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Website · by **denis_berthier** » Mon Sep 19, 2022 5:55 am

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Code: Select all: +-------+-------+-------+ ! 1 2 . ! . . . ! 7 8 . ! ! 4 . 7 ! . 8 . ! 2 . 6 ! ! . 6 8 ! . 2 . ! . 1 4 ! +-------+-------+-------+ ! 2 . . ! . . . ! 8 4 . ! ! . . . ! . . . ! . . . ! ! 7 . . ! . . 4 ! 6 . 1 ! +-------+-------+-------+ ! . . . ! . 7 . ! 1 . . ! ! 6 7 . ! 5 . . ! . . . ! ! 8 1 . ! 9 . 3 ! . . . ! +-------+-------+-------+ 12....78.4.7.8.2.6.68.2..142.....84..........7....46.1....7.1..67.5.....81.9.3...;326;25948 SER = 11.6

Code: Select all: Resolution state after Singles (and whips[1]): +-------------------------+-------------------------+-------------------------+ ! 1 2 359 ! 346 34569 569 ! 7 8 359 ! ! 4 359 7 ! 13 8 159 ! 2 359 6 ! ! 359 6 8 ! 37 2 579 ! 359 1 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 359 13569 ! 1367 13569 15679 ! 8 4 3579 ! ! 359 34589 134569 ! 123678 13569 1256789 ! 359 23579 23579 ! ! 7 3589 359 ! 238 359 4 ! 6 2359 1 ! +-------------------------+-------------------------+-------------------------+ ! 359 3459 23459 ! 2468 7 268 ! 1 23569 23589 ! ! 6 7 2349 ! 5 14 128 ! 349 239 2389 ! ! 8 1 245 ! 9 46 3 ! 45 2567 257 ! +-------------------------+-------------------------+-------------------------+ 189 candidates.

by **totuan** » Mon Sep 19, 2022 12:33 pm

Code: Select all: *--------------------------------------------------------------------------------------* | 1 2 $359 |%346 %34569 %569 | 7 8 $359 | | 4 $359 7 |&13 8 159 | 2 $359 6 | |$359 6 8 |&37 2 579 |$359 1 4 | |----------------------------+----------------------------+----------------------------| | 2 $359 16 | 1367 13569 15679 | 8 4 $3579 | |$359 4 16 |#123678 13569 #1256789 |$359 *23579 *23579 | | 7 8 $359 |&23 359 4 | 6 $359-2 1 | |----------------------------+----------------------------+----------------------------| | 359 359 23459 |#2468 7 #268 | 1 23569 23589 | | 6 7 2349 | 5 14 128 | 349 239 2389 | | 8 1 245 | 9 46 3 | 45 2567 257 | *--------------------------------------------------------------------------------------*

My path for this one:
Tridagon (359) => (2)r6c8=(7)r4c9 and AUR (28)r57c46 => (2)r6c4=(46)r7c4=(6)r7c6
01: Present as diagram: => r6c8<>2, r4c9=7, some singles

Code: Select all: AUR(28)r57c46 || (6)r7c6-r1c6=(46-3)r1c45=r23c4-(3=2)r6c4- || | (2)r6c4------------------------------------(2)r6c8==(7)r4c9* || | (46-28)r57c4=(2)r6c4-

Code: Select all: *-----------------------------------------------------------* | 1 2 #359 | 4 59 6 | 7 8 39 | | 4 59-3 7 | 1 8 *59 | 2 *359 6 | | 59 6 8 | 3 2 7 | 59 1 4 | |-------------------+-------------------+-------------------| | 2 359 1 | 6 359 *59 | 8 4 7 | |b359 4 6 | 7 1 8 |c359 2359 239 | | 7 8 #359 | 2 *359 4 | 6 *359 1 | |-------------------+-------------------+-------------------| |a359 359 4 | 8 7 2 | 1 6 59-3 | | 6 7 29-3 | 5 4 1 |d39 239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | *-----------------------------------------------------------*

02: 3’s r7c1=r5c1-r5c7=r7c7 => r7c1, r8c3<>3
Oddagon (59) => (3)r2c8=(3)r6c58
03: (3)r2c8==r6c58-r6c3=r1c3 => r2c2<>3, stte

