The hardest sudokus (new thread)

Everything about Sudoku that doesn't fit in one of the other sections

99999xxxx non-minimals

Postby dobrichev » Mon Sep 12, 2011 11:51 pm

coloin wrote:Well it may have come from a fruitless discovery ......

but there sure are a lot of seeds in these non-minimals :lol:

Right.

To the auditory - essentially this is coloin's idea to see what happens with puzzle difficulty in 999991110 digit distribution area. Also the suggestion to truncate the search space to 5-rookeries with single representatives is coloin's.

All I did was to find these 941 5-rookeries from a 10GB file and to use the heavy artillery (gridchecker) to generate all 99999xxxx minimal completions.

Champagne's skfr helped in the rating process (2 432 930 puzzles for ~21 hours).

Here is the distribution by skfr rating.
Hidden Text: Show
Count, exemplar, skfr rating, pearl and diamond rating for the given exemplar. Ordered and counted by rating.
Code: Select all
      4 795600800810095076046087095670809050920560780058070609560700908007908560089056007   10.3   1.0   1.0
     23 970850630560700908008069075890506007056070890407908560600085709705290086089607050   10.2   10.2   9.4
     22 896570000500609708017008695780035069905067080060890507670980052009750806058006970   10.1   10.1   7.8
     52 950760800860009075007805960680090507005670089079508600716453098508907006090086750   10.0   1.0   1.0
     23 875900600600870059009065078780009506932456780056780090508007960060590807097608005   9.9   1.0   1.0
      3 850790600670804905009056087780509060905603078006078509507080096090067850068905702   9.8   9.8   9.5
     59 968502704500976800700080596680090057005607089079058600806705900050069078097803065   9.7   9.7   2.6
    108 968500700500976802700084596680091057005607089079058600806705900050069078097800065   9.6   9.6   2.6
    197 987500600500760098062089057809056703056007089070890560705048906608905070090670805   9.5   9.5   7.9
    163 970680530680500097005079608890056070056007809407890056560710980709068005008905760   9.4   9.4   7.9
    289 978610530500708609060059078890506700056070890007890056720960085605087900089005067   9.3   9.3   7.8
   3587 987500600500760298060089057809056700056037089070890560705048906608905070090670805   9.2   9.2   2.6
  10886 987510600500760098060089057809056700056037089070890560705048906608905070090670805   9.1   1.0   1.0
  87755 987510630500760098060089057809056700056007089074890560705008906608905070090670805   9.0   9.0   2.6
  85509 987510630500760098062089057809056700056007089070890560705008906608905070090670805   8.9   8.9   2.6
  31933 987510604500760098060089057809056700056007089070890560705008906608905070290670805   8.8   8.8   2.6
    375 980750600672904508005068097890506700056007089007891056560009870709085060008670905   8.7   8.7   6.6
    196 975800600600970805080056079890500467056708910007069580760090058508607290009085706   8.6   8.6   2.6
  11996 987510600500760098060089057809056700056037089070890560705008906608905070290670805   8.5   8.5   2.6
  52165 987510630500760098060089057809456700056007089070890560705008906608905070090670805   8.4   8.4   2.6
 163063 987512630500760098060089057809056700056007089070890560705008906608905070090670805   8.3   1.0   1.0
  28520 987510604500760098060089057809056700056007089070890562705008906608905070090670805   8.2   7.9   2.6
    163 978602500503708609060059078890506700056070890007890056700960085605087900089105067   8.1   8.1   2.6
  25600 987510604500760098060089057829056700056007089070890560705008906608905070090670805   8.0   8.0   2.6
  92900 987510630500760098060089057809056700056007089070890560705008906608905070090670845   7.9   7.9   2.6
 414092 987512630500670098060089705608900057050067809079058060805706900706095080090800576   7.8   1.0   1.0
 194015 987512600503670098060089705608900057050067809079058060805706900706095080090800576   7.7   1.2   1.2
