The New Sudoku Players' Forum

[P.O.]

Code: Select all

1  .  .  .  .  .  3  .  .
.  6  .  .  .  2  .  .  .
.  .  3  1  5  .  .  .  4
.  .  9  .  .  8  .  7  .
.  .  1  .  .  .  5  .  .
.  4  .  5  .  .  2  .  .
3  .  .  .  1  7  8  .  .
.  .  .  2  .  .  .  5  .
.  .  4  .  .  .  .  .  1

1.....3...6...2.....315...4..9..8.7...1...5...4.5..2..3...178.....2...5...4.....1


basics:

Hidden Text: Show

Code: Select all

( n1r6c6   n1r4c7   n1r8c2   n4r8c7   n4r5c8   n4r2c1   n5r9c6   n1r2c8   n4r7c4
  n4r1c6   n5r4c1   n4r4c5   n2r5c5   n2r4c2   n3r5c2   n3r8c6   n3r9c8   n2r9c1
  n2r3c8   n2r1c3   n2r7c9 )

intersection:
((((8 0) (3 1 1) (7 8 9)) ((8 0) (3 2 1) (7 8 9))))


Code: Select all

1      579    2      6789   6789   4      3      689    56789           
4      6      57     3789   3789   2      79     1      5789           
789    789    3      1      5      69     679    2      4               
5      2      9      36     4      8      1      7      36             
678    3      1      679    2      69     5      4      689             
678    4      678    5      3679   1      2      689    3689           
3      59     56     4      1      7      8      69     2               
6789   1      678    2      689    3      4      5      679             
2      789    4      689    689    5      679    3      1     


[jco]

After basics,

Code: Select all

,---------------------------------------------------------------------,
| 1     (9)57   2      | 6789   6789   4      |  3      68-9   56789  |
| 4      6      57     | 3789   3789   2      |  79     1      5789   |
|(9)78  (9)78   3      | 1      5    *(69)    |*(6)79   2      4      |
|----------------------+----------------------+-----------------------|
| 5      2      9      |*36     4      8      |  1      7     *36     |
| 678    3      1      | 679    2     *69     |  5      4      689    |
| 678    4      678    | 5      3679   1      |  2      689    3689   |
|----------------------+----------------------+-----------------------|
| 3      5-9    56     | 4      1      7      |  8     (69)    2      |
| 6789   1      678    | 2      689    3      |  4      5      79-6   |
| 2      789    4      | 689    689    5      |*(6)79   3      1      |
'---------------------------------------------------------------------'

1. W-wing with transport (9=6)r7c8 - (6)r9c7 = (6)r3c7 - (6=9)r3c6 - (9)r3c12 = (9)r1c2 => -9 r7c2, r1c8
2. Fish(*) (6): r9c7 = r3c7 - r3c6 = r5c6 - r4c4 = r4c9 => -6 r8c9; ste

[Cenoman]

Code: Select all

 +---------------------+---------------------+----------------------+
 |  1      579   2     |  789-6  789-6  4    |  3    a689   56789   |
 |  4      6     57    |  3789   3789   2    |  79    1     5789    |
 | y789    789   3     |  1      5    zE69   |  79-6  2     4       |
 +---------------------+---------------------+----------------------+
 |  5      2     9     | C36     4      8    |  1     7    B36      |
 |  678    3     1     |  679    2     D69   |  5     4     689     |
 |  678    4     678   |  5      3679   1    |  2    A689   3689    |
 +---------------------+---------------------+----------------------+
 |  3     w59    56    |  4      1      7    |  8    v69    2       |
 | x6789   1     678   |  2      689    3    |  4     5     679     |
 |  2      789   4     |  689    689    5    |  679   3     1       |
 +---------------------+---------------------+----------------------+

Kraken column (6)r167c8
(6)r1c8
(6)r6c8 - r4c9 = r4c4 - r5c6 = (6)r3c6
(6-9)r7c8 = r7c2 - r8c1 = r3c1 - (9=6)r3c6
=> -6 r3c7, r1c45; ste

[Leren]