Thanks for the puzzle!
totuan

by **Cenoman** » Mon Sep 19, 2022 12:41 pm

Out of competition

Code: Select all: +----------------------+------------------------------+------------------------+ | 1 2 359* | 346 34569 569 | 7 8 359* | | 4 359* 7 | A13 8 159 | 2 359* 6 | | 359* 6 8 | A37 2 579 | 359* 1 4 | +----------------------+------------------------------+------------------------+ | 2 359* 16 |Ae1367 13569 e15679 | 8 4 Dd3579* | | 359* 4 16 |fa278-136 1359-6 fa278-1569 | 359* 23579 23579 | | 7 8 359* |Ab23 359 4 | 6 Cc2359* 1 | +----------------------+------------------------------+------------------------+ | 359 359 23459 | 2468 7 268 | 1 23569 23589 | | 6 7 2349 | 5 14 128 | 349 239 2389 | | 8 1 E245 | 9 E46 3 | E45 2567 E257 | +----------------------+------------------------------+------------------------+

TH(359)b1346 having two guardians => 7r4c9 = 2r6c8
1. (82)r5c46 = r6c4 - (2)r6c8 = (7)r4c9 - r4c6 = (78)r5c46 => -136 r5c4, -1569 r5c6 (or +278 r5c46); lcls, 3 placements

EDIT: new step #2 replacing my former steps #2, #3. Ending steps renumbered 3, 4

Hidden Text: Show

Code: Select all: +--------------------+----------------------+------------------------+ | 1 2 359 | 4 359 6 | 7 8 359 | | 4 359 7 | 13 8 159 | 2 359 6 | | 359 6 8 | 37 2 579 | 359 1 4 | +--------------------+----------------------+------------------------+ | 2 359 16 | 1367 359 1579 | 8 4 3579 | | 359 4 16 | c278* 16 ca278* | 359 23579 23579 | | 7 8 359 | b23 359 4 | 6 2359 1 | +--------------------+----------------------+------------------------+ | 359 359 4 | 268* 7 28* | 1 23569 23589 | | 6 7 239 | 5 14 128 | 349 239 2389 | | 8 1 25 | 9 46 3 | 45 2567 257 | +--------------------+----------------------+------------------------+

2. UR(28)r57c46 using mixed internal-external (7)r5c6 == (2)r6c4 - (2=87)r5c46 => -7 r4c46, r5c89; lcls, 20 placements

Code: Select all: +--------------------+------------------+----------------------+ | 1 2 a359 | 4 59 6 | 7 8 e359 | | 4 a359 7 | 1 8 59 | 2 fa359 6 | | 59 6 8 | 3 2 7 | 59 1 4 | +--------------------+------------------+----------------------+ | 2 359 1 | 6 359 59 | 8 4 7 | | 359 4 6 | 7 1 8 | 359 2359 2359 | | 7 8 a359 | 2 359 4 | 6 59-3 1 | +--------------------+------------------+----------------------+ | 359 359 4 | 8 7 2 | 1 6 d359 | | 6 7 b239 | 5 4 1 | c39 c239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | +--------------------+------------------+----------------------+

3. (3): [r2c8 = r2c2 - r1c3 = r6c3] = r8c3 - r8c78 = r7c9 - r1c9 = r2c8 => -3 r6c8; lcls, 1 placement

Code: Select all: +-------------------+------------------+---------------------+ | 1 2 359 | 4 59* 6 | 7 8 39 | | 4 c359 7 | 1 8 59* | 2 b359* 6 | | 59 6 8 | 3 2 7 | 59 1 4 | +-------------------+------------------+---------------------+ | 2 d359 1 | 6 359 59 | 8 4 7 | | 59 4 6 | 7 1 8 | 359 2359 239 | | 7 8 59-3 | 2 a359* 4 | 6 59* 1 | +-------------------+------------------+---------------------+ | 3 59 4 | 8 7 2 | 1 6 59 | | 6 7 29 | 5 4 1 | 39 239 8 | | 8 1 25 | 9 6 3 | 4 7 25 | +-------------------+------------------+---------------------+

4. Bivalue oddagon (59)r26, c58, b2 having two guardians => 3r2c8 = 3r6c5
(3)r6c5 = r2c8 - r2c2 = r4c2 => -3 r6c3; ste

by **eleven** » Mon Sep 19, 2022 12:46 pm

Same idea with the 28 UR, but your net took me 7 steps

by **Cenoman** » Mon Sep 19, 2022 1:41 pm

Silly me !
The (28) UR was obvious at my step 3 PMs. Step #3 should have been +7r5c4. Had I seen it, I guess I'd have tried to simplify also my step #2 for the same resolution state. (EDIT: modified my previous post with such a simplification)
So bad !