 309430 987512600500670098060089705608930057050067809079058060805706900706095080090800576   7.6   7.6   2.6
   1822 987510600500760098060389057809056700056007089070890560705008906608905070090670845   7.5   7.5   2.6
     68 978500600500607098060098057890056700056700089007089560700805946605970801089260075   7.4   1.2   1.2
  12073 987510600500760098060089057809056703056007089070890560705008926608905070090670805   7.3   6.6   2.6
  77033 987512600500670098060089705608900057050067809079058060835706900706095080090800576   7.2   6.7   2.6
 207117 987512600503760098060089057809056700056007089070890560705008906608905070090670805   7.1   1.2   1.2
   4176 987500600500764098062089057809056700056007089070890560705008906608905070090673805   7.0   1.2   1.2
   1799 986700500530968070070005986867090050015607890090580607709056048608009705050870069   6.9   1.5   1.5
  10127 987512600500670098060089705608900057050067809079058063805706900706095080090800576   6.8   1.5   1.5
  89781 987510604500670098060089705608900057050067829079058060805706900706095080090800576   6.7   1.2   1.2
 256765 987512600500760098060089057809456700056007089070890560705008906608905070090670805   6.6   1.2   1.2
   1414 987500630510764098060089057809056700056007089070890560705008906608905070090670805   6.5   1.2   1.2
     49 970560800680730905045098276890056700056070089007809560760900058508607090009085607   6.2   1.5   1.5
    436 978500600500607298060098057890056710056703089007089560700805906605970800089060075   5.7   2.0   2.0
   4298 987500600510760098060389057809056700056007089070890560705008906608905070290670805   5.6   1.2   1.2
   1802 987500600500764098060389057809056710056007089070890560705008906608905070090670805   5.2   2.6   2.6
    246 986700530500968070070005986867090051005607890090580607709056048608009705050870069   5.0   1.2   1.2
    286 976810500800594706050076089768900005005067890090058067609700058507289600080605970   4.7   1.2   1.2
   3131 987500600500764098060089157809056700056207089070890560705008906608905070090670805   4.6   1.7   1.7
  16491 987500630500764098060089057809056710056007089070890560705008906608905070090670805   4.5   1.2   1.2
   2329 986710500500968072070005986867090050005607890490580607709056008608009705050870069   4.4   1.2   1.2
  19169 987510600500760098060089057809056700056207089070890560705008906648905070090670805   4.2   2.6   2.6
   4143 987500630510760098060089057809056700056007089070890562705008906608905070090670805   3.8   3.8   2.6
  10825 987502600500670098060089705608930057050067809079058160805706900706095080090800576   3.2   2.8   2.6
    697 986710500500968070072005986867090050005607890090580607709056008608009705050874069   3.0   1.2   1.2
  30767 987510600500764098060089057829056700056007089070890560705008906608905070090670805   2.8   2.8   2.6
  76115 987512600500760098060089057809056700056007089070890560705008906648905070090670805   2.6   2.6   2.6
   1084 980650700670008059045907680890526007056070890007890506560009078708065900109780065   2.0   1.2   1.2
  18885 987500604500670098060089705608900057050067829079058060805706900706195080090800576   1.7   1.2   1.2
  64993 987510604500760098060089057809056700056007089070890560705008906608905070090673805   1.5   1.2   1.2
   1881 987500600510670098060089705608900057050467809079058060805706900706095080092800576   1.2   1.2   1.2

Two of the 941 5-templates are 4-completable, the rest are 3-completable.
These are the complementaries of the 4-completable 5-templates
Code: Select all
....12.34.134..2...423..1...21..3.4.3..24..1.4....13.2.34.2...11...3.42.2..1.4..3
....12.34.134..2...423..1...21..34..3....4.214..12...3.342...1.1...4.3.22...31.4.

The 4-completable templates contributed with 468 999991111 and 916 999992110 puzzles.

I can explain more details if somebody wants to dig deeper.

