The New Sudoku Players' Forum

by **International_DBA** » Mon Apr 01, 2019 10:02 pm

Before you start this one, I believe it has what you call "nasty network forcing chains":
https://andrews-sudoku.blogspot.com/201 ... treme.html

by **Leren** » Tue Apr 02, 2019 8:05 am

Yes, pretty brutal, both Hodoku and I rate this as your hardest yet. I Used 16 non basic moves including 6 nasty forcing chains. Hodoku used 24 non basic moves including 6 nasty forcing chains. Still, I can solve anything, so here is the solution.

Code: Select all: *-----------------------* | 8 6 4 | 5 3 9 | 2 7 1 | | 1 2 9 | 6 4 7 | 8 5 3 | | 3 7 5 | 2 8 1 | 4 6 9 | |-------+-------+-------| | 4 5 7 | 8 9 6 | 1 3 2 | | 6 1 2 | 4 5 3 | 9 8 7 | | 9 3 8 | 7 1 2 | 6 4 5 | |-------+-------+-------| | 5 9 1 | 3 6 8 | 7 2 4 | | 2 4 6 | 1 7 5 | 3 9 8 | | 7 8 3 | 9 2 4 | 5 1 6 | *-----------------------*

Here is just one of Hodoku's forcing chain moves : Forcing Chain Contradiction in r2 =>

r1c9<>4r1c9=4 r1c1<>4 r1c1=8 r2c3<>8 r1c9=4 r7c9<>4 r7c7=4 r7c7<>7 r2c7=7 r2c7<>8 r1c9=4 r1c9<>1 r3c7=1 r3c6<>1 r3c6=6 r2c456<>6 r2c8=6 r2c8<>8r1c9=4 r1c9<>1 r3c7=1 r3c6<>1 r3c6=6 r7c6<>6 r7c6=8 r8c4<>8 r8c9=8 r2c9<>8

If you can understand any of that, you are much cleverer than I am

Leren

by **International_DBA** » Fri Apr 05, 2019 6:11 am

I published this last night:
https://andrews-sudoku.blogspot.com/201 ... lical.html

by **Leren** » Fri Apr 05, 2019 8:13 am

.9...4.7.....5...454..179.8..2...6...69...4.2..1..........7.3....6......7...32..5

A bit tricky to notate but here is a One Trick Pony solution :

Code: Select all: *-----------------------------------------------------* |c12 9 8 | 3 b26b 4 | 5 7 16 | | 6 d12 7 | 89 5 89 |e12 3 4 | | 5 4 3 | 26c 1 7 | 9 f26 8 | |------------+--------------------+-------------------| | 48 57 2 | 1459 49 1359 | 6 1589 1379 | | 3 6 9 | 7 8 15 | 4 15 2 | | 48 57 1 | 24569 a2-6a 3569 | 78 589 379 | |------------+--------------------+-------------------| |f129 e128 5 | 14689e 7 1689e | 3 g124689 169 | | 129 3 6 | 14589 49 1589 | 1278 12489 179 | | 7 18 4 | 69d 3 2 | 18 69 5 | *-----------------------------------------------------* Kraken Row 7 digit 9; 6r6c5 - 2r6c5 = 2r1c5 - 2r1c1 = 2r2c2 - 2r2c7 = 2r3c8 - 2r7c8; 6r6c5 - 2r6c5 = 2r1c5 - 2r1c1 = 2r2c2 - 2r7c2 = 2r7c1 - 9r7c1 6r6c5 - 6r1c5 = 6r3c4 - (6=9) r9c4 - 9r7c46 => - 6 r6c5; stte

Leren

by **SpAce** » Sat Apr 06, 2019 2:13 am

Leren wrote:..35.8.2...1.62.5.5...1...3.....57.1.786..24..........48...6..9...........574.6..

Wow, a real tough one. Me, 20 non-basic moves, Hodoku a mere 17. But we did solve it. At least it solves with linear chains and URs. No nasty network forcing chains etc.

