5, 6r9c4, 3r9c8. Based on guardians then can solve r2c3=7 but the puzzle is still hard (ER-9.4).
My path combines Tridagon & Impossible pattern then the puzzle is downgrade faster.

Code: Select all: *--------------------------------------------------------------------* | 135 12359 *2359 | 4 *259 6 | 7 8 *259 | | 457 2459 2579 | 1 8 *259 |*259 6 3 | | 6 8 *259 |*259 3 7 | 14 *259 14 | |----------------------+----------------------+----------------------| | 2 45 8 | 67 167 3 | 1459 579 1459 | | 345 7 1 | 259 259 2459 | 6 235 8 | | 9 6 5-3 | 8 17 245 | 12345 2357 1245 | |----------------------+----------------------+----------------------| | 157 1259 *2579 | 3 2579 8 |*259 4 6 | | 3578 2359 6 |*2579 4 *259 | 23589 1 *259 | | 358 2359 4 | 2569 *2569 1 | 23589 *2359 7 | *--------------------------------------------------------------------*

Impossible pattern (259) * marked cells => (3)r1c3=(3)r9c8=(7)r7c3=(7)r8c4=(6)r9r5
Note that: 7r7c3/r8c4 or 6r9c5 can kill guardians 7r7c5 & 6r9c4 of Tridagon by (67)B58

Code: Select all: *-----------------------------------------------------------* | . . 259 | . A259 . | . . 259 | | . . . | . . 259 | 259 . . | | . . 259 | 259 . . | . 259 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . 259 | . . . | 259 . . | | . . . | 259 . 259 | . . 259 | | . . . | . 259 . | . 259 . | *-----------------------------------------------------------* A=(2|5|9) => impossible

Impossible pattern combines tridagon:
01: Present as diagram: => r6c3<>3, some singles. The puzzle is now ER-7.1

Code: Select all: (6)r9c5--(6=17)r46c5---------------------------------- || | | || -------------------------- | || | | (7)r7c3/r8c4--r7c5=r46c5-(7=6)r4c4---(6)r9c4 | || | || | (3)r1c3* -----------------------(7)r7c5---------- || || (3)r9c8-r56c8=r6c7* (3)r9c8-r56c8=r6c7*

Code: Select all: *--------------------------------------------------------------------* | 15 1259 3 | 4 259 6 | 7 8 259 | | 4 259 7 | 1 8 59 | 259 6 3 | | 6 8 29 | 259 3 7 |*14 59 *14 | |----------------------+----------------------+----------------------| | 2 4 8 | 67 167 3 | 159 579 59 | | 3 7 1 | 59 59 4 | 6 2 8 | | 9 6 5 | 8 17 2 |*14+3 37 *14 | |----------------------+----------------------+----------------------| | 157 1259 29 | 3 2579 8 | 259 4 6 | | 578 2359 6 | 2579 4 59 | 23589 1 259 | | 58 2359 4 | 2569 2569 1 | 23589 359 7 | *--------------------------------------------------------------------*

02: UR (14)r36c79 => r6c7=3, some singles

Code: Select all: *-----------------------------------------------------------* | 15 1259 3 | 4 259 6 | 7 8 59-2 | | 4 259 7 | 1 8 *59 |*259 6 3 | | 6 8 29 | 259 3 7 | 4 *59 1 | |-------------------+-------------------+-------------------| | 2 4 8 | 67 67 3 | 1 *59 *59 | | 3 7 1 | 59 59 4 | 6 2 8 | | 9 6 5 | 8 1 2 | 3 7 4 | |-------------------+-------------------+-------------------| | 157 1259 29 | 3 2579 8 | 59-2 4 6 | | 578 3 6 | 2579 4 *59 | 589-2 1 *259 | | 58 259 4 | 2569 2569 1 | 589-2 3 7 | *-----------------------------------------------------------*