MD
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Re: The hardest sudokus (new thread)

Postby champagne » Tue Sep 13, 2011 11:19 am

Hi,

dobritchev introduced it's own concept of twin generation, but i can't find where any more.
the basic idea is to generate twins out of the unknown digits in the solution.

I was suspicious about potential efficiency of that twin concept for low number of clues,
so i coded the generation in my program to make an evaluation.

My sample file has been the "01 index" file from my data base of potential hardest, as it is in the current data base

my findings are the following.

1) it's a very fast process :)
2) unhappily not very productive in quantity
3) but likely very good in quality. ;)

I started with 11212 puzzles
in less than 30 seconds, I got about 180 puzzles of the twin form.
all of them but five where already in the database
These are the five

Code: Select all
78.9.....9..7..6....5.4..7.8.....3...2......6..7..4.9...14...5.....5...3....1.2..;11.0;11.0;2.6;23
78.9.....9..7..6....5.4..7.8.....3...2......6..7..4.9...14...5.....5.2......1...3;11.0;11.0;2.6;23
98.6..7..5..7..6......8....6..5..9...4..32..........1.3....6..9.6..5.3.....3....7;10.9;1.2;1.2;23
78.9..6..9..7.......5.4..9.6....3..8.3.........2.9..4...1.........2.4.1.....1.5.9;11.0;1.2;1.2;23
78.9..6..9..7..5......4....8...5..9...78.......6..98..6..5..9...3...........82.1.;11.0;1.2;1.2;23


They all have 23 clues and I did not yet find them in my current search.


Nearly all the puzzles having a twin form have at the end 4 free locations, which means that the twin would come in my standard process, but much slower.

Three gave a start with 6 free locations, which could be a better source for new puzzles.
None of the five puzzles above is coming from these seeds.

At the end, the process seems to be a very good weapon, but for higher number of clues.

champagne
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Re: The hardest sudokus (new thread)

Postby sdk_fan » Wed Sep 14, 2011 5:50 am

Hi, everyone, I am new to this forum and I am recently addicted to programming to solve Sudoku puzzles. But I am curious about your conversation, and I am amazed by so many hard puzzles you are discussing here. Just a question, or some related questions, maybe asked many times (please refer me to the most proper thread please. but some short answers will be appreciated...) is it possible to GUARANTEE to solve any puzzle (with one unique solution) without relying on frank backtracking? Or is there a known set of rules that can guarantee to solve any unique solution puzzle? What would you say about a puzzle that does not succumb to any known technique? Do they exist (and examples if they do) and what property do they have, and what are we going to do about such puzzles? Also some questions about available rules/technics: which rules do you think have too much t&e quality and should be avoided in my program?
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Re: The hardest sudokus (new thread)

Postby champagne » Wed Sep 14, 2011 8:45 am

sdk_fan wrote:Hi, everyone, ...


Hi,

welcome in the forum.

The way to answer properly to your question would require a better understanding of your motivation.
Starting from scratch to day does not seem reasonable.
But this would be a long discussion

Some partial answers :

is it possible to GUARANTEE to solve any puzzle (with one unique solution) without relying on frank backtracking?
I guess yes, but so far using complex nets (or something equivalent)

What would you say about a puzzle that does not succumb to any known technique?


We do our best in that thread to find them. The hardest are solved through these bad complex nets
Up to now, we did not find puzzles resisting to Sudo Explainer or to my solver.

what are we going to do about such puzzles?

On my side try to find nicer way to solve them

which rules do you think have too much t&e quality and should be avoided in my program?

IMO as soon as your enter the chains field, the rule itself is generally ok
but if the logic involve to many candidates, then there is not that much difference with a pure T&E process.

champagne
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Re: The hardest sudokus (new thread)

Postby sdk_fan » Wed Sep 14, 2011 1:31 pm

champagne wrote:
The way to answer properly to your question would require a better understanding of your motivation.

champagne


Thank Champaign, for your hospitality. I am not wicked man I will not hide my motivation. I think I find a universal method to address all Sudoku puzzles without guessing, I just submitted my article to Notice of the AMS, which also published JF Crook's algorithm which I really do not find anything new in there. I have no math or computer background, but I do have a engineering one, and some commonsense, I guess. I just want to know the theory part of the puzzle, and is it something worthwhile or proper to do like submitting it to a magazine.


champagne wrote:Up to now, we did not find puzzles resisting to Sudo Explainer or to my solver.

