The New Sudoku Players' Forum

by **P.O.** » Tue Apr 18, 2023 3:33 pm

for this puzzle i have a rather difficult one-step solution with a ordinary forcing-chain and a 'simpler' solution using the Dynamic+Dynamic Forcing Chain method.

Code: Select all: . . 1 . . . . 7 2 . . . . 6 . 8 5 9 9 . . . . 8 1 4 . . . . . 3 9 7 . . . . . 5 7 2 . 6 . . . 7 8 1 . . . . . 5 2 3 . . . . . 1 4 9 . . . . . . 7 3 . . . . 5 . 4 ..1....72....6.8599....814.....397.....572.6...781.....523.....149......73....5.4 34568 68 1 49 459 345 36 7 2 234 27 34 1247 6 1347 8 5 9 9 267 356 27 25 8 1 4 36 24568 1268 4568 46 3 9 7 128 158 348 189 348 5 7 2 349 6 138 23456 269 7 8 1 46 2349 239 35 68 5 2 3 489 1467 69 189 1678 1 4 9 267 258 567 236 238 3678 7 3 68 1269 289 16 5 1289 4

by **Cenoman** » Tue Apr 18, 2023 8:07 pm

The reasonable solution in two steps:

Code: Select all: +------------------------+----------------------+-----------------------+ | 3458-6 8-6 1 | b49 b459 b345 | a36 7 2 | | 234 27 34 | 1247 6 1347 | 8 5 9 | | 9 c267 356 | c27 c25 8 | 1 4 3-6 | +------------------------+----------------------+-----------------------+ | 24568 1268 4568 | 46 3 9 | 7 128 158 | | 348 189 348 | 5 7 2 | 349 6 138 | | 23456 269 7 | 8 1 46 | 2349 239 35 | +------------------------+----------------------+-----------------------+ | 68 5 2 | 3 489 1467 | 69 189 1678 | | 1 4 9 | 267 258 567 | 236 238 3678 | | 7 3 68 | 1269 289 16 | 5 1289 4 | +------------------------+----------------------+-----------------------+

1. (6=3)r1c7 - (3=495)r1c456 - (5=276)r3c245 => -6 r1c12, r3c9; lcls, 15 placements

Code: Select all: +--------------------+------------------+-----------------+ | 345 8 1 | 49 59 34 | 6 7 2 | | 234 27 34 | 1 6 347 | 8 5 9 | | 9 67 d56 | 27 25 8 | 1 4 3 | +--------------------+------------------+-----------------+ | 456 1 d456 |e 46 3 9 | 7 2 8 | | 348 9 348 | 5 7 2 | 34 6 1 | | 2346 26 7 | 8 1 46 | 34 9 5 | +--------------------+------------------+-----------------+ | 68 5 2 | 3 4 a16-7 | 9 b18 67 | | 1 4 9 | e67 8 5 | 2 3 67 | | 7 3 d68 | 29 29 16 | 5 c18 4 | +--------------------+------------------+-----------------+

2. (1)r7c6 = r7c8 - (1=8)r9c8 - (8=564)r349c3 - (4=67)r48c4 => -7 r7c6; ste

For one step only, I need multi-krakens:

Hidden Text: Show

by **SteveG48** » Wed Apr 19, 2023 12:01 pm

Code: Select all: *---------------------------------------------------------------------* | 34568 68 1 | 49 459 345 | 36 7 2 | | 234 27 34 | 1247 6 1347 | 8 5 9 | | 9 a267 36-5 | a27 a25 8 | 1 4 a36 | *----------------------+-----------------------+----------------------| |i24568 h1268 hi4568 | h46 3 9 | 7 b128 bh158 | | 348 189 348 | 5 7 2 | 349 6 b138 | | 23456 269 7 | 8 1 46 | 2349 239 b35 | *----------------------+-----------------------+----------------------| | 68 5 2 | 3 489 f1467 | 69 189 1678 | | 1 4 9 |eg267 258 f567 |d236 c238 3678 | | 7 3 g68 | f1269 289 f16 | 5 c1289 4 | *---------------------------------------------------------------------*