Code: Select all

*------------------------------------------------------*
| 1     579  2   |b6789 b6789  4     | 3   c689  56789 |
| 4     6    57  | 3789  3789  2     | 79   1    5789  |
| 789B  789  3   | 1     5    a6-9aA | 679  2    4     |
|----------------+-------------------+-----------------|
| 5     2    9   | 36    4     8     | 1    7    36    |
| 678c  3    1   | 679   2     69b   | 5    4    689   |
| 678d  4   d678 | 5     3679  1     | 2    689e 3689  |
|----------------+-------------------+-----------------|
| 3     59D  56  | 4     1     7     | 8    69E  2     |
| 6789C 1    678 | 2     689   3     | 4    5    679   |
| 2     789  4   | 689   689   5     | 679  3    1     |
*------------------------------------------------------*

Kraken Column 8 Digit 6:

9r3c6 - 6r3c6 = 6r1c45                 - 6 r1c8;

9r3c6 - 6r3c6 = 6r5c6 - 6r5c1 = 6r6c13 - 6 r6c8;

9r3c6 - 9r3c1 = 9r8c1 - 9r7c2 = 9 r7c8 - 6 r7c8; => - 9 r3c6; stte

Leren

[rjamil]

Solve with Pattern Overlay Method / Templating moves upto double-digit:

Code: Select all

 +-----------------+----------------+-----------------+
 | 1     5789  2   | 6789  6789  4  | 3    689  56789 |
 | 4     6     578 | 3789  3789  2  | 79   1    5789  |
 | 789   789   3   | 1     5     69 | 679  2    4     |
 +-----------------+----------------+-----------------+
 | 5     2     9   | 36    4     8  | 1    7    36    |
 | 678   3     1   | 679   2     69 | 5    4    689   |
 | 678   4     678 | 5     3679  1  | 2    689  3689  |
 +-----------------+----------------+-----------------+
 | 3     59    56  | 4     1     7  | 8    69   2     |
 | 6789  1     678 | 2     689   3  | 4    5    679   |
 | 2     789   4   | 689   689   5  | 679  3    1     |
 +-----------------+----------------+-----------------+

#VT: (1 1 2 1 2 8 9 11 12)
S-d POM: 6 @ r1c4589 r2c2 r3c67 r4c49 r5c1469 r6c13589 r7c38 r8c1359 r9c457
Digit 6 not in 8 Templates => -6 @ r6c5 r8c9;

S-d POM: 7 @ r1c2459 r2c34579 r3c127 r4c8 r5c14 r6c135 r7c6 r8c139 r9c27
Digit 7 not in 9 Templates => -7 @ r1c2;

S-d POM: 8 @ r1c24589 r2c3459 r3c12 r4c6 r5c19 r6c1389 r7c7 r8c135 r9c245
Digit 8 not in 11 Templates => -8 @ r1c2 r2c3;

Code: Select all

 +----------------+----------------+-----------------+
 | 1     59   2   | 6789  6789  4  | 3    689  56789 |
 | 4     6    57  | 3789  3789  2  | 79   1    5789  |
 | 789   789  3   | 1     5     69 | 679  2    4     |
 +----------------+----------------+-----------------+
 | 5     2    9   | 36    4     8  | 1    7    36    |
 | 678   3    1   | 679   2     69 | 5    4    689   |
 | 678   4    678 | 5     379   1  | 2    689  3689  |
 +----------------+----------------+-----------------+
 | 3     59   56  | 4     1     7  | 8    69   2     |
 | 6789  1    678 | 2     689   3  | 4    5    79    |
 | 2     789  4   | 689   689   5  | 679  3    1     |
 +----------------+----------------+-----------------+

D-d POM: 6 @ r1c4589 r2c2 r3c67 r4c49 r5c1469 r6c1389 r7c38 r8c135 r9c457
and POM: 5 @ r1c29 r2c39 r3c5 r4c1 r5c7 r6c4 r7c23 r8c8 r9c6
Digit 6 not in 7 Templates => -6 @ r1c9 r6c8;