I read somewhere in your forum that Sudoku Explainer cannot give hint on
500000009020100070008000300040702000000050000000006010003000800060004020900000005
I think eleven posted this puzzle answering a claim that SE can explain any puzzle.
I downloaded SE and did find it fail to explain step 6 or 7.
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Re: The hardest sudokus (new thread)

Postby champagne » Wed Sep 14, 2011 3:32 pm

sdk_fan wrote:
champagne wrote:Up to now, we did not find puzzles resisting to Sudo Explainer or to my solver.

I read somewhere in your forum that Sudoku Explainer cannot give hint on
500000009020100070008000300040702000000050000000006010003000800060004020900000005
I think eleven posted this puzzle answering a claim that SE can explain any puzzle.
I downloaded SE and did find it fail to explain step 6 or 7.


That one is a very old puzzle produced by Mike B metcalf.
Sudoku Explainer solves it and rates it 11.8 11.8 11.3

If I understand, the on line step by step version has a bug and does not produce the text explaining the move.
This does not change the fact that the puzzle is solved




sdk_fan wrote:I think I find a universal method to address all Sudoku puzzles without guessing, I just submitted my article to Notice of the AMS, which also published JF Crook's algorithm which I really do not find anything new in there. I have no math or computer background, but I do have a engineering one, and some commonsense, I guess. I just want to know the theory part of the puzzle, and is it something worthwhile or proper to do like submitting it to a magazine.


All "universal methods" I know are using chains in different ways;

My solver uses AIC's nets with AHS and AAHS. As such, he failed to solve "fata Morgane" and "Trompe l'oeil". 2 puzzles found by Tarek.
I added then the EXOCET analysis and from that moment, found no new failure.

Sudoku Explainer uses more and more complex "left justified chains" plus, for hardest puzzles, "nested chains"

You should also have a look at Denis Berthier whips and braids but I never studied that process.

I red than other solver uses T&E as escape lane.

If your algorithm solves all the puzzles included in my data base

here

then you have a good chance to have it resisting to all puzzles.

Last but not least if you don't create dirty paths (too long), then you will have brought something of high value.

champagne
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Re: The hardest sudokus (new thread)

Postby sdk_fan » Wed Sep 14, 2011 4:42 pm

Thank you again Champaign for your treasure box of puzzles. I will run them, and let you guys know the result. But I randomly pick a puzzle form each file and they are resolved within one min (I use Python, which is slow). What do you comment on the speed?

My method does not use any chain techniques, (at least I do not understand chains,.... hehehe). But what is a dirty path, I do not think I am using it, because no path is particularly dirtier than the other.....I am not using a escape lane-- I deleted my function of guess-attacking.

My method is: try to put a possible value on a box, and then, I continue with putting another value on another box...., If you guys are frowning :? .... hahah, I am happy I am getting you there :lol: .

But honestly, I am not using any method you are using, and I do not think I am guessing. By the way the damned Notices refused my paper, which may make you guys find me very funny :oops: .
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xxxxx1110 minimal puzzles

Postby coloin » Wed Sep 14, 2011 9:05 pm

Here is a few of the puzzles i made - with the method - and MD really took it furthur......

This is one of the many 4-templates which solve with 3 clues
Code: Select all
..1..2.34.3..142..4.23...1...423.1..12..4...33....142..1.4..3.2.43.2...12..1.3.4.


Combining with all the possible essentially different 5-templates gives many many non-minimal puzzles with 999991110 clue distribution [48 clues]

Picking out some of these with a high ER
And there might be 100,000 minimal puzzles from each non-minimal each with at least this ER.