03: oddagon (59) * marked cells => (2)r2c7=(2)r8c9 => r2c7=2, r8c9=2

Code: Select all: *-----------------------------------------------------------* | 15 a1259 3 | 4 259 6 | 7 8 59 | | 4 59 7 | 1 8 59 | 2 6 3 | | 6 8 b29 |c259 3 7 | 4 59 1 | |-------------------+-------------------+-------------------| | 2 4 8 | 67 67 3 | 1 59 59 | | 3 7 1 | 59 59 4 | 6 2 8 | | 9 6 5 | 8 1 2 | 3 7 4 | |-------------------+-------------------+-------------------| | 157 1259 29 | 3 2579 8 | 59 4 6 | | 578 3 6 | 579 4 59 | 589 1 2 | | 58 59-2 4 |d2569 2569 1 | 589 3 7 | *-----------------------------------------------------------*

04: 2’s abcd => r9c2<>2

Code: Select all: *--------------------------------------------------* |a15 f2-1 3 | 4 e259 6 | 7 8 59 | | 4 59 7 | 1 8 59 | 2 6 3 | | 6 8 29 | 259 3 7 | 4 59 1 | |----------------+----------------+----------------| | 2 4 8 | 67 d67 3 | 1 59 59 | | 3 7 1 | 59 59 4 | 6 2 8 | | 9 6 5 | 8 1 2 | 3 7 4 | |----------------+----------------+----------------| |b157 12 29 | 3 c579 8 | 59 4 6 | | 578 3 6 | 579 4 59 | 589 1 2 | | 58 59 4 | 26 d26 1 | 589 3 7 | *--------------------------------------------------*

05: (1)r1c1=(1-7)r7c1=r7c5-(67=2)r46c5-r1c5=r1c2 => r1c2<>1, stte

Thanks for the puzzle!
totuan

Website · by **denis_berthier** » Tue Jan 31, 2023 7:22 am

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No one has a solution with RT?
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by **DEFISE** » Tue Jan 31, 2023 1:26 pm

Hi Denis,
I have a solution in W10 + OR3-W6 without UR, RT and 2nd impossible pattern.
You must have it too.

by **marek stefanik** » Tue Jan 31, 2023 2:29 pm

The main TH loses its potential RTs when you place 7r7c5, after which the puzzle is just 9.0 skfr, but not over.
There is another TH where the RTs are useful, which you can find in totuan's solution (a bit concealed by the impossible pattern):

Code: Select all: *-----------------------------------------------------------* | . . 259 | . #259 . | . . #259 | | . . . | . . *#259 |*#259 . . | | . . 259 |#259 . . | . #259 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . 259 | . . # |*#259 . . | | . . . |#259 . 259 | . . #259 | | . . . | . #259 . | . #259 . | *-----------------------------------------------------------*

TH 259# without a rectangle cell => RT 259*
The remaining 2|5|9 in r2 is in r2c12, in c3 takes r7c3 and is eliminated out of the RT, i.e. contra.

Marek

Website · by **denis_berthier** » Tue Jan 31, 2023 3:08 pm

DEFISE wrote:Hi Denis,
I have a solution in W10 + OR3-W6 without UR, RT and 2nd impossible pattern.
You must have it too.

I François,
Actually, in the same conditions, I have one in W10+OR3W8
With eleven's pattern #97-15clues, I have one in W5+0R4W5

by **DEFISE** » Tue Jan 31, 2023 6:10 pm

Finally I implemented the ORk-whips, it's kind of fun.

After basics :

Code: Select all: |-----------------------------------------------------------| | 135 12359 2359 | 4 259 6 | 7 8 259 | | 457 2459 2579 | 1 8 259 | 259 6 3 | | 6 8 259 | 259 3 7 | 14 259 14 | |-----------------------------------------------------------| | 2 45 8 | 67 167 3 | 1459 579 1459 | | 345 7 1 | 259 259 2459 | 6 235 8 | | 9 6 35 | 8 17 245 | 12345 2357 1245 | |-----------------------------------------------------------| | 157 1259 2579 | 3 2579 8 | 259 4 6 | | 3578 2359 6 | 2579 4 259 | 23589 1 259 | | 358 2359 4 | 2569 2569 1 | 23589 2359 7 | |-----------------------------------------------------------|

Tridagon (2,5,9) in b2p267,b3p348,b8p267,b9p168
with 3 guardians: 7r7c5,6r9c4,3r9c8

whip[3]: r4n5{c8 c2}- r6c3{n5 n3}- r5n3{c1 .} => -5r5c8
whip[8]: c7n8{r9 r8}- c7n3{r8 r6}- r5c8{n3 n2}- c9n2{r6 r1}- c5n2{r1 r7}- r8n2{c4 c2}- r8n3{c2 c1}- r5n3{c1 .} => -2r9c7

