200e200w's Nightmare #16

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200e200w's Nightmare #16

Postby 200e200w » Sun Feb 11, 2018 11:11 am

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

Enjoy solving!

200e200w
200e200w
 
Posts: 153
Joined: 20 January 2018

Re: 200e200w's Nightmare #16

Postby Cenoman » Sun Feb 11, 2018 10:48 pm

A krakenless solution with 4 AIC's
Code: Select all
 +----------------------+----------------------+----------------------+
 |fB247    3      456   |  2678    267   289   |  1568   49    1568   |
 |fA47    f46     8     |  1567   a1-67  159   |  2      49    3      |
 |  1    eC269   D569   | d268     4     3     |  568    7     568    |
 +----------------------+----------------------+----------------------+
 |  5      7      3     | c12     b12    6     |  4      8     9      |
 |  48     468    46    |  9       5     7     |  13     23    12     |
 |  9      1      2     |  3       8     4     |  56     56    7      |
 +----------------------+----------------------+----------------------+
 |  238    5      7     |  1268    9     128   |  368    236   4      |
 |  6     F248    1     | G24578  H237   258   |  9      235   258    |
 |  2348   2489  E49    |  24568   236   258   |  7      1     2568   |
 +----------------------+----------------------+----------------------+

(1)r2c5 = r4c5 - (1=2)r4c4 - r3c4 = r3c2 - (247=6)b1p145 => -6 r2c5
(7)r2c1 = (7-2)r1c1 = (2-9)r3c2 = r3c3 - (9=4)r9c3 - r8c2 = (4-7)r8c4 = (7)r8c5 => -7 r2c5; 4 placements

Code: Select all
 +----------------------+---------------------+----------------------+
 |  247    3      456   |  2678    67   289   |  1568   49    1568   |
 |  47     46     8     |  567     1    59    |  2      49    3      |
 |  1      269    569   |  268     4    3     |  568    7     568    |
 +----------------------+---------------------+----------------------+
 |  5      7      3     |  1       2    6     |  4      8     9      |
 |  48     468    46    |  9       5    7     |  13    d23    12     |
 |  9      1      2     |  3       8    4     |  56     56    7      |
 +----------------------+---------------------+----------------------+
 |  238    5      7     |  28-6    9    1     |  368   d236   4      |
 |  6      248    1     |  24578  b37   258   |  9     c235   258    |
 |  2348   2489   49    |  24568  a36   258   |  7      1     2568   |
 +----------------------+---------------------+----------------------+

(6=3)r9c5 - r8c5 = r8c8 - (32=6)r57c8 => -6 r7c4; 7 placements

Code: Select all
 +---------------------+--------------------+---------------------+
 |f*24     3     e45   |  2678   67   28    |  158   9     1568   |
 |  7      6      8    |  5      1    9     |  2     4     3      |
 |  1     g29     59   | h268    4    3     |  58    7     568    |
 +---------------------+--------------------+---------------------+
 |  5      7      3    |  1      2    6     |  4     8     9      |
 |  48     48     6    |  9      5    7     |  13    23    12     |
 |  9      1      2    |  3      8    4     |  56    56    7      |
 +---------------------+--------------------+---------------------+
 | a3-28   5      7    | i28     9    1     | b368  b236   4      |
 |  6     c248    1    |  47     37  c258   |  9    c235  c258    |
 |  2348   2489  d49   |  46     36   258   |  7     1     258    |
 +---------------------+--------------------+---------------------+

(3)r7c1 = r7c78 - (3258=4)r8c2689 - r9c3 = r1c3 - (4=2)r1c1* - r3c2 = r3c4 - (2=8)r7c4 => -28 r7c1; stte


An now, for fans of "One-step, stte finish, otherwise nothing..."
Code: Select all
 +----------------------+----------------------+----------------------+
 |  247    3      456   |  2678    267   289   |  1568   49    1568   |
 |  47     46     8     |  1567    167   159   |  2      49    3      |
 |  1      269    569   |  268     4     3     |  568    7     568    |
 +----------------------+----------------------+----------------------+
 |  5      7      3     |  12      12    6     |  4      8     9      |
 |  48     468    46    |  9       5     7     |  13     23    12     |
 |  9      1      2     |  3       8     4     |  56     56    7      |
 +----------------------+----------------------+----------------------+
 |  238    5      7     |  1268    9     128   |  368    236   4      |
 |  6      248    1     |  24578   237   258   |  9      235   258    |
 |  2348   2489   49    |  24568   236   258   |  7      1     2568   |
 +----------------------+----------------------+----------------------+

Multi-Kraken: cell (236)r9c5 + row (6)r7c478 + row (2)r7c1468
Code: Select all
(2)r9c5 - r789c6 = (2)r1c6
(3)r9c5 - r8c5 = (3-5)r8c8 = (5-6)r6c8 = (6)r7c8           (2)r7c1 - r1c1 = (2)r3c2
                                                \        //
(6)r9c5 - r7c4 =  (6-3)r7c7 = r5c7 - (3=2)r5c8  - (2)r7c8 = (2)r7c4
               \\                               /        \\
                  ........ (6)r7c8 ............            (2-1)r7c6 = r7c4 - (1=2)r4c4

 =>-2r3c4; stte
Cenoman
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Re: 200e200w's Nightmare #16

Postby Sudtyro2 » Mon Feb 12, 2018 5:54 pm

Hi Cenoman,
Impressive solutions!