by **totuan** » Mon Sep 19, 2022 2:33 pm

Code: Select all: *--------------------------------------------------------------------------------------* | 1 2 359 |&346 &34569 &569 | 7 8 359 | | 4 359 7 |%13 8 159 | 2 359 6 | | 359 6 8 |%37 2 579 | 359 1 4 | |----------------------------+----------------------------+----------------------------| | 2 359 16 | 1367 13569 15679 | 8 4 3579 | | 359 4 16 |*28(1367) 13569 *28(15679)| 359 23579 23579 | | 7 8 359 |#2-3 359 4 | 6 2359 1 | |----------------------------+----------------------------+----------------------------| | 359 359 23459 |*28(46) 7 *28(6) | 1 23569 23589 | | 6 7 2349 | 5 14 128 | 349 239 2389 | | 8 1 245 | 9 46 3 | 45 2567 257 | *--------------------------------------------------------------------------------------*

I studied more and see that one can present UR simpler: UR(28)r57c46 => (1367)r5c4=(15679)r5c6=(46)r7c4=(6)r7c6

(2)r6c4=(28)r5c46/r7c4-(1345679)r5c46/r7c4==(6)r7c6-(6)r1c6=(46-3)r1c45=r12c4 => r6c4<>3, r6c4=2

Again, thanks for the puzzle!
totuan

by **eleven** » Mon Sep 19, 2022 6:29 pm

Perfect (UR28: 2r6c4=6r7c6), gives one AIC for 7r4c9.

That's an oddagon step to finish:

Code: Select all: *-----------------------------------------------------------* | 1 2 e#59+3 | 4 #59 6 | 7 8 d39 | | 4 59-3 7 | 1 8 #59 | 2 359 6 | | 59 6 8 | 3 2 7 | 59 1 4 | |--------------------+----------------+---------------------| | 2 #59+3 1 | 6 359 #59 | 8 4 7 | | 359 4 6 | 7 1 8 | 359 2359 239 | | 7 8 359 | 2 359 4 | 6 359 1 | |--------------------+----------------+---------------------| | 359 #59+3 4 | 8 7 2 | 1 6 c359 | | 6 7 a#29+3 | 5 4 1 | b39 b239 8 | | 8 1 #25 | 9 6 3 | 4 7 25 | *-----------------------------------------------------------*

oddagon 59 (r4c2-r4c6-r2c6-r2c5-r1c3-r89c3-r7c2), 4 guardians:
3r47c2,r1c3 == 3r8c3 - r8c78 = r7c9 - r1c9 = r1c3 => -3r2c2, ste

by **DEFISE** » Tue Sep 20, 2022 7:51 am

Hard without using UR !
And implementing Ork-whips in my software is rather boring.
So I'll use a long chain.

After basics:

Code: Select all: |-----------------------------------------------------------------------------| | 1 2 359 | 346 34569 569 | 7 8 359 | | 4 359 7 | 13 8 159 | 2 359 6 | | 359 6 8 | 37 2 579 | 359 1 4 | |-----------------------------------------------------------------------------| | 2 359 16 | 1367 13569 15679 | 8 4 3579 | | 359 4 16 | 123678 13569 1256789 | 359 23579 23579 | | 7 8 359 | 23 359 4 | 6 2359 1 | |-----------------------------------------------------------------------------| | 359 359 23459 | 2468 7 268 | 1 23569 23589 | | 6 7 2349 | 5 14 128 | 349 239 2389 | | 8 1 245 | 9 46 3 | 45 2567 257 | |-----------------------------------------------------------------------------|