Trid-OR3-whip[6]: r4c4{n7 n6}- OR3{{n7r7c5,n6r9c4 | n3r9c8}}- r5c8{n3 n2}- r6c8{n2 n5}- r6c3{n5 n3}- r5n3{c1 .} => -7r6c5
Single(s): 1r6c5, 7r6c8
Trid-OR3-whip[5]: r8n7{c1 c4}- r4c4{n7 n6}- OR3{{ n7r7c5,n6r9c4 | n3r9c8}}- r5n3{c8 c1}- c1n4{r5 .} => -7r2c1
Single(s): 7r2c3
Trid-OR3-whip[4]: r8n7{c1 c4}- r4c4{n7 n6}- OR3{{ n7r7c5,n6r9c4 | n3r9c8}}- r5n3{c8 .} => -3r8c1
Trid-OR3-ctr-whip[4]: r8n8{c7 c1}- r8n7{c1 c4}- r4c4{n7 n6}- OR3{{all guardians |.}} => -3r8c7
Single(s): 3r8c2

Code: Select all: |--------------------------------------------------| | 135 1259 2359 | 4 259 6 | 7 8 259 | | 45 2459 7 | 1 8 259 | 259 6 3 | | 6 8 259 | 259 3 7 | 14 259 14 | |--------------------------------------------------| | 2 45 8 | 67 67 3 | 1459 59 1459 | | 345 7 1 | 259 259 2459 | 6 23 8 | | 9 6 35 | 8 1 245 | 2345 7 245 | |--------------------------------------------------| | 157 1259 259 | 3 2579 8 | 259 4 6 | | 578 3 6 | 2579 4 259 | 2589 1 259 | | 58 259 4 | 2569 2569 1 | 3589 2359 7 | |--------------------------------------------------|

Now it’s solvable with "Simplest first" in W10 but I used my "Few steps" to reduce the number of steps:

Hidden Text: Show

Denis, we don't get the same because I didn't follow a global Simplest-first logic, for example I used a whip[8] from the start. My resolution is not entirely automatic.

Website · by **denis_berthier** » Wed Feb 01, 2023 4:57 am

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Thanks for your solutions. The one below will use two impossible patterns: tridagon and eleven #87 in his 15-clue list

"Standard" start, with an anti-tridagon with 3 guardians:

Code: Select all: hidden-pairs-in-a-row: r3{n1 n4}{c7 c9} ==> r3c9≠9, r3c9≠5, r3c9≠2, r3c7≠9, r3c7≠5, r3c7≠2 hidden-triplets-in-a-block: b5{n1 n6 n7}{r6c5 r4c5 r4c4} ==> r6c5≠5, r6c5≠2, r4c5≠9, r4c5≠5, r4c4≠9, r4c4≠5 whip[1]: r4n9{c9 .} ==> r5c8≠9 +-------------------+-------------------+-------------------+ ! 135 12359 2359 ! 4 259 6 ! 7 8 259 ! ! 457 2459 2579 ! 1 8 259 ! 259 6 3 ! ! 6 8 259 ! 259 3 7 ! 14 259 14 ! +-------------------+-------------------+-------------------+ ! 2 45 8 ! 67 167 3 ! 1459 579 1459 ! ! 345 7 1 ! 259 259 2459 ! 6 235 8 ! ! 9 6 35 ! 8 17 245 ! 12345 2357 1245 ! +-------------------+-------------------+-------------------+ ! 157 1259 2579 ! 3 2579 8 ! 259 4 6 ! ! 3578 2359 6 ! 2579 4 259 ! 23589 1 259 ! ! 358 2359 4 ! 2569 2569 1 ! 23589 2359 7 ! +-------------------+-------------------+-------------------+ OR3-anti-tridagon[12] for digits 2, 9 and 5 in blocks: b2, with cells: r1c5, r2c6, r3c4 b3, with cells: r1c9, r2c7, r3c8 b8, with cells: r7c5, r8c6, r9c4 b9, with cells: r7c7, r8c9, r9c8 with 3 guardians: n7r7c5 n6r9c4 n3r9c8

There are also several instances of eleven's pattern, with various numbers of guardians. They are not all useful; I keep them only for completeness.

