Pencilmark only Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby udosuk » Wed Oct 25, 2006 5:17 am

Ruud wrote:A new record: 592 candidates, 1 solution...

Great achievement!:) Getting closer and closer to the magical 600 mark...
Code: Select all
757 365 777 773 640 654 713 777 777
766 777 362 320 340 760 762 740 776
767 777 377 777 773 536 737 757 517
577 777 777 537 677 777 327 206 533
767 775 757 737 777 777 627 677 737
777 735 777 377 775 736 737 776 735
775 771 773 573 573 777 573 773 551
734 775 354 777 365 777 777 777 575
775 331 777 277 675 777 763 257 777

757365777773640654713777777766777362320340760762740776767777377777773536737757517
577777777537677777327206533767775757737777777627677737777735777377775736737776735
775771773573573777573773551734775354777365777777777575775331777277675777763257777

Quite interesting is the "complementary pencilmarks":
Code: Select all
5      168    .      7      356789 3589   457    .      .
69     .      1679   146789 156789 6789   679    56789  9
6      .      1      .      7      249    4      5      245
2      .      .      24     3      .      146    134569 247
6      8      5      4      .      .      346    3      4
.      48     .      1      8      49     4      9      48
8      78     7      27     27     .      27     7      2578
489    8      1589   .      168    .      .      .      28
8      1478   .      13     38     .      67     135    .
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Postby Ruud » Wed Oct 25, 2006 1:05 pm

udosuk wrote:Getting closer and closer to the magical 600 mark...

Very close indeed:D

598 candidates
Code: Select all
12345689  23456789  12345689  1245678   1234567   1456789   1456789   12356789  123456789
1234589   12346789  12346789  123456789 12578     12356789  146789    1235789   1356789
12345789  12346789  12346789  123456789 1234567   1235789   13456789  18        136789
13456789  23456789  4679      12346789  123456789 123456789 2467      123456789 145679
1356789   236789    2346789   124568    123456789 123456789 12345679  123456789 134679
1234589   123456789 123456789 12458     123458    123589    12345679  123456789 12345679
125789    12356789  12356789  123456789 123456789 12356789  2345678   124578    123456789
123456789 2356789   23456789  12345679  2345679   123456789 34567     1234578   23456789
12356789  36789     12356789  1356789   12356789  12356789  123456789 123578    35678

1 solution
Code: Select all
952731864413685927786942513149263785328574196567819342835496271274158639691327458

compact notation
Code: Select all
776 677 776 373 771 177 177 767 777
736 757 757 777 323 767 157 727 576
737 757 757 777 771 727 577 102 547
577 677 055 757 777 777 251 777 175
567 647 657 372 777 777 775 777 555
736 777 777 332 732 726 775 777 775
327 767 767 777 777 767 673 333 777
777 667 677 775 675 777 471 733 677
767 447 767 567 767 767 777 723 463

complementary candidate grid
Code: Select all
7         1         7         39        89        23        23        4         .
67        5         5         .         3469      4         235       46        24
6         5         5         .         89        46        2         2345679   245
2         1         12358     5         .         .         13589     .         238
24        145       15        379       .         .         8         .         258
67        .         .         3679      679       467       8         .         8
346       4         4         .         .         4         19        369       .
.         14        1         8         18        .         1289      69        1
4         1245      4         24        4         4         .         469       1249

With the complementary grid, it is easier to spot the single 4 in row 9, followed by a single 4 in box 3.
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Postby gsf » Wed Oct 25, 2006 1:07 pm

Ruud wrote:A new record: 592 candidates, 1 solution.

nice job Ruud

[ edit: multiple solution puzzle deleted -- still can't crack 500 -- sorry for any confusion ]
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Postby Pyrrhon » Thu Oct 26, 2006 4:25 pm

Here is my purpose:

622 candidates, 1 solution, solvable with logic steps by humans

Code: Select all
123456789   123456789   123456789  123456789  123456789   123456789   123456789  158         58
12345679    12345679    12345679   139        12345679    12345679    12345679   123456789   12345679
3457        123456789   123456789  123456789  123456789   123456789   123456789  123456789   123456789
3457        123456789   34         123456789  123456789   123456789   234        123456789   123456789
123456789   123456789   123456789  148        123456789   123456789   24         123456789   123456789
12345679    12345679    12345679   123456789  12345679    12345679    12345679   123456789   12345679
25          123456789   123456789  123456789  2457        123456789   26         123456789   123456789
123456789   123456789   123456789  123456789  167         123456789   123456789  168         123456789
123456789   15          123456789  123456789  123456789   123456789   123456789  123456789   123456789


Solution in tiny text:


829463715
475912683
361785942
784256391
956137428
132894576
598641237
243578169
617329854
Last edited by Pyrrhon on Thu Oct 26, 2006 1:22 pm, edited 1 time in total.
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Postby Ruud » Thu Oct 26, 2006 4:56 pm

[obsolete post deleted]
Last edited by Ruud on Thu Oct 26, 2006 5:54 pm, edited 1 time in total.
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Postby JPF » Thu Oct 26, 2006 5:06 pm

An easy way to build a table with 593 candidates :

Take a 17 clues valid puzzle.
For each empty cell : 9 candidates
For each cell with a clue : 1 candidate equal to the clue.

