The New Sudoku Players' Forum

[200e200w]

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

[Cenoman]

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

[Sudtyro2]

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

[Cenoman]

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.

[Sudtyro2]

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

Merci, Cenoman, pour l'effort vraiment impressionnant!

SteveC

[eleven]

... 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.

[Cenoman]

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).

[eleven]

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.

[denis_berthier]

.
I found this thread while I was searching for something else.

SER = 7.3

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 247   3     456   ! 25678 267   2589  ! 1568  4569  1568  !
   ! 47    46    8     ! 1567  167   159   ! 2     4569  3     !
   ! 1     269   569   ! 2568  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  !
   +-------------------+-------------------+-------------------+

The puzzle has a relatively easy solution in W5:

Code: Select all

hidden-pairs-in-a-column: c8{n4 n9}{r1 r2} ==> r2c8 ≠ 6, r2c8 ≠ 5, r1c8 ≠ 6, r1c8 ≠ 5
whip[1]: r2n5{c6 .} ==> r1c4 ≠ 5, r1c6 ≠ 5, r3c4 ≠ 5
biv-chain[4]: r3n2{c4 c2} - b1n9{r3c2 r3c3} - r9c3{n9 n4} - b8n4{r9c4 r8c4} ==> r8c4 ≠ 2
whip[4]: r8n3{c5 c8} - r5c8{n3 n2} - r7n2{c8 c1} - r7n3{c1 .} ==> r8c5 ≠ 2
z-chain[5]: r2c2{n6 n4} - r8n4{c2 c4} - r8n7{c4 c5} - c5n3{r8 r9} - c5n6{r9 .} ==> r2c4 ≠ 6
biv-chain[4]: r2n6{c2 c5} - c5n1{r2 r4} - r4c4{n1 n2} - r3n2{c4 c2} ==> r3c2 ≠ 6
biv-chain[5]: r2n6{c2 c5} - c5n1{r2 r4} - b5n2{r4c5 r4c4} - r3n2{c4 c2} - b1n9{r3c2 r3c3} ==> r3c3 ≠ 6
finned-swordfish-in-rows: n6{r7 r6 r3}{c4 c8 c7} ==> r1c7 ≠ 6
t-whip[5]: c6n2{r9 r1} - c6n9{r1 r2} - r2n5{c6 c4} - r2n1{c4 c5} - r4c5{n1 .} ==> r9c5 ≠ 2
biv-chain[4]: r9c5{n6 n3} - r8n3{c5 c8} - c8n5{r8 r6} - c8n6{r6 r7} ==> r7c4 ≠ 6, r9c9 ≠ 6
whip[1]: c9n6{r3 .} ==> r3c7 ≠ 6
biv-chain[3]: b9n6{r7c8 r7c7} - c7n3{r7 r5} - r5c8{n3 n2} ==> r7c8 ≠ 2
naked-quads-in-a-block: b8{r7c4 r7c6 r8c6 r9c6}{n2 n1 n8 n5} ==> r9c4 ≠ 8, r9c4 ≠ 5, r9c4 ≠ 2, r8c4 ≠ 8, r8c4 ≠ 5
hidden-single-in-a-column ==> r2c4 = 5
biv-chain[4]: r3c3{n5 n9} - r9c3{n9 n4} - r9c4{n4 n6} - r3n6{c4 c9} ==> r3c9 ≠ 5
biv-chain[4]: r9c4{n6 n4} - r9c3{n4 n9} - c2n9{r9 r3} - r3n2{c2 c4} ==> r3c4 ≠ 6
hidden-single-in-a-row ==> r3c9 = 6
naked-triplets-in-a-column: c4{r3 r4 r7}{n8 n2 n1} ==> r1c4 ≠ 8, r1c4 ≠ 2
z-chain[4]: r3c4{n8 n2} - b1n2{r3c2 r1c1} - r7n2{c1 c6} - r7n1{c6 .} ==> r7c4 ≠ 8
stte

If one insists on having a 1-step solution, the simplest that can be found uses a whip[10]:

Code: Select all

whip[10]: r3n2{c2 c4} - r4n2{c4 c5} - r4n1{c5 c4} - r7n1{c4 c6} - r7n2{c6 c8} - r5c8{n2 n3} - c7n3{r5 r7} - r8n3{c8 c5} - r9c5{n3 n6} - b9n6{r9c9 .} ==> r1c1 ≠ 2
stte

However, this is absurdly complex, considering that the puzzle is in W5.


Here is an intermediate solution, based on my recent fewer steps algorithm, using whips of length no more than 6 (only 1 more than the W rating):
Instead of the 15 non-W1 steps in the simplest-first solution, it has only 5 steps not in W1.

Code: Select all

Step 1:
whip[6]: c5n1{r2 r4} - r4c4{n1 n2} - r3n2{c4 c2} - r3n9{c2 c3} - b1n6{r3c3 r1c3} - c3n5{r1 .} ==> r2c5 ≠ 6
Step 2:
biv-chain[6]: r8n7{c5 c4} - b8n4{r8c4 r9c4} - r9c3{n4 n9} - b1n9{r3c3 r3c2} - b1n2{r3c2 r1c1} - b1n7{r1c1 r2c1} ==> r2c5 ≠ 7
singles ==> r2c5 = 1, r4c5 = 2, r4c4 = 1, r7c6 = 1
Step 3:
z-chain[6]: r8n4{c2 c4} - r8n7{c4 c5} - r1c5{n7 n6} - r2n6{c4 c8} - c8n9{r2 r1} - r1n4{c8 .} ==> r2c2 ≠ 4
singles ==> r2c2 = 6, r5c3 = 6
Step 4:
whip[5]: c9n6{r1 r9} - r9c5{n6 n3} - r8n3{c5 c8} - r7c8{n3 n2} - r5c8{n2 .} ==> r3c7 ≠ 6
Step 5:
whip[6]: b1n2{r3c2 r1c1} - r7n2{c1 c8} - r5c8{n2 n3} - c7n3{r5 r7} - b9n6{r7c7 r9c9} - r3n6{c9 .} ==> r3c4 ≠ 2
stte

As the algorithm makes random choices at each step, it should be run several times in order to find fewer steps. But I considered that 5 steps instead of 15 was good enough and I was lazy to try it more than once.

[denis_berthier]

... Artificial Intelligence ...

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.

if you give up on neural nets (that are totally useless for such pure logic problems as Sudoku), symbolic AI techniques can find sk-loops or J-Exocets in a fraction of a second.