Pencilmark only Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby udosuk » Fri Oct 27, 2006 6:49 am

Excellent job Uwe!:)

Here is the 777-code and complementary grids of the 623-candidate modification from Ruud:
Code: Select all
777 777 777 777 777 777 777 422 022
775 775 775 521 775 775 775 777 775
164 777 777 777 777 777 777 777 777
164 777 140 777 777 777 340 777 777
777 777 777 442 777 777 240 777 777
775 775 775 777 775 775 775 777 775
220 777 777 777 264 777 210 777 777
777 777 777 777 414 777 777 412 777
777 420 777 777 777 777 777 777 777

777777777777777777777422022775775775521775775775777775164777777777777777777777777
164777140777777777340777777777777777442777777240777777775775775777775775775777775
220777777777264777210777777777777777777414777777412777777420777777777777777777777

.       .       .       .       .       .       .       234679  1234679
8       8       8       24678   8       8       8       .       8
12689   .       .       .       .       .       .       .       .
12689   .       1256789 .       .       .       156789  .       .
.       .       .       235679  .       .       1356789 .       .
8       8       8       .       8       8       8       .       8
1346789 .       .       .       13689   .       1345789 .       .
.       .       .       .       234589  .       .       234579  .
.       2346789 .       .       .       .       .       .       .

BTW Uwe only the xyz-wing is required to reduce it to singles... The shortest route (:?:) goes like this:

60 singles
1 naked/hidden triple: elimination in r1c3
1 xyz-wing: fixing r3c2
20 singles

I wonder if a simple short xy-chain could replace the 2 intermediate steps there...:?:
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Postby Ruud » Fri Oct 27, 2006 12:26 pm

I slightly altered the approach by Pyrrhon, and found this grid:

628 candidates, 1 solution. It can be solved with basic techniques.

Code: Select all
2346789   2346789   2346789   345789    345789    345679    456789    123456789 123456789
12346789  123678    1236789   13456789  13589     356789    1356789   123456789 12345789
12346789  123456789 12346789  123456789 135789    3456789   12456789  123456789 12345789
123456789 1235689   12356789  123456789 123456789 23456789  3456789   123456789 123456789
12356789  12356789  12356789  123456789 1235789   23456789  123456789 12356789  123456789
12356789  12356789  12356789  123456789 123456789 123456789 3456789   123456789 12345789
12345689  12345689  12345689  123456789 1234689   23469     123456789 1234589   123458
123456789 23456789  23456789  2346789   23789     234679    3456789   12345678  12345678
123456789 123456789 123456789 12346789  123789    1234679   13456789  123456789 1234578

342875916879136542651294837487962351916358274523741689264513798195687423738429165


only 101 candidates are disabled in this puzzle...

[edit]

The following puzzle also breaks a record. It has a mere 625 candidates, but each cell has 6 or more candidates.

Code: Select all
12346789  13456789  123456789 1236789   1346789   1234678   123456789 12345679  2346789
123456789 13456789  123456789 123456789 1346789   1234678   123456789 123456789 123456789
123456789 3456789   123456789 123456789 3456789   2345678   23456789  345679    23456789
123456789 123456789 12345678  1235678   12345678  12345678  123456789 1234567   12345678
23456789  3456789   123456789 13456789  3456789   2345678   123456789 345679    23456789
123456789 3456789   12345679  123456789 1346789   123467    12345679  134679    124679
123456789 345789    12345789  1234789   134789    123456789 134579    134579    124789
234689    3456789   2345689   123689    123456789 12345678  123456789 234679    12346789
23456789  3456789   123456789 12356789  13456789  12345678  123456789 345679    123456789

No need to post the solution. It can be solved with simple techniques.

And then this remarkable puzzle with 628 candidates. Interesting to see that all candidates for digit 6 are present, and only a single candidate for digit 9 is missing.