We get (81-17) x 9 + 17 = 593 candidates.

Am I missing something ?

JPF
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Postby gsf » Thu Oct 26, 2006 5:09 pm

Pyrrhon wrote:Here is my purpose:

629 candidates, 1 solution, solvable with logic steps by humans


this puzzle has 7,408,714 solutions
Last edited by gsf on Thu Oct 26, 2006 1:16 pm, edited 1 time in total.
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Postby gsf » Thu Oct 26, 2006 5:12 pm

JPF wrote:We get (81-17) x 9 + 17 = 593 candidates.
Am I missing something ?

N candidates, no cell with less than 2 candidates
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Postby JPF » Thu Oct 26, 2006 5:18 pm

thanks gsf.
I missed that point.

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Postby Pyrrhon » Thu Oct 26, 2006 5:26 pm

Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

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Postby daj95376 » Thu Oct 26, 2006 6:32 pm

Pyrrhon wrote:Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

Pyrrhon

Impressive PM Sudoku ... and such a simple solution. It's interesting where starting with one Hidden Single can lead.
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Postby gsf » Thu Oct 26, 2006 7:03 pm

Pyrrhon wrote:Thanx Ruud and gsf, there was a failure in transcribing of cell R9C2 and a consecutive fault in counting, both are corrected now in my original post.

singles reduce the puzzle to this
Code: Select all
  8   279  29  |  4    6    3  | 79    1    5
 46  4567  567 |  9    1    2  | 67    8    3
  3   69    1  |  7    8    5  | 69    4    2
---------------+---------------+---------------
  7    8    4  |  2    5    6  |  3    9    1
  9   56   56  |  1    3    7  |  4    2    8
  1   23   23  |  8    9    4  |  5    7    6
---------------+---------------+---------------
  5   79    8  |  6    4    1  |  2    3   79
  2   349  39  |  5    7    8  |  1    6   49
 46    1   67  |  3    2    9  |  8    5   47

what's the next move?
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Postby Pyrrhon » Thu Oct 26, 2006 7:22 pm

Hint in tiny text:
The next move could be a xy-wing or a xyz-wing. If made both, the rest are singles.
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Postby Ruud » Thu Oct 26, 2006 9:53 pm

Great achievement, Pyrrhon!

Human intelligence boldly goes where no computer has gone before...

Just for the record books, a maximized version of your grid:

623 candidates, same solution, same level of difficulty.

Code: Select all
123456789 123456789 123456789 123456789 123456789 123456789 123456789 158       58
12345679  12345679  12345679  1359      12345679  12345679  12345679  123456789 12345679
3457      123456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789
3457      123456789 34        123456789 123456789 123456789 234       123456789 123456789
123456789 123456789 123456789 148       123456789 123456789 24        123456789 123456789
12345679  12345679  12345679  123456789 12345679  12345679  12345679  123456789 12345679
25        123456789 123456789 123456789 2457      123456789 26        123456789 123456789
123456789 123456789 123456789 123456789 167       123456789 123456789 168       123456789
123456789 15        123456789 123456789 123456789 123456789 123456789 123456789 123456789


Ruud
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Postby Pyrrhon » Fri Oct 27, 2006 5:00 am

I have made only two attempts for pencilmark only sudoku. The second one had lead to 618 candidates. So for sure a computer can top it, if somebody implements my way. My way was like the following:

1) Take a 17 given sudoku that you can solve.
2) Set all empty cells to 123456789 and the cells with a given digit get this given digit as candidate
3) Attempt step by step to each cell with only one candidate to add any other digit (only one) in a way so that you can still solve the puzzle, if not possible let the single candidate in this cell
4) Attempt to the cells with only one candidate to make hidden singles in a row, line or block in way where you must not delete a candidate in any bivalued cell. If possible you can set this cell to 123456789 and you must delete this candidate in the other cells. (If such hidden single is not possible you can delete the second value in the bivalued cell with a hidden single itself.)
5) If you have now at least 2 candidates in all cells you can look whether it is possible to add some candidates in cells so that the puzzle can still be solved.

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