(5=(2673)*)r3c2459 - (3=185**2)b6p2369 - 2r89c8 = r7c8 - (2|*7=6)r8c4 - 6b9p3679 = 6r8c4&r9c3 - (6|*6)r4c234|**5r4c9 = (6,5)r4c13 => -5 r4c3 ; ste

by **DonM** » Thu Apr 20, 2023 5:15 am

ER=7.1
2 fairly basic AICs:
(I’m old-school: back in the day we tended to reserve Krakens and the like, if possible, for at least ER>8)

Code: Select all: *--------------------------------------------------------------------* | 34568 68 1 | 49 459 345 | 36 7 2 | | 234 27 34 | 1247 6 1347 | 8 5 9 | | 9 267 356 | 27 25 8 | 1 4 36 | |----------------------+----------------------+----------------------| | 24568 1268 4568 | 46 3 9 | 7 128 158 | | 348 189 348 | 5 7 2 | 349 6 138 | | 23456 269 7 | 8 1 46 | 2349 239 35 | |----------------------+----------------------+----------------------| | 68 5 2 | 3 489 1467 | 69 189 1678 | | 1 4 9 | 267 258 567 | 236 238 3678 | | 7 3 68 | 1269 289 16 | 5 1289 4 | *--------------------------------------------------------------------*

(6)r7c7=hNP(68)r1c12-(5)r1c1=(5-3)r3c3=(3)r3c9 => r1c7<>3 many singles

Code: Select all: *-----------------------------------------------------------* | 345 8 1 | 49 59 34 | 6 7 2 | | 234 27 34 | 1247 6 1347 | 8 5 9 | | 9 267 56 | 27 25 8 | 1 4 3 | |-------------------+-------------------+-------------------| | 456 1 456 | 46 3 9 | 7 2 8 | | 348 9 348 | 5 7 2 | 34 6 1 | | 2346 26 7 | 8 1 46 | 34 9 5 | |-------------------+-------------------+-------------------| | 68 5 2 | 3 4 167 | 9 18 67 | | 1 4 9 | 67 8 5 | 2 3 67 | | 7 3 68 | 1269 29 16 | 5 18 4 | *-----------------------------------------------------------*

Remembering SteveK's Quantums: based on a unique rectangle type3 (34)r56c17 Quantum almost naked pair:
(Fwiw, if one uses naked triple (167) in box 8, (6)r9c46 could be just (6)r9c6)

(6)r9c46=(6)r9c3-(6=8)r7c1-(8)r5c1=QNP(26)r6c12-(6)r6c6=(6)r4c4 => r8c4<>6 stte

by **P.O.** » Thu Apr 20, 2023 8:23 am

thank you for your answers,
all the puzzles i have posted lately are only challenging if you are looking for a one-step solution, otherwise they are easy to solve with a few simple techniques.
so here are my two solutions: the first by a rather complicated forcing-chain and the second obtained by the Dynamic+Dynamic Forcing Chain method which, although the process to find the solution is more complex than that of ordinary forcing-chains, is much simpler.
first solution:

Code: Select all: let A be: r3c5=2 - r3c4{n2 n7} - r3c2{n27 n6} - b3n6{r3c9 r1c7} - r7c7{n6 n9} - c8n9{r79 r6} - r6c2{n69 n2} - c7n2{r6 r8} - r8c4{n27 n6} 2r3c5 => r4c3 <> 4,5,6,8 A - r4c4{n6 n4} r3c5=2 - r3c4{n2 n7} - r3c2{n27 n6} - r3c9{n6 n3} - r3c3{n36 n5} A - r9n6{c46 c3} r3c5=2 - r3c4{n2 n7} - r3c2{n27 n6} - b3n6{r3c9 r1c7} - r7c7{n6 n9} - r5n9{c7 c2} - r5n1{c2 c9} - b6n8{r5c9 r4c89} => r3c5 <> 2 ste.

second solution:
n5r3c3 OR n5r4c3 => r9c6 <> 1 ste.
r3c3=5 context:

Hidden Text: Show

Code: Select all: ((5 0) (3 3 1) (3 5 6)) n5r3c3 ((7 1 21) (3 4 2) (2 7)) n7r3c4 ((3 1 10) (3 9 3) (3 6)) n3r3c9 ((2 1 9) (3 5 2) (2 5)) n2r3c5 ((5 1 2 2) ((4 1 4) (2 4 5 6 8)) ((6 1 4) (2 3 4 5 6))) n5r46c1 ((5 1 1 2) ((1 5 2) (4 5 9)) ((1 6 2) (3 4 5))) n5r1c56 ((7 1 21) (3 4 2) (2 7)) n7r3c4 ((7 2 1) (2 2 1) (2 7)) n7r2c2 ((7 2 2 2) ((7 6 8) (1 4 6 7)) ((8 6 8) (5 6 7))) n7r78c6 ((3 1 10) (3 9 3) (3 6)) n3r3c9 ((6 2 10) (3 2 1) (2 6 7)) n6r3c2 ((5 2 9) (6 9 6) (3 5)) n5r6c9 ((6 2 9) (1 7 3) (3 6)) n6r1c7 ((8 2 2 52) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n8r45c9 ((1 2 2 52) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n1r45c9 ((6 2 2 11) ((7 9 9) (1 6 7 8)) ((8 9 9) (3 6 7 8))) n6r78c9 ((3 2 1 2) ((8 7 9) (2 3 6)) ((8 8 9) (2 3 8))) n3r8c78 ((2 1 9) (3 5 2) (2 5)) n2r3c5 ((7 2 9) (3 4 2) (2 7)) n7r3c4 ((2 2 2 2) ((8 4 8) (2 6 7)) ((9 4 8) (1 2 6 9))) n2r89c4 ((2 2 1 2) ((2 1 1) (2 3 4)) ((2 2 1) (2 7))) n2r2c12 ((6 2 10) (3 2 1) (2 6 7)) n6r3c2 ((3 3 9) (3 9 3) (3 6)) n3r3c9 ((8 3 9) (1 2 1) (6 8)) n8r1c2 ((6 3 5) (1 7 3) (3 6)) n6r1c7 ((5 2 9) (6 9 6) (3 5)) n5r6c9 ((5 3 1) (4 1 4) (2 4 5 6 8)) n5r4c1 ((8 3 2 32) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n8r45c9 ((1 3 2 32) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n1r45c9 ((6 2 9) (1 7 3) (3 6)) n6r1c7 ((9 3 9) (7 7 9) (6 9)) n9r7c7 ((8 3 9) (1 2 1) (6 8)) n8r1c2 ((6 3 2 2) ((7 9 9) (1 6 7 8)) ((8 9 9) (3 6 7 8))) n6r78c9 ((8 2 2 52) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n8r45c9 ((8 3 2 13) ((7 8 9) (1 8 9)) ((8 8 9) (2 3 8)) ((9 8 9) (1 2 8 9))) n8r789c8 ((1 2 2 52) ((4 9 6) (1 5 8)) ((5 9 6) (1 3 8))) n1r45c9 ((1 3 2 13) ((7 8 9) (1 8 9)) ((9 8 9) (1 2 8 9))) n1r79c8

Code: Select all: 34 8 1 49 459 345 6 7 2 234 7 34 14 6 134 8 5 9 9 6 5 7 2 8 1 4 3 5 1 46 46 3 9 7 2 8 348 9 348 5 7 2 34 6 1 346 2 7 8 1 46 34 39 5 68 5 2 3 48 1467 9 18 67 1 4 9 26 58 567 23 38 67 7 3 68 1269 89 16 5 18 4 1r9c6 => r4c34 <> 6 r9c6=1 - r9c8{n1 n8} - r9c3{n8 n6} r9c6=1 - r9c8{n1 n8} - r7c8{n8 n3} - r7c7{n3 n2} - r7c4{n2 n6} => r9c6 <> 1

r4c3=5 context:

Hidden Text: Show

Code: Select all: ((5 0) (4 3 4) (4 5 6 8)) n5r4c3 ((5 1 7) (1 1 1) (3 4 5 6 8)) n5r1c1 ((5 1 1) (6 9 6) (3 5)) n5r6c9 ((5 1 7) (1 1 1) (3 4 5 6 8)) n5r1c1 ((3 2 41) (1 6 2) (3 4 5)) n3r1c6 ((8 2 10) (1 2 1) (6 8)) n8r1c2 ((5 2 3) (3 5 2) (2 5)) n5r3c5 ((5 2 1) (8 6 8) (5 6 7)) n5r8c6 ((9 2 1 31) ((1 4 2) (4 9)) ((1 5 2) (4 5 9))) n9r1c45 ((4 2 1 31) ((1 4 2) (4 9)) ((1 5 2) (4 5 9))) n4r1c45 ((4 2 1 11) ((2 1 1) (2 3 4)) ((2 3 1) (3 4))) n4r2c13 ((4 2 1 11) ((1 4 2) (4 9)) ((1 5 2) (4 5 9)) ((1 6 2) (3 4 5))) n4r1c456 ((3 2 41) (1 6 2) (3 4 5)) n3r1c6 ((6 3 9) (1 7 3) (3 6)) n6r1c7 ((3 3 1) (3 9 3) (3 6)) n3r3c9 ((3 3 1 2) ((2 1 1) (2 3 4)) ((2 3 1) (3 4))) n3r2c13 ((8 2 10) (1 2 1) (6 8)) n8r1c2 ((6 3 10) (1 7 3) (3 6)) n6r1c7 ((6 3 1 11) ((3 2 1) (2 6 7)) ((3 3 1) (3 5 6))) n6r3c23 ((5 2 3) (3 5 2) (2 5)) n5r3c5 ((3 3 41) (1 6 2) (3 4 5)) n3r1c6 ((5 3 1) (8 6 8) (5 6 7)) n5r8c6 ((9 3 1 31) ((1 4 2) (4 9)) ((1 5 2) (4 5 9))) n9r1c45 ((4 3 1 31) ((1 4 2) (4 9)) ((1 5 2) (4 5 9))) n4r1c45 ((2 3 2 11) ((8 5 8) (2 5 8)) ((9 5 8) (2 8 9))) n2r89c5 ((2 3 2 11) ((2 4 2) (1 2 4 7)) ((3 4 2) (2 7))) n2r23c4 ((4 2 1 31) ((1 4 2) (4 9)) ((1 5 2) (4 5 9))) n4r1c45 ((3 3 76) (1 6 2) (3 4 5)) n3r1c6 ((4 3 1 17) ((2 1 1) (2 3 4)) ((2 3 1) (3 4))) n4r2c13

Code: Select all: 5 8 1 49 49 3 6 7 2 234 27 34 127 6 17 8 5 9 9 27 6 27 5 8 1 4 3 248 126 5 46 3 9 7 128 18 348 19 34 5 7 2 34 6 18 234 269 7 8 1 46 234 239 5 6 5 2 3 48 147 9 18 178 1 4 9 67 28 5 23 238 678 7 3 8 169 29 16 5 12 4 r9c6=1 - r9c8{n1 n2} - 18r4c89 => r5c9 <> 1,8 => r9c1 <> 1

by **SteveG48** » Thu Apr 20, 2023 2:33 pm

DonM! Long time no see. Welcome home.

by **DonM** » Thu Apr 20, 2023 4:25 pm

SteveG48 wrote:DonM! Long time no see. Welcome home.

Thanks Steve. A return after, if memory serves, 9 years.

by **DonM** » Thu Apr 20, 2023 5:05 pm

P.O. wrote:thank you for your answers,
all the puzzles i have posted lately are only challenging if you are looking for a one-step solution, otherwise they are easy to solve with a few simple techniques…

Yes, I’ve noticed that the challenge now seems to be a one-step solution posted often the same day the puzzle is posted but, unless I’m missing something, in order to do that, one has to first find the back door which is manually majorly time-consuming. So, is the routine people are using is to use a solver such as Hoduko to find the back door then manually create the one-step? Just asking for a friend.

by **P.O.** » Thu Apr 20, 2023 5:38 pm

i am not a manual solver i use algorithms from start to finish, this is what i like to do, make tools, algorithms, which i then use to accomplish different tasks.
it is not necessary to explicitly search for anti-backdoors in order to build a one-step solution, the program calculates all the eliminations it can find using a set of configurable techniques, then tests them to find which ones solve the puzzle
in easy puzzles the anti-backdoors are often easily accessible

by **DonM** » Thu Apr 20, 2023 6:35 pm

P.O. wrote:it is not necessary to explicitly search for anti-backdoors in order to build a one-step solution, the program calculates all the eliminations it can find using a set of configurable techniques, then tests them to find which ones solve the puzzle. in easy puzzles the anti-backdoors are often easily accessible

But, inevitably, the program is looking for the back door.