Tridagon (3,5,9) in b1p357, b3p357, b4p249, b6p348
2 guardians: 7r4c9 , 2r6c8

whip[11]: r6c4{n2 n3}- r2c4{n3 n1}- b2n3{r2c4 r1c5}- r3c4{n3 n7}- r4c4{n7 n6}- c5n6{r4 r9}- c5n4{r9 r8}- r7n4{c4 c3}- c3n3{r7 r8}- r8c7{n3 n9}- r8c8{n9 .} => -2r6c8
Single: 2r6c4
One guardian remaining => + 7r4c9
Single(s): 7r9c8, 6r9c5, 6r7c8
Hidden pairs: 78r5c46 => -1r5c4 -3r5c4 -6r5c4 -1r5c6 -5r5c6 -6r5c6 -9r5c6
Single(s): 6r5c3, 1r4c3, 1r5c5, 4r8c5, 8r7c4, 7r5c4, 3r3c4, 1r2c4, 6r4c4, 4r1c4, 8r5c6, 2r7c6, 1r8c6, 6r1c6, 7r3c6, 4r7c3, 8r8c9, 4r9c7
Box/Line: 5b9c9 => -5r1c9 -5r5c9
whip[3]: r2n3{c8 c2}- c3n3{r1 r8}- c7n3{r8 .} => -3r6c8
Box/Line: 3b6r5 => -3r5c1
Single: 3r7c1
Xwing in columns: 5c17r35 => -5r5c8
whip[4]: r2n3{c8 c2}- c3n3{r1 r6}- r6n5{c3 c5}- c6n5{r4 .} => -5r2c8
Single(s): 5r6c8, 5r5c1, 9r3c1, 5r3c7
whip[3]: r6n9{c3 c5}- r1n9{c5 c9}- r7n9{c9 .} => -9r8c3
STTE

Website · by **denis_berthier** » Tue Sep 20, 2022 11:50 am

DEFISE wrote:implementing ORk-whips in my software is rather boring.

Yep. We have to manage two parameters k and n.
In CSP-Rules, I need a different rule for each k and n, because each pair has a different priority.
However, it isn't a big deal, because I use a rule generator.

So I'll use a long chain.

Always useful to reduce the number of guardians

Website · by **denis_berthier** » Tue Sep 20, 2022 11:52 am

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Users of UR. It's not what I had in mind, but it's interesting to see that it can simplify the solution.

Website · by **denis_berthier** » Tue Sep 20, 2022 11:57 am

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I proposed this puzzle because it has a simplest-first solution using only chains of lengths ≤ 5 and it has a large number (11) of direct eliminations by ORk-chains based on the anti-tridagon pattern, if one uses both ORk-forcing-whips and ORk-whips.

Code: Select all: hidden-pairs-in-a-column: c3{n1 n6}{r4 r5} ==> r5c3≠9, r5c3≠5, r5c3≠4, r5c3≠3, r4c3≠9, r4c3≠5, r4c3≠3 singles ==> r5c2=4, r6c2=8 biv-chain[3]: r9c7{n5 n4} - r9c5{n4 n6} - b9n6{r9c8 r7c8} ==> r7c8≠5 +-------------------------+-------------------------+-------------------------+ ! 1 2 359 ! 346 34569 569 ! 7 8 359 ! ! 4 359 7 ! 13 8 159 ! 2 359 6 ! ! 359 6 8 ! 37 2 579 ! 359 1 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 359 16 ! 1367 13569 15679 ! 8 4 3579 ! ! 359 4 16 ! 123678 13569 1256789 ! 359 23579 23579 ! ! 7 8 359 ! 23 359 4 ! 6 2359 1 ! +-------------------------+-------------------------+-------------------------+ ! 359 359 23459 ! 2468 7 268 ! 1 2369 23589 ! ! 6 7 2349 ! 5 14 128 ! 349 239 2389 ! ! 8 1 245 ! 9 46 3 ! 45 2567 257 ! +-------------------------+-------------------------+-------------------------+ OR2-anti-tridagon[12] for digits 3, 5 and 9 in blocks: b1, with cells: r1c3, r2c2, r3c1 b3, with cells: r1c9, r2c8, r3c7 b4, with cells: r6c3, r4c2, r5c1 b6, with cells: r6c8, r4c9, r5c7 with 2 guardians: n7r4c9 n2r6c8

This is the main part, combining OR2-Forcing-Whips and OR2-Whips for 10 direct tridagon eliminations:

Code: Select all: Trid-OR2-forcing-whip-elim[2] based on OR2-Trid[12] for n2r6c8 and n7r4c9: || n2r6c8 - || n7r4c9 - partial-whip[1]: c8n7{r5 r9} - ==> r9c8≠2 Trid-OR2-forcing-whip-elim[3] based on OR2-Trid[12] for n2r6c8 and n7r4c9: || n2r6c8 - || n7r4c9 - partial-whip[2]: c8n7{r5 r9} - c8n6{r9 r7} - ==> r7c8≠2 Trid-OR2-forcing-whip-elim[3] based on OR2-Trid[12] for n7r4c9 and n2r6c8: || n7r4c9 - || n2r6c8 - partial-whip[2]: r6c4{n2 n3} - r3c4{n3 n7} - ==> r4c4≠7 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠9 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠6 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠5 Trid-OR2-whip[4]: r5n8{c6 c4} - b5n7{r5c4 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c6≠1 Trid-OR2-whip[4]: r5n8{c4 c6} - b5n7{r5c6 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c4≠6 biv-chain[4]: r8c5{n1 n4} - r9c5{n4 n6} - r5n6{c5 c3} - b4n1{r5c3 r4c3} ==> r4c5≠1 Trid-OR2-whip[4]: r5n8{c4 c6} - b5n7{r5c6 r4c6} - OR2{{n7r4c9 | n2r6c8}} - r6c4{n2 .} ==> r5c4≠3 Trid-OR2-whip[4]: r5n8{c4 c6} - b5n7{r5c6 r4c6} - OR2{{n7r4c9 | n2r6c8}} - b5n2{r6c4 .} ==> r5c4≠1

The rest is easy. The final OR2-forcing-whip is probably not necessary, but it comes out in the simplest-first strategy.

Code: Select all: hidden-pairs-in-a-row: r5{n1 n6}{c3 c5} ==> r5c5≠9, r5c5≠5, r5c5≠3 naked-triplets-in-a-column: c5{r5 r8 r9}{n6 n1 n4} ==> r4c5≠6, r1c5≠6, r1c5≠4 singles ==> r1c4=4, r1c6=6, r7c3=4 biv-chain[4]: r5c5{n1 n6} - r9n6{c5 c8} - r9n7{c8 c9} - r4n7{c9 c6} ==> r4c6≠1 hidden-pairs-in-a-block: b5{n1 n6}{r4c4 r5c5} ==> r4c4≠3 t-whip[5]: r7n6{c8 c4} - c4n8{r7 r5} - c4n2{r5 r6} - r5c6{n2 n7} - c8n7{r5 .} ==> r9c8≠6 singles ==> r7c8=6, r9c5=6, r5c5=1, r4c4=6, r4c3=1, r5c3=6, r8c5=4, r9c7=4, r2c4=1, r8c6=1, r8c9=8 whip[1]: b8n2{r7c6 .} ==> r7c9≠2 hidden-pairs-in-a-column: c6{n2 n8}{r5 r7} ==> r5c6≠7 Trid-OR2-forcing-whip-elim[2] based on OR2-Trid[12] for n7r4c9 and n2r6c8: || n7r4c9 - || n2r6c8 - partial-whip[1]: b9n2{r8c8 r9c9} - ==> r9c9≠7 hidden-single-in-a-block ==> r9c8=7 whip[1]: b9n5{r9c9 .} ==> r1c9≠5, r4c9≠5, r5c9≠5 biv-chain[4]: r4n7{c9 c6} - r3n7{c6 c4} - b2n3{r3c4 r1c5} - r1c9{n3 n9} ==> r4c9≠9 z-chain[4]: c5n3{r6 r1} - c3n3{r1 r8} - r8n2{c3 c8} - r6n2{c8 .} ==> r6c4≠3 singles ==> r6c4=2, r5c6=8, r5c4=7, r3c4=3, r7c6=2, r7c4=8, r3c6=7, r4c9=7 finned-x-wing-in-rows: n3{r1 r7}{c9 c3} ==> r8c3≠3 whip[1]: r8n3{c8 .} ==> r7c9≠3 finned-x-wing-in-columns: n3{c9 c3}{r1 r5} ==> r5c1≠3 hidden-single-in-a-column ==> r7c1=3 whip[1]: r5n3{c9 .} ==> r6c8≠3 x-wing-in-columns: n5{c1 c7}{r3 r5} ==> r5c8≠5 finned-x-wing-in-columns: n5{c8 c6}{r2 r6} ==> r6c5≠5 whip[1]: b5n5{r4c6 .} ==> r4c2≠5 biv-chain[3]: r3n9{c1 c7} - r1c9{n9 n3} - b1n3{r1c3 r2c2} ==> r2c2≠9 biv-chain[3]: r2n9{c6 c8} - r2n3{c8 c2} - r4c2{n3 n9} ==> r4c6≠9 singles ==> r4c6=5, r2c6=9, r1c5=5 finned-x-wing-in-rows: n9{r1 r8}{c3 c9} ==> r7c9≠9 stte

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