Code: Select all
13456789  1356789   13456789  1356789   156789    156789    145689    123456789 13456789
123456789 12456789  123456789 356789    123456789 256789    1245689   2456789   2456789
123456789 12346789  12346789  136789    12356789  126789    1234689   123456789 123456789
123456789 123456789 123456789 1356789   123456789 1256789   145679    1235679   123456789
2345679   12345679  123456789 123456789 123456789 123456789 123456789 12346789  12345679
2345679   1235679   12345679  123456789 12345679  123456789 124569    12345679  12345679
123456789 12356789  123456789 123456789 12456789  1246789   123456789 25678     2456789
23456789  123456789 123456789 1346789   12346789  12346789  2456789   23456789  23456789
2456789   256789    123456789 1456789   1246789   12456789  245689    2456789   2456789

Also a perfect puzzle for human solvers.

:!:Another record puzzle: 633 candidates. Only 96 candidates eliminated.

Code: Select all
123456789 2356789   123456789 1235679   12356789  123456789 12456789  1245789   123456789
123456789 123456789 12456789  135679    123456789 123456789 12456789  15789     12456789
134567    23456789  12456789  1345679   123456789 123456789 12456789  145789    12456789
12456789  123456789 2456789   135679    12356789  12356789  1245679   13579     1235679
3456789   3456789   456789    12345679  12356789  123456789 123456789 123456789 12345679
2456789   256789    2456789   123456789 1256789   123456789 12456789  12345789  123456789
12346789  236789    246789    12345679  1256789   2346789   12456789  12456789  123456789
12346789  123456789 12456789  1345679   123456789 123456789 1456789   123456789 12345689
123456789 2356789   123456789 1345679   123456789 123456789 123456789 134589    12345689

I wonder how far we can go...
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Postby udosuk » Mon Oct 30, 2006 6:06 am

I envy those using a big laptop/monitor with 1280x1024 or wider displays... I couldn't see the full PM grids properly on my tiny laptop...:(

Here are presentations which could be shown properly on my screen...:idea:
Code: Select all
628 candidates (1st grid):
357 357 357 167 167 175 077 777 777
757 716 717 577 523 137 537 777 767
757 777 757 777 527 177 677 777 767
777 733 737 777 777 377 177 777 777
737 737 737 777 727 377 777 737 777
737 737 737 777 777 777 177 777 767
773 773 773 777 753 351 777 763 762
777 377 377 357 307 355 177 776 776
777 777 777 757 707 755 577 777 766

357357357167167175077777777757716717577523137537777767757777757777527177677777767
777733737777777377177777777737737737777727377777737777737737737777777777177777767
773773773777753351777763762777377377357307355177776776777777777757707755577777766

15   15   15   126  126  128  123  .    .
5    459  45   2    2467 124  24   .    6
5    .    5    .    246  12   3    .    6
.    47   4    .    .    1    12   .    .
4    4    4    .    46   1    .    4    .
4    4    4    .    .    .    12   .    6
7    7    7    .    57   1578 .    67   679
.    1    1    15   1456 158  12   9    9
.    .    .    5    456  58   2    .    69

625 candidates, 6 or more candidates in each cell:
757 577 777 717 557 756 777 775 357
777 577 777 777 557 756 777 777 777
777 177 777 777 177 376 377 175 377
777 777 776 736 776 776 777 774 776
377 177 777 577 177 376 777 175 377
777 177 775 777 557 754 775 555 655
777 167 767 747 547 777 565 565 647
353 177 373 713 777 776 777 355 757
377 177 777 737 577 776 777 175 777

757577777717557756777775357777577777777557756777777777777177777777177376377175377
777777776736776776777774776377177777577177376777175377777177775777557754775555655
777167767747547777565565647353177373713777776777355757377177777737577776777175777

5   2   .   45  25  59  .   8   15
.   2   .   .   25  59  .   .   .
.   12  .   .   12  19  1   128 1
.   .   9   49  9   9   .   89  9
1   12  .   2   12  19  .   128 1
.   12  8   .   25  589 8   258 358
.   126 6   56  256 .   268 268 356
157 12  17  457 .   9   .   158 5
1   12  .   4   2   9   .   128 .