Code: Select all
                                                                                    q2                              SE     
56..897..7.815.9.6..96.7.5889...65.76.78.5.92.5.79.68.98..7..653.596.87..765.8..9 #  3406 FNBP C48/M2.78.84          9.7         
5....97..7.815.9....96.7.58.9....5.7..7..5.92.5.79.68.98..7..653.59..87..765.8..9 # 95278 FNBP C40/M2.18.728        10.4         
5...........1.......96.7.58...........7..5.92.5.79.68..8.....653..9...7..76..8..9 # 95278 FNBP C26.m/M2.18.364      10.4         
                                                                                                                                 
56..897..7.816.9.5..97.5.6897...85.68.65.7.92.5.69.87.68..7..593.795.68..958.6..7 #  3406 FNBP C48/M2.78.84          9.7         
56..897.....16...5...7.5.6.97...85.68.65.7.92.5.69.87.68..7..593...5.6....5..6... # 96000 FNBP C37/M2.8.2460        10.1         
5...897.....1..........5.6.97...85....6....92...6..87..8..7..593..........5..6... # 96000 FNBP C24.m/M2.3.37179     10.4


And these minimal puzzles exceed their rating with 48 clues.

Next i could do is look for 23-24 puzzles in the lists with xxxxx1110 clue counts.....

I am half expecting that this area of "puzzle space" is unexplored

C
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Re: The hardest sudokus (new thread)

Postby champagne » Thu Sep 15, 2011 10:01 am

dobrichev wrote:Here is one non-minimal puzzle with 999911111 digit distribution.

Code: Select all
.6..12.34.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12..45 10.4/10.4/10.0


Here are its 23-clue minimals - 11111-part fixed, non-givens fixed, 9999-part minimized.


Hi,

As coloin says, that kind of puzzle can give a good start to extract seeds.

My process for minimal search out of a non minimal puzzle was limited to a much smaller number of clues, so I took the opportunity of that example to revise the process.

I made a full run that I stopped after several hours thinking that something was going wrong, seen the size of the output file.

At that point, I already had 1.5 million minimal puzzles (if the results are ok)
with the following distribution

Hidden Text: Show
Code: Select all
clues   nb
23   44
24   1676
25   16062
26   72110
27   187641
28   313895
29   357445
30   285953
31   163022
32   66257
33   18940
34   3691
35   462
36   33
37   1


I restarted the run, keeping in output only minimal puzzles with less than 25 clues.
after about 20 hours, I think I got all the puzzles i was looking for and I stopped the process.

I got the following results

Code: Select all
clues   nb
23   124
24   4622


1) we have more 23 puzzles that in dobritchev lot.
and it seems ok.
2) If i apply a proportional ratio, it seems that the pattern generated 1.5 * 124 / 44 =
about 4.5 million minimal puzzles.


the 124 "23 clues" puzzles include all the list published by dobritchev.
I found the additional ones