Five AICs, no sweat. (Pure manual, no cheating or post-game optimization.) Btw, why do you post solution grids? That's not exactly nice for other solvers.

My steps: Show

Code: Select all: .------------------------.---------------------.------------------. | 679 469 3 | 5 79 8 | 1 2 c46 | | 8 49 1 | 3 6 2 | 49 5 7 | | 5 269 269-7 | d49 1 d4(7) | d89 d689 3 | :------------------------+---------------------+------------------: | 2369 2369 2469 | 2489 2389 5 | 7 3689 1 | | 139 7 8 | 6 39 139 | 2 4 5 | | 12369 5 2469 | 12489 23789 47 | 389 3689 68 | :------------------------+---------------------+------------------: | 4 8 a2(7) | 12 235 6 | 35 137 9 | | 23679 12369 2679 | 1289 23589 139 | 345 137 c24 | | b239 b1239 5 | 7 4 139 | 6 138 c28 | '------------------------'---------------------'------------------'

Step 1: (7=2)r7c3 - r9c12 = (246)r981c9 - (6=8947)r3c8746 => -7 r3c3

Code: Select all: .--------------------.----------------.---------------------. | 7 46 3 | 5 9 8 | 1 2 a46 | | 8 49 1 | 3 6 2 | a49 5 7 | | 5 269 269 | 4 1 7 | a(8)9 689 3 | :--------------------+----------------+---------------------: | 2369 2369 4 | 289 28 5 | 7 3689 1 | | 19 7 8 | 6 3 19 | 2 4 5 | | 12369 5 269 | 1289 7 4 | 39-8 3689 b6(8) | :--------------------+----------------+---------------------: | 4 8 27 | 12 25 6 | 35 137 9 | | 2369 12369 2679 | 1289 258 139 | 45 17 24 | | 239 1239 5 | 7 4 139 | 6 18 28 | '--------------------'----------------'---------------------'

Step 2: (8=946)b3p743 - (6=8)r6c9 => -8 r6c7

Code: Select all: .----------------------.-------------------.-----------------. | 7 46 3 | 5 9 8 | 1 2 46 | | 8 49 1 | 3 6 2 | 49 5 7 | | 5 269 269 | 4 1 7 | 8 69 3 | :----------------------+-------------------+-----------------: | 2369 2369 4 | 289 28 5 | 7 3689 1 | | a1(9) 7 8 | 6 3 b19 | 2 4 5 | | 1236-9 5 26-9 | 1289 7 4 | d3(9) 3689 68 | :----------------------+-------------------+-----------------: | 4 8 27 | c12 c25 6 | c35 137 9 | | 2369 12369 2679 | 1289 258 b139 | 45 17 24 | | 239 1239 5 | 7 4 b139 | 6 18 28 | '----------------------'-------------------'-----------------'

Step 3: (9=1)r5c1 - r[5=89]c6 - (1=253)r7c457 - (3=9)r6c7 => -9 r6c13

Code: Select all: .-----------------------.---------------------.-----------------. | 7 46 3 | 5 9 8 | 1 2 46 | | 8 b49 1 | 3 6 2 | c49 5 7 | | 5 269 b269 | 4 1 7 | 8 69 3 | :-----------------------+---------------------+-----------------: | 2369 2369 4 | 289 28 5 | 7 3689 1 | | 19 7 8 | 6 3 19 | 2 4 5 | | 1236 5 26 | 1289 7 4 | 39 3689 68 | :-----------------------+---------------------+-----------------: | 4 8 27 | 12 25 6 | d35 d137 9 | | 2369 12369 a26(9)-7 | D12(8)-9 D258 139 | Dd45 d1(7) 24 | | 239 1239 5 | 7 4 139 | 6 18 28 | '-----------------------'---------------------'-----------------'

Step 4: (9)r8c3 = (94)b1p95 - r2c7 = (4537)b9p4125&(458)r8c754 => -7 r8c3, -9 r8c4