628 candidates, candidate 6 in all cells, only 1 cell missing candidate 9:
577 537 577 537 437 437 473 777 577
777 677 777 137 777 237 673 277 277
777 757 757 517 737 617 753 777 777
777 777 777 537 777 637 475 735 777
375 775 777 777 777 777 777 757 775
375 735 775 777 775 777 671 775 775
777 737 777 777 677 657 777 236 277
377 777 777 557 757 757 277 377 377
277 237 777 477 657 677 273 277 277

577537577537437437473777577777677777137777237673277277777757757517737617753777777
777777777537777637475735777375775777777777777777757775375735775777775777671775775
777737777777677657777236277377777777557757757277377377277237777477657677273277277

2    24   2    24   234  234  237  .    2
.    3    .    124  .    134  37   13   13
.    5    5    245  4    345  57   .    .
.    .    .    24   .    34   238  48   .
18   8    .    .    .    .    .    5    8
18   48   8    .    8    .    378  8    8
.    4    .    .    3    35   .    1349 13
1    .    .    25   5    5    13   1    1
13   134  .    23   35   3    137  13   13

633 candidates (only 96 initially eliminated candidates!):
777 337 777 735 737 777 677 667 777
777 777 677 535 777 777 677 427 677
574 377 677 575 777 777 677 467 677
677 777 277 535 737 737 675 525 735
177 177 077 775 737 777 777 777 775
277 237 277 777 637 777 677 767 777
757 317 257 775 637 357 677 677 777
757 777 677 575 777 777 477 777 773
777 337 777 575 777 777 777 563 773

777337777735737777677667777777777677535777777677427677574377677575777777677467677
677777277535737737675525735177177077775737777777777775277237277777637777677767777
757317257775637357677677777757777677575777777477777773777337777575777777777563773

.    14   .    48   4    .    3    36   .
.    .    3    248  .    .    3    2346 3
289  1    3    28   .    .    3    236  3
3    .    13   248  4    4    38   2468 48
12   12   123  8    4    .    .    .    8
13   134  13   .    34   .    3    6    .
5    145  135  8    34   15   3    3    .
5    .    3    28   .    .    23   .    7
.    14   .    28   .    .    .    267  7
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Postby tarek » Mon Oct 30, 2006 10:44 am

udosuk wrote:I envy those using a big laptop/monitor with 1280x1024 or wider displays... I couldn't see the full PM grids properly on my tiny laptop...:(

What if I told you that I have a 1920*1200 wide screen which can 90 degrees rotate ??!!!:D

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Postby udosuk » Mon Oct 30, 2006 11:25 am

tarek wrote:What if I told you that I have a 1920*1200 wide screen which can 90 degrees rotate ??!!!:D

Go ahead... Show off your b@tt...:twisted:
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Postby tarek » Tue Oct 31, 2006 9:28 am

udosuk wrote:Go ahead... Show off your b@tt...:twisted:
High definition is not for everyone:D ..........

Spirit of Oct 31
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no-given SuDoku -- pencilmark-only SuDoku

Postby Pat » Tue Nov 28, 2006 4:34 pm

history:

Bob Hanson (2005.Nov.16) wrote:no-given Sudoku -- twisted idea


A colleague of mine just pointed out that the real information unit in solving SuDoku is
"X is not possible in cell A."
Thus, it would be conceivable to construct a SuDoku puzzle with no givens at all -
one just has to provide enough "elimination clues" in the form
    r3c2 is not 6
    r4c5 is not 8
Thus my questions:
  1. Has anyone ever presented Sudoku puzzles that have these sorts of "elimination clues" instead of givens?
  2. Has anyone ever presented Sudoku puzzles that have a mixture of, say 15 givens and 5 "elimination clues"?
  3. What is the fewest number of "elimination clues" that are necessary to solve an NxN SuDoku?
    (Note that each "given" constitutes up to 28 "elimination clues".)
I would think it easy to construct an "unsolvable" 16-given 9x9 SuDoku,
then provide -- how many -- perhaps one? -- "elimination clue"
that would provide just the information necessary to, say, produce a hidden n-tuple and complete the puzzle.
That would be considerably less information than a 17-given SuDoku.
And maybe one or two choice clues with a 15-given SuDoku? ... Where does this end?