I had initially looked in the 2s grid for a stte elimination at 2r3c4 or 2r1c1 starting from the 5-link Oddagon(*) and its seven Guardians(#) shown below. Fully six of those Guardians can either see the stte cells directly or via simple X-Y chains. The one remaining "tough" Guardian is 2r7c8.

Any thoughts or observations about whether that Guardian can see either stte cell? A network solution would be fine with me!

Code: Select all
+-----------------+-----------------+-----------------+
| 47-2* 3    456  | 2678#  267 289  | 1568 49   1568  |
| 47    46   8    | 1567   167 159  | 2    49   3     |
| 1     269* 569  | 68-2*  4   3    | 568  7    568   |
+-----------------+-----------------+-----------------+
| 5     7    3    | 12#    12  6    | 4    8    9     |
| 48    468  46   | 9      5   7    | 13   23   12    |
| 9     1    2    | 3      8   4    | 56   56   7     |
+-----------------+-----------------+-----------------+
| 238*  5    7    | 1268*  9   128# | 368  236# 4     |
| 6     248  1    | 24578# 237 258  | 9    235  258   |
| 2348# 2489 49   | 24568# 236 258  | 7    1    2568  |
+-----------------+-----------------+-----------------+

SteveC
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Posts: 483
Joined: 15 April 2013

Re: 200e200w's Nightmare #16

Postby Cenoman » Mon Feb 12, 2018 11:09 pm

Sudtyro2 wrote:I had initially looked in the 2s grid for a stte elimination at 2r3c4 or 2r1c1 starting from the 5-link Oddagon(*) and its seven Guardians(#) shown below. Fully six of those Guardians can either see the stte cells directly or via simple X-Y chains. The one remaining "tough" Guardian is 2r7c8.

Any thoughts or observations about whether that Guardian can see either stte cell? A network solution would be fine with me!

SteveC


Hi Steve,
Asking for thoughts or observations when actually you are entrusting an impossible mission is some kind of understatement...
But nothing is impossible !
As far as Artificial Intelligence can produce "thoughts or observations" you find hereafter those of my solver (note that the right side of the net is the same as in my solution):
Code: Select all
        (6)r7c8 = r6c8 - (6=5)r6c7 - r1c7             (6)r3c3 - (6=4)r2c2                                             (2)r7c1  -  r1c1  = (2)r3c2
       /                                \\            //               \                                              //                       \
(2)r7c8                                (5)r1c3 - (5)r3c3               (4=258)r8c269 - (5)r8c8 = (5-6)r6c8 = (6-2)r7c8 = (2)r7c4.............. -(2)r3c4
       \                                //            \\               /                                              \\                       /
        (2)r5c8 =  (2-1)r5c9  = (1-5)r1c9             (9)r3c3 - (9=4)r9c3                                             (2-1)r7c6 = r7c4 - (1=2)r4c4

=> (2)r7c8 - (2)r3c4 q.e.d.

Hopefully, this is up to your expectation... I would be disappointed if you were disappointed.

Urgency is over. Impossible is going on. Just for miracles, a delay is requested.
Cenoman
Cenoman
 
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Location: Paris, France

Re: 200e200w's Nightmare #16

Postby Sudtyro2 » Tue Feb 13, 2018 12:08 pm

Cenoman wrote: => (2)r7c8 - (2)r3c4 q.e.d.

Merci, Cenoman, pour l'effort vraiment impressionnant!

SteveC
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Posts: 483
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Re: 200e200w's Nightmare #16

Postby eleven » Tue Feb 13, 2018 11:21 pm

Cenoman wrote:... Artificial Intelligence ...

After reading about alphago and alpha zero, where they found the best openings from scratch in some days - developed by mankind in centuries - , it is probably not hard to to make a neural net, which solves the hard puzzles in a most efficient way.
In minutes sk loops and jexocets could be discovered. Spoiling a lot of the fun.
I like AI, but it has it's disadvantages.
eleven
 
Posts: 1708
Joined: 10 February 2008

Re: 200e200w's Nightmare #16

Postby Cenoman » Wed Feb 14, 2018 10:08 am

eleven wrote:After reading about alphago and alpha zero, where they found the best openings from scratch in some days - developed by mankind in centuries - , it is probably not hard to to make a neural net, which solves the hard puzzles in a most efficient way.
In minutes sk loops and jexocets could be discovered. Spoiling a lot of the fun.
I like AI, but it has it's disadvantages.


First, I may have been emphatic when referencing my solver as AI. I did so because it uses techniques that a human brain uses in manual solving. Nothing more, but it is unable to sustain any comparison to alphago and alpha zero, or other high level AI development.

I am a very modest manual solver. My interest in sudoku started first in taking sudoku problems as a nice subject for computer programming. Everyone takes its fun where he likes. At least, I have written every line of code in my solver, and I am happy when it solves rather hard puzzles.

I wonder if a net as the one displayed above can be found manually. Personally, I am unable to find it. Without computer aid, I would have not answered Steve's request. However, the net exists, well hidden in the puzzle structure.

You fear to see the highest level techniques, SK loops and exocets, discovered easily. Any sudoku player aspires to solve harder puzzles than the last one he has solved. One day, he has to learn these techniques. I admire manual solvers, able to handle them with paper and pencil. They can be proud of that, and maybe they should add the mention "Manually solved" to their posts. But there is no shame to be a CAS (Computer Aided Solver).
Cenoman
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Re: 200e200w's Nightmare #16

Postby eleven » Wed Feb 14, 2018 10:58 pm

Agreed. The net can be found manually, but you would find a lot of useless nets before, and this takes a lot of time.
AI is just a general topic, it will change the world, and it is open, how it will develop, to our good or bad.
eleven
 
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