Code: Select all: OR7-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b9, with cells: r9c8, r7c7, r8c9 b2, with cells: r3c4, r2c6, r1c5 b3, with cells: r3c8, r2c7, r1c9 2-cell blocks: b7, with cells: r7c3, r8c2 b8, with cells: r9c5, r8c4 b1, with cells: r2c2, r1c3 with 7 guardians: n3r1c3 n4r2c2 n7r7c3 n3r8c2 n7r8c4 n6r9c5 n3r9c8 OR5-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b9, with cells: r8c9, r9c8, r7c7 b2, with cells: r1c5, r3c4, r2c6 b3, with cells: r1c9, r3c8, r2c7 2-cell blocks: b7, with cells: r9c2, r7c3 b8, with cells: r8c6, r7c5 b1, with cells: r3c3, r2c2 with 5 guardians: n4r2c2 n7r7c3 n7r7c5 n3r9c2 n3r9c8 OR6-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b9, with cells: r8c9, r7c7, r9c8 b2, with cells: r1c5, r2c6, r3c4 b3, with cells: r1c9, r2c7, r3c8 2-cell blocks: b7, with cells: r7c3, r9c2 b8, with cells: r8c4, r9c5 b1, with cells: r2c2, r3c3 with 6 guardians: n4r2c2 n7r7c3 n7r8c4 n3r9c2 n6r9c5 n3r9c8 OR6-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b8, with cells: r8c6, r9c4, r7c5 b3, with cells: r2c7, r3c8, r1c9 b2, with cells: r2c6, r3c4, r1c5 2-cell blocks: b7, with cells: r9c2, r7c3 b9, with cells: r8c9, r7c7 b1, with cells: r3c3, r1c2 with 6 guardians: n1r1c2 n3r1c2 n7r7c3 n7r7c5 n3r9c2 n6r9c4 OR7-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b2, with cells: r2c6, r3c4, r1c5 b9, with cells: r8c9, r9c8, r7c7 b8, with cells: r8c6, r9c4, r7c5 2-cell blocks: b1, with cells: r3c3, r1c2 b3, with cells: r2c7, r1c9 b7, with cells: r9c2, r7c3 with 7 guardians: n1r1c2 n3r1c2 n7r7c3 n7r7c5 n3r9c2 n6r9c4 n3r9c8 OR6-anti-eleven#97[15] for digits 2, 9 and 5 anti-block: 4 anti-column: 1 3-cell blocks: b3, with cells: r1c9, r3c8, r2c7 b8, with cells: r8c6, r9c4, r7c5 b9, with cells: r8c9, r9c8, r7c7 2-cell blocks: b1, with cells: r3c3, r2c2 b2, with cells: r1c5, r2c6 b7, with cells: r9c2, r7c3 with 6 guardians: n4r2c2 n7r7c3 n7r7c5 n3r9c2 n6r9c4 n3r9c8

The first tridagon eliminations:
z-chain[3]: b5n5{r5c6 r6c6} - r6c3{n5 n3} - r5n3{c1 .} ==> r5c8≠5
Trid-OR3-whip[3]: r6n7{c8 c5} - OR3{{n7r7c5 n3r9c8 | n6r9c4}} - r4c4{n6 .} ==> r6c8≠3
Trid-OR3-whip[4]: c1n8{r9 r8} - r8n7{c1 c4} - OR3{{n7r7c5 n3r9c8 | n6r9c4}} - r4c4{n6 .} ==> r9c1≠3
Trid-OR3-whip[4]: r8n8{c7 c1} - r8n7{c1 c4} - OR3{{n7r7c5 n3r9c8 | n6r9c4}} - r4c4{n6 .} ==> r8c7≠3
whip[1]: b9n3{r9c8 .} ==> r9c2≠3
Trid-OR3-whip[4]: r8n7{c1 c4} - r4c4{n7 n6} - OR3{{n6r9c4 n7r7c5 | n3r9c8}} - r5n3{c8 .} ==> r8c1≠3
hidden-single-in-a-block ==> r8c2=3