D-d POM: 6 @ r1c458 r2c2 r3c67 r4c49 r5c1469 r6c139 r7c38 r8c135 r9c457
and POM: 8 @ r1c4589 r2c459 r3c12 r4c6 r5c19 r6c1389 r7c7 r8c135 r9c245
Digit 6 not in 6 Templates => -6 @ r5c1 r6c9;

D-d POM: 6 @ r1c458 r2c2 r3c67 r4c49 r5c469 r6c13 r7c38 r8c135 r9c457
and POM: 9 @ r1c24589 r2c4579 r3c1267 r4c3 r5c469 r6c589 r7c28 r8c159 r9c2457
Digit 6 not in 2 Templates => -6 @ r1c4 r1c5 r3c7 r5c6 r6c3 r7c8 r8c1 r8c3 r9c4 r9c5
Digit 6 in all 2 Templates => 6 @ r1c8 r3c6 r6c1 r7c3 r8c5 r9c7;

D-d POM: 7 @ r1c459 r2c34579 r3c127 r4c8 r5c14 r6c35 r7c6 r8c139 r9c2
and POM: 1 @ r1c1 r2c8 r3c4 r4c7 r5c3 r6c6 r7c5 r8c2 r9c9
Digit 7 not in 2 Templates => -7 @ r1c9 r2c4 r2c5 r2c9 r3c2 r8c1 r8c3
Digit 7 in all 2 Templates => 7 @ r8c9 r9c2;

D-d POM: 7 @ r1c45 r2c37 r3c17 r4c8 r5c14 r6c35 r7c6 r8c9 r9c2
and POM: 5 @ r1c29 r2c39 r3c5 r4c1 r5c7 r6c4 r7c2 r8c8 r9c6
Digit 7 not in 1 Template => -7 @ r1c4 r2c3 r3c7 r5c1 r6c5
Digit 7 in all 1 Template => 7 @ r1c5 r2c7 r3c1 r5c4 r6c3;

D-d POM: 8 @ r1c49 r2c459 r3c2 r4c6 r5c19 r6c89 r7c7 r8c13 r9c45
and POM: 1 @ r1c1 r2c8 r3c4 r4c7 r5c3 r6c6 r7c5 r8c2 r9c9
Digit 8 not in 3 Templates => -8 @ r5c9 r6c9 r8c1
Digit 8 in all 3 Templates => 8 @ r3c2 r6c8;

D-d POM: 8 @ r1c49 r2c459 r3c2 r4c6 r5c1 r6c8 r7c7 r8c3 r9c45
and POM: 5 @ r1c29 r2c39 r3c5 r4c1 r5c7 r6c4 r7c2 r8c8 r9c6
Digit 8 not in 1 Template => -8 @ r1c9 r2c4 r2c5 r9c4
Digit 8 in all 1 Template => 8 @ r1c4 r2c9 r9c5;

D-d POM: 9 @ r1c29 r2c45 r3c7 r4c3 r5c69 r6c59 r7c28 r8c1 r9c4
and POM: 1 @ r1c1 r2c8 r3c4 r4c7 r5c3 r6c6 r7c5 r8c2 r9c9
Digit 9 not in 1 Template => -9 @ r1c9 r2c4 r5c9 r6c5 r7c2
Digit 9 in all 1 Template => 9 @ r1c2 r2c5 r6c9; stte

R. Jamil

[P.O.]

hi R.Jamil
after initialization, the puzzle is solved with the combination (6 9), which you have in your resolution path
but it can also be solved without resorting to combinations
since you have the templates #VT: (1 1 2 1 2 8 9 11 12), if you check their validity, you will notice that there is only one left for each value

[rjamil]

Hi P.O.,

if you check their validity, you will notice that there is only one left for each value

Yes, after each double-digit POM combination and elimination/placement occurred, I see there are only one instance of each digit POM left. If I understand your above statement correctly, just removing invalid instances of each digit POM is sufficient to solve the puzzle. But, for this, one need to keep all instances of each digit stored in memory first.