Code: Select all: .-------------------.---------------.----------------------. | 7 46 3 | 5 9 8 | 1 2 46 | | 8 49 1 | 3 6 2 | 49 5 7 | | 5 269 269 | 4 1 7 | 8 69 3 | :-------------------+---------------+----------------------: | 236 236 4 | 289 c28 5 | 7 689 1 | | 9 7 8 | 6 3 1 | 2 4 5 | | 1 5 e(2)-6 | d289 7 4 | d39 e(3)89-6 a(6)8 | :-------------------+---------------+----------------------: | 4 8 7 | 12 25 6 | c35 13 9 | | 236 12369 269 | 18 b58 39 | b45 7 a24 | | 23 1239 5 | 7 4 39 | 6 18 a28 | '-------------------'---------------'----------------------'

Step 5: (6=824)r698c9 - (4=85)r8c57 - (8|5=23)r4c5,r7c7 - (2|3)r6c47 = (23)r6c38 => -6 r6c38; stte

Btw, International_DBA, can you give a link to your Facebook group? This was the first one of yours I tried, and it was pretty nice. Fun to do a multi-stepper for a change.

by **International_DBA** » Sat Apr 06, 2019 6:40 am

Here is a link to my Facebook group.
It has just over 4000 members.
It has links back to my blog and the stronger members sometimes explain how they work out the answers:
https://www.facebook.com/groups/722318601312015/

by **SpAce** » Sun Apr 07, 2019 4:41 am

Leren wrote:Yes, pretty brutal, both Hodoku and I rate this as your hardest yet. I Used 16 non basic moves including 6 nasty forcing chains. Hodoku used 24 non basic moves including 6 nasty forcing chains. Still, I can solve anything, so here is the solution.

This one took me seven moves, including one memory chain. A bit more tedious than the last one, but not hard. Many elimination opportunities around so the hardest part was to try to pick effective ones. I don't know how well I did but at least 7 < 24. (Actually my copy of Hodoku lists 26 non-basic moves, including just one forcing chain, but you may have different settings).

...5..2..1.........7..8...9..7...........39..93.7.2.4...13......46..53.....92.5.6

My steps: Show

Code: Select all: .--------------------.-------------------.----------------------. | 348 6 489 | 5 13479 179 | 2 378 13478 | | 1 25 24589 | 246 34679 679 | 4678 35678 34578 | | c(3)4 7 b245 | 1246 8 16 | 146 a(5)6-3 9 | :--------------------+-------------------+----------------------: | c468 125 7 | 1468 14569 1689 | 168 23568 12358 | | c468 125 2458 | 1468 1456 3 | 9 25678 12578 | | 9 3 b58 | 7 156 2 | 168 4 158 | :--------------------+-------------------+----------------------: | 5 9 1 | 3 67 678 | 478 278 2478 | | 2 4 6 | 18 17 5 | 3 9 78 | | 7 8 3 | 9 2 4 | 5 1 6 | '--------------------'-------------------'----------------------'

Step 1: (5)r3c8 = (58)r36c3 - (8=463)r453c1 => -3 r3c8

Code: Select all: .-------------------.------------------------.---------------------------. | 48 6 489 | 5 13479 179 | 2 378 13478 | | 1 25 24589 | 246 34679 679 | 4678 35678 34578 | | 3 7 245 | 1246 8 16 | 146 56 9 | :-------------------+------------------------+---------------------------: |e(468) 125 7 |e(1468) 14569 e(8)169 |e(168) 2358-6 12358 | | 468 125 2458 | 1468 1456 3 | 9 e25(7)8-6 d12578 | | 9 3 58 | 7 b156 2 | a1(6)8 4 158 | :-------------------+------------------------+---------------------------: | 5 9 1 | 3 b67 d678 | 478 278 2478 | | 2 4 6 | c18 b17 5 | 3 9 c78 | | 7 8 3 | 9 2 4 | 5 1 6 | '-------------------'------------------------'---------------------------'