If you want to experiment with this, by the way,
there is a hidden feature of Sudoku Assistant
that if you click on the background of a cell and enter a NEGATIVE number, it removes a mark.
I'm not sure any other program has this feature or how useful it is. Maybe. I suppose they all do.

Sudoku Assistant
http://www.stolaf.edu/people/hansonr/sudoku


~ Pat
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Postby 999_Springs » Fri Mar 23, 2007 7:36 pm

Why can't you mix the order of the candidates to make it seem harder to the person solving the puzzle?

Or you could put in duplicate candidates to make it even harder...

so, say, 1235689 becomes 155692839.

25th post!

edit: wow when i was 13 some of the posts i made were really dumb
Last edited by 999_Springs on Thu Mar 20, 2014 12:21 am, edited 1 time in total.
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Once upon a time I was a teenager who was active on here 2007-2011
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Re: Pencilmark only Sudoku

Postby tarek » Sun Mar 16, 2014 12:33 am

2 nasty puzzles

Code: Select all
+------------------------------+------------------------------+------------------------------+
|  12459      259     2345679  | 2356789   12345679  1245789  | 1245679     257       2357   |
|   459     12346789   123589  |  234569    12345     124567  |  123578   12345679    567    |
| 2345789    145679     168    | 1245789     258     2356789  |   348      345679   1256789  |
+------------------------------+------------------------------+------------------------------+
| 3456789    245789   1234569  | 23456789    579     12456789 |  123567    256789   1456789  |
| 12345789   124578     456    |   359       1379      157    |   456      235689   12356789 |
| 1234569    123458   3456789  | 12345689    135     12345678 | 1456789    123568   1234567  |
+------------------------------+------------------------------+------------------------------+
|  134589    134567     267    | 1234578     258     1235689  |   249      134569   1235678  |
|    34    123456789   235789  |  345689    456789    145678  |  125789  123456789    156    |
|  34578      358      14569   |  235689   13456789   234578  | 1345678     158      15689   |
+------------------------------+------------------------------+------------------------------+

+------------------------------+------------------------------+------------------------------+
|  136789     1259     123569  | 1235689   1235789   1234578  |  123457     2357     134789  |
|   1459   123456789   123589  |  25679      1235     24579   |  123578  123456789    3567   |
|  145789    145679   1234579  |   2489    12346789    2678   |  235679    345679    356789  |
+------------------------------+------------------------------+------------------------------+
| 1456789    34589      2469   | 23456789   13579    12456789 |   2467     15678    3456789  |
| 1345679     1457    12346789 |  13579    12346789   13579   |  123478     569     1345679  |
| 1234567    23459      3468   | 12345689   13579    12345678 |   1468     12567    1234569  |
+------------------------------+------------------------------+------------------------------+
|  123457    134567   1345789  |   2348    12346789    1268   | 1356789    134569    123569  |
|   3457    13456789   235789  |  13568      5789     13458   |  125789  123456789    1569   |
|  123679     3578     356789  | 2356789   1235789   1245789  |  145789     1589     123479  |
+------------------------------+------------------------------+------------------------------+


I think that I have managed to re-confirm using gsf's Sudoku that these are 2 of many Pencil-mark sudokus with singles backdoor size 4. Size 5 doesn't look far to reach :idea:
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Re: Pencilmark only Sudoku

Postby dobrichev » Mon Mar 17, 2014 6:48 am

Hi tarek,

Have these 2 something in common with the backdoor size 4 ordinary sudoku family?
I can supply you with BD size 3 ordinary puzzles if you think they can be used as seed in your search.