Code: Select all: +-------------------+-------------------+-------------------+ ! 135 1259 2359 ! 4 259 6 ! 7 8 259 ! ! 457 2459 2579 ! 1 8 259 ! 259 6 3 ! ! 6 8 259 ! 259 3 7 ! 14 259 14 ! +-------------------+-------------------+-------------------+ ! 2 45 8 ! 67 167 3 ! 1459 579 1459 ! ! 345 7 1 ! 259 259 2459 ! 6 23 8 ! ! 9 6 35 ! 8 17 245 ! 12345 257 1245 ! +-------------------+-------------------+-------------------+ ! 157 1259 2579 ! 3 2579 8 ! 259 4 6 ! ! 578 3 6 ! 2579 4 259 ! 2589 1 259 ! ! 58 259 4 ! 2569 2569 1 ! 23589 2359 7 ! +-------------------+-------------------+-------------------+

The above eliminations lead to a chain of trivial reductions of the EL97-ORk-relations (I've postponed them all until now):

Code: Select all: At least one candidate of a previous El97-OR5-relation has been eliminated. There remains a El97-OR4-relation between candidates: n4r2c2 n7r7c3 n7r7c5 n3r9c8 At least one candidate of a previous El97-OR6-relation has been eliminated. There remains a El97-OR5-relation between candidates: n4r2c2 n7r7c3 n7r8c4 n6r9c5 n3r9c8 At least one candidate of a previous El97-OR6-relation has been eliminated. There remains a El97-OR5-relation between candidates: n1r1c2 n3r1c2 n7r7c3 n7r7c5 n6r9c4 At least one candidate of a previous El97-OR6-relation has been eliminated. There remains a El97-OR5-relation between candidates: n4r2c2 n7r7c3 n7r7c5 n6r9c4 n3r9c8 At least one candidate of a previous El97-OR7-relation has been eliminated. There remains a El97-OR6-relation between candidates: n1r1c2 n3r1c2 n7r7c3 n7r7c5 n6r9c4 n3r9c8 At least one candidate of a previous El97-OR5-relation has been eliminated. There remains a El97-OR4-relation between candidates: n1r1c2 n7r7c3 n7r7c5 n6r9c4 At least one candidate of a previous El97-OR6-relation has been eliminated. There remains a El97-OR5-relation between candidates: n1r1c2 n7r7c3 n7r7c5 n6r9c4 n3r9c8

More eliminations, based on each of the two contradictory patterns:
Trid-OR3-whip[4]: r6n7{c8 c5} - r4c4{n7 n6} - OR3{{n6r9c4 n7r7c5 | n3r9c8}} - r5c8{n3 .} ==> r6c8≠2
Trid-OR3-whip[4]: r6c5{n1 n7} - r4c4{n7 n6} - OR3{{n6r9c4 n7r7c5 | n3r9c8}} - b6n3{r5c8 .} ==> r6c7≠1
El97-OR4-whip[4]: r7n1{c1 c2} - OR4{{n1r1c2 n7r7c3 n7r7c5 | n6r9c4}} - r4c4{n6 n7} - r8n7{c4 .} ==> r7c1≠7
biv-chain[5]: b9n8{r8c7 r9c7} - c7n3{r9 r6} - r5n3{c8 c1} - c1n4{r5 r2} - c1n7{r2 r8} ==> r8c1≠8
singles ==> r9c1=8, r8c7=8
whip[5]: c7n3{r9 r6} - r5c8{n3 n2} - b3n2{r3c8 r1c9} - c5n2{r1 r7} - b7n2{r7c2 .} ==> r9c7≠2
Trid-OR3-whip[5]: r6n7{c8 c5} - r4c4{n7 n6} - OR3{{n6r9c4 n7r7c5 | n3r9c8}} - r5n3{c8 c1} - r6c3{n3 .} ==> r6c8≠5
singles ==> r6c8=7, r6c5=1
Trid-OR3-whip[5]: r8n7{c1 c4} - r4c4{n7 n6} - OR3{{n6r9c4 n7r7c5 | n3r9c8}} - r5n3{c8 c1} - c1n4{r5 .} ==> r2c1≠7
singles ==> r2c3=7, r8c1=7, r7c5=7, r4c5=6, r4c4=7, r9c4=6