Step 2: (6)r6c7 = (671)r678c5 - (1=87)r8c49 - (8)r7c6|(7)r5c9 = (8146)r4c6147&(7)r5c8 => -6 r45c8

Code: Select all: .-------------------.--------------------.-------------------------. | 48 6 489 | 5 13479 179 | 2 378 13478 | | 1 25 24589 | 246 34679 679 | 478 35678 3478-5 | | 3 7 b245 | 1246 8 b16 | c14 ab(5)6 9 | :-------------------+--------------------+-------------------------: | 468 125 7 | 1468 14569 1689 | d168 238-5 12358 | | 468 125 2458 | 1468 1456 3 | 9 278-5 12578 | | 9 3 cd58 | 7 156 2 | d168 4 e18(5) | :-------------------+--------------------+-------------------------: | 5 9 1 | 3 67 678 | 478 278 2478 | | 2 4 6 | 18 17 5 | 3 9 78 | | 7 8 3 | 9 2 4 | 5 1 6 | '-------------------'--------------------'-------------------------'

Step 3: (5)r3c8 = (615)r3c863 - (1|5)r3c7,r6c3 = (18)r46c7,r6c3 - (1|8=5)r6c9 => -5 r2c9,r45c8

Code: Select all: .--------------------.------------------------.------------------------. | f4(8) 6 489 | 5 13479 179 | 2 g378 g13478 | | 1 25 24589 | 246 34679 679 | g47(8) 56 g3478 | | 3 7 245 | 1246 8 16 | 14 56 9 | :--------------------+------------------------+------------------------: | f46-8 125 7 | 1468 14569 a16(8)9 | 16-8 238 1235-8 | | f468 125 2458 | 1468 1456 3 | 9 278 12578 | | 9 3 e5(8) | 7 c156 2 | de168 4 e158 | :--------------------+------------------------+------------------------: | 5 9 1 | 3 b67 b678 | 478 278 2478 | | 2 4 6 | c18 17 5 | 3 9 d7(8) | | 7 8 3 | 9 2 4 | 5 1 6 | '--------------------'------------------------'------------------------'

Step 4:

(8)r4c6 = (86)r7c65 - (8|6)r8c4,r6c5 = (86)@r8c9*,r6c7 - (8)r6c[79=@3] - r[45=1]c1 - b3p[23*6=4] => -8 r4c179

Code: Select all: .-----------------.---------------------.---------------------. | 48 6 489 | 5 13479 179 | 2 378 13478 | | 1 25 24589 | 246 34679 679 | d47(8) 56 3478 | | 3 7 245 | 1246 8 c16 | d14 56 9 | :-----------------+---------------------+---------------------: | 46 125 7 | 1468 14569 1689 | 16 238 1235 | | 468 125 2458 | 1468 1456 3 | 9 278 12578 | | 9 3 58 | 7 a156 2 | a1(6)-8 4 158 | :-----------------+---------------------+---------------------: | 5 9 1 | 3 b67 b678 | d47(8) 278 2478 | | 2 4 6 | 18 17 5 | 3 9 78 | | 7 8 3 | 9 2 4 | 5 1 6 | '-----------------'---------------------'---------------------'

Step 5: (6)r6c[7=5] - r7c[5=6] - (6=1)r3c6 - (1=478)r326c7 => -8 r6c7

Code: Select all: .---------------------.--------------------.-----------------. | 48 6 489 | 5 349 79 | 2 378 1 | | 1 25 489 | 246 349 679 | 78 56 378 | | 3 7 25 | 126 8 16 | 4 56 9 | :---------------------+--------------------+-----------------: | a46 125 7 | 1468 459 1689 | b16 38 235 | | a4(6)-8 125 2458 | 1468 45 3 | 9 78 2578 | | 9 3 f5(8) | 7 c16 2 | b16 4 f58 | :---------------------+--------------------+-----------------: | 5 9 1 | 3 d67 d68 | 78 2 4 | | 2 4 6 | e18 17 5 | 3 9 e78 | | 7 8 3 | 9 2 4 | 5 1 6 | '---------------------'--------------------'-----------------'