I would say that if one is doing everything manually, finding exclusions in easy puzzles is easy, but finding back-doors is not quite so easy -or let’s say it’s easy, but tedious- and would still take time manually, presumably by testing cells with only 2 digits. Or one can use a computer solver to quickly find it and then fashion a one-step.

I understand the interest in finding one-step solutions and some of them are quite innovative. I’m just trying to figure out the routine people are following. It’s quite different from the solving we did years ago.

(Btw, I like the puzzles you put up. They have a nice variable level of challenge.)

by **P.O.** » Thu Apr 20, 2023 7:25 pm

the program does not look for anti-backdoors, i have a procedure that looks for and finds all anti-backdoors, the program looks for eliminations and it happens that among these there are some anti-backdoors
as i said i am not a manual solver and like you i sometimes wonder how manual solvers arrive at their solution, but i have no answer to this question
only manual solvers would be able to describe the procedure they follow
regarding the one-step solution for me it's just a challenge that adds interest to the resolution of the puzzle

by **SteveG48** » Thu Apr 20, 2023 8:07 pm

DonM wrote:
P.O. wrote:thank you for your answers,
all the puzzles i have posted lately are only challenging if you are looking for a one-step solution, otherwise they are easy to solve with a few simple techniques…

Yes, I’ve noticed that the challenge now seems to be a one-step solution posted often the same day the puzzle is posted but, unless I’m missing something, in order to do that, one has to first find the back door which is manually majorly time-consuming. So, is the routine people are using is to use a solver such as Hoduko to find the back door then manually create the one-step? Just asking for a friend.

That's certainly the way that I do it. I believe that what you describe was also the challenge and approach back in Dan's day, which is where I came on board. The way that I look at it is that ordinary Sudoku solving uses multiple logic steps as a means to an end. When we play the "one step" game, the logic is the end in itself.

Like you, I enjoy the level of difficulty posed by P.O.'s puzzles, but it often requires rather complex chains and star notation. I like solutions that can be written in pure bi-directional AICs following the rules posted by David P. Bird way back when, but I'm often driven to the kinds of thing I posted in this thread.

by **DonM** » Thu Apr 20, 2023 10:43 pm

Just for giggles, the below was one of my last contributions years ago. You can see the difference in the emphasis at the time. I guess it was the beginning of the end of an era that spanned close to a decade. I started in the UK Eureka forum around 2006, but changed over to the U.S. based Players’ Forum around 2008 after the Eureka forum got hacked for the 2nd time losing all the valuable threads where some of the now well-known solving methods and patterns were born.

http://forum.enjoysudoku.com/suggest-a-play-sap-1-t31515.html

by **yzfwsf** » Fri Apr 21, 2023 1:08 am

Whip[14]: Supposing 5r1c5 will result in all candidates in cell r6c9 being impossible => r1c56,r3c3<>5
5#r1c5 - r3c5(5=2*) - r3c4(2=7^) - r3c2(2*7=6$) - r3c9(6=3@) - r1c7(3=6) - r7c7(6=9) - 9r5(c7=c2) - r6c2(6$9=2) - 2c7(r6=r8) - r8c4(7^2=6%) - 6r9(c46=c3) - 6r4(c2$4%3=c1) - 5c1(r1#4=r6) - r6c9(3@5=.)
stte

by **totuan** » Sat Apr 22, 2023 5:51 pm

Wow…, welcome back DonM! Nice to see you, after very long time (from ttt, my old nickname

)

ttt/totuan

The New Sudoku Players' Forum

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