Code: Select all: +----------------+----------------+----------------+ ! 135 1259 2359 ! 4 259 6 ! 7 8 259 ! ! 45 2459 7 ! 1 8 259 ! 259 6 3 ! ! 6 8 259 ! 259 3 7 ! 14 259 14 ! +----------------+----------------+----------------+ ! 2 45 8 ! 7 6 3 ! 1459 59 1459 ! ! 345 7 1 ! 259 259 2459 ! 6 23 8 ! ! 9 6 35 ! 8 1 245 ! 2345 7 245 ! +----------------+----------------+----------------+ ! 15 1259 259 ! 3 7 8 ! 259 4 6 ! ! 7 3 6 ! 259 4 259 ! 8 1 259 ! ! 8 259 4 ! 6 259 1 ! 359 2359 7 ! +----------------+----------------+----------------+ At least one candidate of a previous El97-OR5-relation has just been eliminated. There remains a El97-OR2-relation between candidates: n4r2c2 n3r9c8

El97-OR2-whip[3]: OR2{{n3r9c8 | n4r2c2}} - r4c2{n4 n5} - r4c8{n5 .} ==> r9c8≠9
El97-OR2-whip[3]: r5n3{c1 c8} - OR2{{n3r9c8 | n4r2c2}} - r4c2{n4 .} ==> r5c1≠5

The end is easy, in W4:

Code: Select all: whip[1]: r5n5{c6 .} ==> r6c6≠5 biv-chain[3]: b1n3{r1c3 r1c1} - r5c1{n3 n4} - r2c1{n4 n5} ==> r1c3≠5 biv-chain[3]: b6n3{r6c7 r5c8} - r5c1{n3 n4} - b5n4{r5c6 r6c6} ==> r6c7≠4 hidden-pairs-in-a-column: c7{n1 n4}{r3 r4} ==> r4c7≠9, r4c7≠5 biv-chain[3]: r6c3{n5 n3} - r5c1{n3 n4} - r2c1{n4 n5} ==> r3c3≠5 t-whip[4]: c3n2{r3 r7} - c3n5{r7 r6} - r6n3{c3 c7} - c7n2{r6 .} ==> r2c2≠2 biv-chain[4]: r2n2{c7 c6} - r6c6{n2 n4} - r5n4{c6 c1} - r2c1{n4 n5} ==> r2c7≠5 z-chain[4]: r6n3{c7 c3} - c3n5{r6 r7} - c7n5{r7 r9} - c7n3{r9 .} ==> r6c7≠2 naked-pairs-in-a-row: r6{c3 c7}{n3 n5} ==> r6c9≠5 finned-x-wing-in-rows: n2{r6 r2}{c6 c9} ==> r1c9≠2 t-whip[4]: r3c3{n9 n2} - b3n2{r3c8 r2c7} - r7n2{c7 c2} - c2n1{r7 .} ==> r1c2≠9 z-chain[5]: c7n9{r9 r2} - b3n2{r2c7 r3c8} - r3c3{n2 n9} - r1n9{c3 c5} - b8n9{r9c5 .} ==> r8c9≠9 whip[1]: b9n9{r9c7 .} ==> r2c7≠9 naked-single ==> r2c7=2 whip[1]: r7n2{c3 .} ==> r9c2≠2 whip[1]: r8n9{c6 .} ==> r9c5≠9 naked-pairs-in-a-column: c8{r3 r4}{n5 n9} ==> r9c8≠5 hidden-pairs-in-a-column: c2{n1 n2}{r1 r7} ==> r7c2≠9, r7c2≠5, r1c2≠5 biv-chain[3]: r2c6{n9 n5} - r3n5{c4 c8} - b3n9{r3c8 r1c9} ==> r1c5≠9 hidden-single-in-a-column ==> r5c5=9 t-whip[2]: c5n5{r1 r9} - r8n5{c6 .} ==> r1c9≠5 singles ==> r1c9=9, r3c8=5 r4c8=9 biv-chain[3]: c4n5{r5 r8} - r9c5{n5 n2} - c8n2{r9 r5} ==> r5c4≠2 naked-single ==> r5c4=5 whip[1]: b5n2{r6c6 .} ==> r8c6≠2 biv-chain[3]: r8c6{n5 n9} - r2n9{c6 c2} - r9c2{n9 n5} ==> r9c5≠5 stte

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#8323 in 63,137 T&E(3) min-expands

#8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands

Re: #8323 in 63,137 T&E(3) min-expands