Step 6: (6)r[5=4]c1 - r[4=6]c7 - r6c5 = (68)r7c56 - r8c[4=9] - (8)r6c[9=3] => -8 r5c1

Code: Select all: .----------------.-------------------.----------------. | 8 6 49 | 5 349 b79 | 2 37 1 | | 1 2-5 49 | 246 349 b679 | 78 a(5)6 378 | | 3 7 25 | 126 8 16 | 4 56 9 | :----------------+-------------------+----------------: | 46 d12(5) 7 | 1468 d459 c1689 | 16 38 23 | | 46 125 25 | 1468 45 3 | 9 78 27 | | 9 3 8 | 7 16 2 | 16 4 5 | :----------------+-------------------+----------------: | 5 9 1 | 3 67 68 | 78 2 4 | | 2 4 6 | 18 17 5 | 3 9 78 | | 7 8 3 | 9 2 4 | 5 1 6 | '----------------'-------------------'----------------'

Step 7: (5=6)r2c8 - (6=79)r12c6 - r4c6 = (95)r4c52 => -5 r2c2; stte

by **International_DBA** » Wed Apr 10, 2019 6:04 am

I published this just now:
https://andrews-sudoku.blogspot.com/201 ... lical.html

by **Leren** » Wed Apr 10, 2019 9:38 am

.4..3.....6..8......9..52..7...63..889.....7..2.4...6........8.........995...1...

Definitely a One Trick Pony.

Code: Select all: *-------------------------------------------------------* | 125 4 57 | 1267 3 679 | 8 159 567 | | 1235 6 357 | 127 8 479 | 1347 13459 3457 | | 13 8 9 | 67 14 5 | 2 134 67 | |--------------+------------------+---------------------| | 7 1 4 | 9 6 3 | 5 2 8 | | 8 9 6 | 15 15 2 | 34 7 34 | | 35 2 35 | 4 7 8 | 9 6 1 | |--------------+------------------+---------------------| |a46 a37 12 |a3567 9 a467 |a13467 8 2347-5 | |b46 b37 128 | 3678-5 24-5 b467 |b13467 b1345 9 | | 9 5 28 | 3678 24 1 | 3467 34 2347 | *-------------------------------------------------------*

ALS XZ Rule: X = 1, Z = 5: (5=1) r7c12467 - (1=5) r8c12678 => - 5 r7c9, r9c45; stte. Or, if you want to use less cells :

Code: Select all: *-----------------------------------------------------* | 125 4 57 | 1267 3 679 | 8 159 567 | | 1235 6 357 | 127 8 479 | 1347 13459 3457 | | 13 8 9 | 67 14 5 | 2 134 67 | |--------------+-----------------+--------------------| | 7 1 4 | 9 6 3 | 5 2 8 | | 8 9 6 | 15 15 2 | 34 7 34 | | 35 2 35 | 4 7 8 | 9 6 1 | |--------------+-----------------+--------------------| | 46 37 c12 |a3567 9 467 | 13467 8 b23457 | | 46 37 d128 | 35678 e24-5 467 | 13467 1345 9 | | 9 5 28 | 3678 24 1 | 3467 34 2347 | *-----------------------------------------------------*

L2 Wing : (5) r7c4 = (5-2) r7c9 = r7c3 - r8c3 = (2) r8c5 => - 5 r8c5; lclste

Leren

by **SpAce** » Wed Apr 10, 2019 11:31 pm

Code: Select all: .--------------------.--------------------.----------------------. | 125 4 57 | 1267 3 679 | 8 159 567 | | 1235 6 357 | 127 8 479 | 1347 13459 3457 | | 13 8 9 | 67 14 5 | 2 134 67 | :--------------------+--------------------+----------------------: | 7 1 4 | 9 6 3 | 5 2 8 | | 8 9 6 | 15 15 2 | 34 7 34 | | 35 2 35 | 4 7 8 | 9 6 1 | :--------------------+--------------------+----------------------: | 46 37 12 | 3567 9 b467 | 13467 8 23457 | | 46 37 ac(28)-1 | 35678 a245 b467 | 13467 1345 9 | | 9 5 c28 | b3678 b24 1 | 3467 b34 2347 | '--------------------'--------------------'----------------------'