Waiting for news...
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Re: Pencilmark only Sudoku

Postby tarek » Mon Mar 17, 2014 10:48 pm

dobrichev wrote:Have these 2 something in common with the backdoor size 4 ordinary sudoku family?
I can supply you with BD size 3 ordinary puzzles if you think they can be used as seed

Thanks dobrichev but I'm not adopting a clear strategy where that would be useful.
The regular (vanilla) sudoku is a special case of a pencilmark sudoku. You can add candidates to the vanilla sudoku until there is multiple solutions. You can evaluate that minimal puzzle then as it may have become more difficult (I haven't adopted this strategy but it sounds promising)

I have a few singles backdoor size 5 but I haven't prepared them yet. I have a few symmetric puzzles as well
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Re:

Postby Smythe Dakota » Tue Mar 18, 2014 11:51 pm

Ruud wrote: .... Is      this       the      way     to     do      it,     udosuk?

I assume this is the old alt-255 trick, or something similar.

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Re:

Postby tarek » Wed Mar 19, 2014 9:42 am

gsf wrote:here are, in row order, the singles <backdoor-size,number-backdoors>
for the 57 pm-only grids from a few posts back
it took 1h55m @ 3.2GHz and some reworked backdoor logic
there are some 5's but no 6's

Code: Select all
4 11    4  1    4  2    4  3    5 33    4  4    4  2    5 47
4 15    4  3    4  2    4  1    5 31    5 48    4  6    4  4
4  1    4  1    4  3    5 48    4  4    4  1    5 35    4  2
4  1    4  2    5 31    5 27    4  1    4  2    4  1    4  4
4  4    5 41    4  1    4  4    4  2    4  3    4  7    4  1
4  5    5 34    5 44    4  4    4  4    4  1    4  8    5 36
4  2    4  1    4  2    5 47    4  4    4  3    5 20    5 35
5 43

The link to these puzzles is broken. But this post suggest that the Singles backdoor size 5 barrier has already been reached ....
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Re: Pencilmark only Sudoku

Postby tarek » Wed Mar 19, 2014 2:02 pm

Only one sweep produced this minimal singles backdoor size 5. There is only 1 set possible. The Size 6 therefore looks very very possible

Code: Select all
.-----------------------------------------------------------------------------------------------.
| 136789    1234789   12345789  | 12356789  25789     1245789   | 12356789  136789    134789    |
| 123679    124       1234578   | 12345679  12358     123457    | 235689    236       123479    |
| 12345679  123456    12345678  | 123456    123458    1234567   | 12345689  123456    12345679  |
:-----------------------------------------------------------------------------------------------:
| 13456789  134589    12345789  | 123456789 123456789 12456789  | 2356789   356789    156789    |
| 34569     1345679   123456789 | 12345689  24568     12345678  | 2345689   34569     145679    |
| 1234569   123457    1234578   | 12345689  12345689  12345678  | 125689    1269      123567    |
:-----------------------------------------------------------------------------------------------:
| 13456789  456789    12456789  | 13456789  12356789  456789    | 23456789  456789    13456789  |
| 136789    478       124578    | 1356789   1235789   1345789   | 2356789   689       134789    |
| 123679    123479    12345789  | 12356789  12358     1234578   | 12356789  123679    123479    |
.-----------------------------------------------------------------------------------------------.
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Re: Pencilmark only Sudoku

Postby dobrichev » Wed Mar 19, 2014 8:36 pm

To me counting the sets is waste of time (unless it is the first puzzle of a kind).

BTW, do you stuck to some intermediate format of pencilmarks representation? Text file, one puzzle per line. Champagne's skfr can be modified to accept PM only puzzles...
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