R. Jamil

[P.O.]

even before making the size 2 combinations the validity of the templates can be checked and as you can count them you can collect them in memory especially when there are so few
this may or may not be enough, but for this puzzle it is enough because there is only one template left for each value

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 |  1      579    2      | 6789   6789   4      | 3     f689    56789  |
 |  4      6      57     | 3789   3789   2      | 79     1      5789   |
 |ag789   g789    3      | 1      5      6-9    |g679    2      4      |
 *-----------------------+----------------------+----------------------|
 |  5      2      9      |c36     4      8      | 1      7     d36     |
 |  678    3      1      | 679    2    ab69     | 5      4      689    |
 |  678    4      678    | 5      3679   1      | 2     e689    3689   |
 *-----------------------+----------------------+----------------------|
 |  3    cd59    d56     | 4      1      7      | 8     e69     2      |
 | b6789   1      678    | 2      689    3      | 4      5      679    |
 |  2      789    4      | 689    689    5      | 679    3      1      |
 *---------------------------------------------------------------------*


9r3c1,r5c6 = 9r8c1&6r5c6 - 9r7c2|6r4c4 = (56)r7c23&6r4c9 - 6r67c8 = r1c8 - (6=789)r3c127 => -9 r3c6 ; ste

Hmm. Looks the same as Cenoman.

[rjamil]

Hi P.O..

even before making the size 2 combinations the validity of the templates can be checked and as you can count them you can collect them in memory especially when there are so few
this may or may not be enough, but for this puzzle it is enough because there is only one template left for each value

Agreed. But, as you see, I did not make validity of any size combination at all, and as you already said that this may or may not be enough to solve the puzzle upto quad-digit (and, I think, it will not use to solve the puzzle and/or as considered as step to advance the move also). Actually, it is complately (overlapped) superceeded by POM elimination/placement move. Each double-digit and above POM move automatically remove invalid instance(s) by eiminating/placing the digit.

Please do not consider my point of view as criticizing or any kind of degrading, but I completely avoiding such routine that won't help to solve the puzzle, except StrmCkr's Zero State check routine, which helps to determine the puzzle unsolvable state way before any other option.

R. Jamil

[P.O.]

hi R.Jamil,
i agree with you
as i've already said, combining templates is enough to solve all puzzles
any additional techniques i use are only meant to shorten the solution path
this is merely a challenge, but it's not necessary to find the solution, and it can sometimes be debatable whether these procedures are still only template-based

[rjamil]

hi R.Jamil,
i agree with you
as i've already said, combining templates is enough to solve all puzzles
any additional techniques i use are only meant to shorten the solution path
this is merely a challenge, but it's not necessary to find the solution, and it can sometimes be debatable whether these procedures are still only template-based

Combining templates is enough, but combining upto 4 digits may not be enough to solve all the puzzles. It may go upto all 9 digits combined to solve some puzzles.

Similarly, I learned C language in 1990, after completing my graduation, when computers have maximum 4 MB RAM installed and run under MS-DOS command prompt (Last ver. was 6.22 published in Jun-1994). My writing style is to keep program as short as possible and to utilize minimum memory in RAM as well as Harddisk. However, code may not be so complicated so that others may have difficulty to understand.

R. Jamil

[P.O.]

this isn't proof, but so far, no single-solution puzzle has required more than size 6 templates to solve.
for multi-solution puzzles, you need to go up to size 9 templates to obtain all the solutions.

regarding programming, my priority is to have correct code
space and time are optimizations

[rjamil]

Hi P.O.,

no single-solution puzzle has required more than size 6 templates to solve.

I didn't know about it until now. However, my intention is to code upto quad-digit POM move only. Similarly, I have no plan to release separate solver using singleton and POM / Templating moves only. One solver for vanila Sudoku and Sukaku bulk puzzles each is sufficient, Anybody test easily with comment out one or many techniques to see the effect manually.

R. Jamil

[P.O.]

Code: Select all

6r3c7 => r3c127 <> 7
 r3c7=6 - c6n6{r3 r5} - r4n6{c4 c9} - c8n6{r6 r7} - r7c3{n6 n5} - r2c3{n5 n7}
 
=> r3c7 <> 6
ste.