Almost-DDS:

(2)r8c[3=5] - (2=46738)r78c6,r9c584 - (8)r[9=3]c3 => -1 r8c3; stte

by **International_DBA** » Mon Apr 22, 2019 5:51 am

I published this last night:
https://andrews-sudoku.blogspot.com/201 ... treme.html

by **Leren** » Mon Apr 22, 2019 7:20 am

.4...28.1.1.......6.....45.4..........1..93.2829.6........2..1..5..7..4...6..8..3

Solvable with a few Skyscrapers/Finned X Wings and some moderately fancy AIC's. I did it quickly in 8 non-basic moves. Hodoku did a bit better with 6. No doubt someone can provide an elegant solution.

There is a single candidate elimination stte list at 2 r2c7, 3 r4c3, 2 r8c1, 1 r9c1, 9 r9c2, 7 r9c7 & 2 r9c8 although as I usually say, proving any of these is likely to be problematic.

Leren

by **SpAce** » Mon Apr 22, 2019 4:37 pm

Leren wrote:Solvable with a few Skyscrapers/Finned X Wings and some moderately fancy AIC's. I did it quickly in 8 non-basic moves. Hodoku did a bit better with 6. No doubt someone can provide an elegant solution.

That wouldn't be me. Five moves and nothing elegant. Hodoku's default solution for this one wasn't that bad, actually. Of course it could do this in two, if it wanted to, but that would look pretty awful.

My original steps (5): Show

Code: Select all: .4...28.1.1.......6.....45.4..........1..93.2829.6........2..1..5..7..4...6..8..3

Code: Select all: .----------------------.------------------.-------------------. | 3579 4 357 | 5679 359 2 | 8 369 1 | | 3579 1 3578 | 56789 3589 4 | 2679 2369 679 | | 6 a7(8)9-3 2 | 1789 1389 17 | 4 5 79 | :----------------------+------------------+-------------------: | 4 c(3)67 c357 | 2 158 157 | 1569 689 569 | | 57 67 1 | 4578 458 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :----------------------+------------------+-------------------: | 379 b3789 4 | 359 2 356 | 5679 1 56789 | | 12 5 b38 | 139 7 136 | 269 4 689 | | 12 79 6 | 1459 1459 8 | 2579 29 3 | '----------------------'------------------'-------------------'

Step 1: (8)r3c2 = (83)b7p26 - (3)r4c[3=2] => -3 r3c2

Code: Select all: .--------------------.-------------------.---------------------. | 3579 4 357 | 5679 59 2 | 8 369 1 | | 3579 1 3578 | 56789 589 4 | 2679 2369 679 | | 6 789 2 | 1789 3 17 | 4 5 79 | :--------------------+-------------------+---------------------: | 4 367 37-5 | 2 158 157 | 1569 689 c(5)69 | | a7(#5) 67 1 | 45+78 45+8 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :--------------------+-------------------+---------------------: | 379 3789 4 | 359 2 356 | 5679 1 c56789 | | 12 5 38 | 139 7 136 | 269 4 689 | | 12 79 6 | 45+19 45+19 8 | b279#5 29 3 | '--------------------'-------------------'---------------------'

Step 2: UR(45)r59c45 using externals

(5)r5c1 == (5)r9c7 - (5)r[7=4]c9 => -5 r4c3

Code: Select all: .------------------.---------------------.-------------------. | 379 4 357 | 5679 59 2 | 8 369 1 | | 379 1 3578 | 56789 589 4 | 2679 2369 679 | | 6 89-7 2 | 1789 3 b1(7) | 4 5 79 | :------------------+---------------------+-------------------: | 4 367 37 | 2 158 b157 | 1569 689 569 | | 5 a6(7) 1 | a478 48 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :------------------+---------------------+-------------------: | 379 3789 4 | 359 2 356 | 5679 1 56789 | | 12 5 38 | 139 7 136 | 269 4 689 | | 12 79 6 | 1459 1459 8 | 2579 29 3 | '------------------'---------------------'-------------------'

Step 3: Kite: (7)r5c[2=4] - (7)r[4=3]c6 => -7 r3c2

Code: Select all: .--------------------.-------------------.--------------------. | 379 4 357 | 5679 59 2 | 8 369 1 | | 379 1 a3578 | 56789 589 4 | 2679 2369 679 | | 6 b89 2 | 1789 3 c17 | 4 5 b79 | :--------------------+-------------------+--------------------: | 4 367 d(3)7 | 2 158 d157 | 1569 689 569 | | 5 67 1 | 478 48 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :--------------------+-------------------+--------------------: | 379 3789 4 | 359 2 356 | 5679 1 56789 | | 12 5 a(8)-3 | 139 7 136 | 269 4 689 | | 12 79 6 | 1459 1459 8 | 2579 29 3 | '--------------------'-------------------'--------------------'

Step 4: (8)r[8=2]c3 - (8=97)r3c29 - r3c6 = (73)r4c63 => -3 r8c3

Code: Select all: .------------------.--------------------.--------------------. | 379 4 357 | 5679 59 2 | 8 369 1 | | 379 1 357 | 56789 589 4 | 269 2369 679 | | 6 8 2 | 179 3 17 | 4 5 79 | :------------------+--------------------+--------------------: | 4 367 37 | 2 c18 17 | ef6(9) c689 5 | | 5 ef67 1 | 478 48 9 | 3 d68 2 | | 8 2 9 | 3 6 5 | 1 7 4 | :------------------+--------------------+--------------------: | 37 379 4 | 59 2 6 | 57 1 8 | | 12 5 8 | a1(9) 7 3 | 26-9 4 69 | | 12 f7(9) 6 | 145-9 b145-9 8 | 57 29 3 | '------------------'--------------------'--------------------'

Step 5:

(9=1)r8c4 - r9c5 = (18)r4c58 - (8=6)r5c8 - r4c7,r5c2 = (9)r4c7&(79)r59c2 => -9 r8c7,r9c45; lcte

Added: Post-game analysis reveals that I could have done it in four moves with the same strategy (but didn't). My original third move (Kite) turns out to be unnecessary if I change the following move a bit (which actually becomes simpler too).

My slightly optimized steps (4): Show

Code: Select all: .4...28.1.1.......6.....45.4..........1..93.2829.6........2..1..5..7..4...6..8..3

Code: Select all: .----------------------.------------------.-------------------. | 3579 4 357 | 5679 359 2 | 8 369 1 | | 3579 1 3578 | 56789 3589 4 | 2679 2369 679 | | 6 a7(8)9-3 2 | 1789 1389 17 | 4 5 79 | :----------------------+------------------+-------------------: | 4 c(3)67 c357 | 2 158 157 | 1569 689 569 | | 57 67 1 | 4578 458 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :----------------------+------------------+-------------------: | 379 b3789 4 | 359 2 356 | 5679 1 56789 | | 12 5 b38 | 139 7 136 | 269 4 689 | | 12 79 6 | 1459 1459 8 | 2579 29 3 | '----------------------'------------------'-------------------'

Step 1: (8)r3c2 = (83)b7p26 - (3)r4c[3=2] => -3 r3c2

Code: Select all: .--------------------.-------------------.---------------------. | 3579 4 357 | 5679 59 2 | 8 369 1 | | 3579 1 3578 | 56789 589 4 | 2679 2369 679 | | 6 789 2 | 1789 3 17 | 4 5 79 | :--------------------+-------------------+---------------------: | 4 367 37-5 | 2 158 157 | 1569 689 c(5)69 | | a7(#5) 67 1 | 45+78 45+8 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :--------------------+-------------------+---------------------: | 379 3789 4 | 359 2 356 | 5679 1 c56789 | | 12 5 38 | 139 7 136 | 269 4 689 | | 12 79 6 | 45+19 45+19 8 | b279#5 29 3 | '--------------------'-------------------'---------------------'

Step 2: UR(45)r59c45 using externals

(5)r5c1 == (5)r9c7 - (5)r[7=4]c9 => -5 r4c3

Code: Select all: .---------------------.--------------------.-------------------. | 379 4 357 | 5679 59 2 | 8 369 1 | | 379 1 357-8 | 56789 589 4 | 2679 2369 679 | | 6 c7(8)9 2 | c1789 3 c17 | 4 5 79 | :---------------------+--------------------+-------------------: | 4 367 a37 | 2 158 b157 | 1569 689 569 | | 5 67 1 | 478 48 9 | 3 68 2 | | 8 2 9 | 135 6 135 | 15 7 4 | :---------------------+--------------------+-------------------: | 379 379-8 4 | 359 2 356 | 5679 1 56789 | | 12 5 a3(8) | 139 7 136 | 269 4 689 | | 12 79 6 | 1459 1459 8 | 2579 29 3 | '---------------------'--------------------'-------------------'

Step 3: (8=37)r84c3 - r4c6 = (718)r3c642 => -8 r2c3,r7c2

Code: Select all: .------------------.--------------------.--------------------. | 379 4 357 | 5679 59 2 | 8 369 1 | | 379 1 357 | 56789 589 4 | 269 2369 679 | | 6 8 2 | 179 3 17 | 4 5 79 | :------------------+--------------------+--------------------: | 4 367 37 | 2 c18 17 | ef6(9) c689 5 | | 5 ef67 1 | 478 48 9 | 3 d68 2 | | 8 2 9 | 3 6 5 | 1 7 4 | :------------------+--------------------+--------------------: | 37 379 4 | 59 2 6 | 57 1 8 | | 12 5 8 | a1(9) 7 3 | 26-9 4 69 | | 12 f7(9) 6 | 145-9 b145-9 8 | 57 29 3 | '------------------'--------------------'--------------------'

Step 4:

(9=1)r8c4 - r9c5 = (18)r4c58 - (8=6)r5c8 - r4c7,r5c2 = (9)r4c7&(79)r59c2 => -9 r8c7,r9c45; lcte

by **International_DBA** » Sun May 19, 2019 6:51 am

This one might take a little longer:
https://andrews-sudoku.blogspot.com/201 ... treme.html

by **SpAce** » Wed May 22, 2019 8:39 pm

International_DBA wrote:This one might take a little longer:
https://andrews-sudoku.blogspot.com/201 ... treme.html

Code: Select all
.7.....2..9......3..5237.9.4.....9....6.....8.3..4..6...34....6...5..4..15...6.7.

Not really. Took me about 10 minutes to find the solution with a single coloring round using the most obvious starting cluster. I use coloring to find elimination steps, not to guess solutions, so it was a pure accident. It means that the puzzle's backdoors are too easy to hit. That's very disappointing with a puzzle that's otherwise difficult (or tedious), because it pretty much kills any motivation to solve it via normal proving steps.

The same thing happened with one of your earlier puzzles, but I can't remember which one. I didn't let it bother then because it was pretty quick to solve via eliminations too, but in this case the normal way would probably be so tedious that I don't feel like even starting after stumbling on the solution in minutes.

Thus, the concealment level of backdoors is something you might want to consider when estimating the actual difficulty of a puzzle for a manual solver. In this case the doors were wide open from the start, which totally destroyed the puzzle's nominal difficulty.

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