Hidden Text: Show
Code: Select all
.6...........7..2.2.43..1.......14...3.4..8.2...2...13..1...3...4..9....3...2...5
.6...........7..2.2.43..1......314...3.4..8.2...2...1...1...3...4..9....3...2...5
.6...........7..2.2.43..1....2..14...3.4..8.....2...13..1...3...4..9....3...2...5
.6...........7..2.2.43..1....2.314...3.4..8.....2...1...1...3...4..9....3...2...5
.6.........3.7..2.2.43..1......314.....4..8.2...2...1...1...3...4..9....3...2...5
.6.........3.7..2.2.43..1......314..1..4..8.2...2.......1...3...4..93.......2...5
.6.........3.7..2.2.43..1....2.314.....4..8.....2...1...1...3...4..9....3...2...5
.6.........3.7..2.2.43..1....2.314..1..4..8.....2.......1...3...4..93.......2...5
.6........1..7..2.2.43..1.......14...3.4..8.2...2....3..1...3...4..9....3...2...5
.6........1..7..2.2.43..1......314.....4..8.2...2....3..1...3...4..9....3...2...5
.6........1..7..2.2.43..1....2..14...3.4..8.....2....3..1...3...4..9....3...2...5
.6........1..7..2.2.43..1....2.314.....4..8.....2....3..1...3...4..9....3...2...5
.6........13.7..2.2.43..1......314.....4..8.2...2.......1...3...4..9....3...2...5
.6........13.7..2.2.43..1......314.....4..8.2...2.......1...3...4..93.......2...5
.6........13.7..2.2.43..1....2.314.....4..8.....2.......1...3...4..9....3...2...5
.6........13.7..2.2.43..1....2.314.....4..8.....2.......1...3...4..93.......2...5
.6.....3.....7....2.43..1.......14...3.4..8.2...2...13..1.......4..9.2..3...2...5
.6.....3.....7..2.2.43..1....2..14...3.4..8.....2...13..1.......4..9....3...2...5
.6.....3...3.7....2.4...1......314..1..4..8.2...2.......1...3...4..932......2...5
.6.....3...3.7..2.2.4...1......314..1..4..8.2...2.......1...3...4..93.......2...5
.6.....3...3.7..2.2.4...1....2.314..1..4..8.....2.......1...3...4..93.......2...5
.6.....3..1..7....2.43..1.......14...3.4..8.2...2....3..1.......4..9.2..3...2...5
.6.....3..1..7....2.43..1......314.....4..8.2...2.......1...3...4..9.2..3...2...5
.6.....3..1..7....2.43..1......314.....4..8.2...2....3..1.......4..9.2..3...2...5
.6.....3..1..7..2.2.43..1......314.....4..8.2...2.......1...3...4..9....3...2...5
.6.....3..1..7..2.2.43..1....2..14...3.4..8.....2....3..1.......4..9....3...2...5
.6.....3..1..7..2.2.43..1....2.314.....4..8.....2.......1...3...4..9....3...2...5
.6.....3..1..7..2.2.43..1....2.314.....4..8.....2....3..1.......4..9....3...2...5
.6.....3..13.7....2.4...1......314.....4..8.2...2.......1...3...4..932......2...5
.6.....3..13.7..2.2.4...1......314.....4..8.2...2.......1...3...4..93.......2...5
.6.....3..13.7..2.2.4...1....2.314.....4..8.....2.......1...3...4..93.......2...5
.6...2.......7..2...43..1.......14...3.4..8.2...2...13.21...3...4..9....3.......5
.6...2.......7..2...43..1......314...3.4..8.2...2...1..21...3...4..9....3.......5
.6...2.......7..2...43..1....2..14...3.4..8.........13.21...3...4..9....3...2...5
.6...2.......7..2...43..1....2..14...3.4..8.....2...13.21...3...4..9....3.......5
.6...2.......7..2...43..1....2.314...3.4..8.........1..21...3...4..9....3...2...5
.6...2.......7..2...43..1....2.314...3.4..8.....2...1..21...3...4..9....3.......5
.6...2.......7..2.2.43..1....2..14...3.4..8.........13..1...3...4..9....3...2...5
.6...2.......7..2.2.43..1....2.314...3.4..8.........1...1...3...4..9....3...2...5
.6...2.....3.7..2...43..1......314.....4..8.2...2...1..21...3...4..9....3.......5
.6...2.....3.7..2...43..1......314..1..4..8.2...2......21...3...4..93...........5
.6...2.....3.7..2...43..1....2.314.....4..8.........1..21...3...4..9....3...2...5
.6...2.....3.7..2...43..1....2.314.....4..8.....2...1..21...3...4..9....3.......5
.6...2.....3.7..2...43..1....2.314..1..4..8............21...3...4..93.......2...5
.6...2.....3.7..2...43..1....2.314..1..4..8.....2......21...3...4..93...........5
.6...2.....3.7..2.2.43..1....2.314.....4..8.........1...1...3...4..9....3...2...5
.6...2.....3.7..2.2.43..1....2.314..1..4..8.............1...3...4..93.......2...5
.6...2....1..7..2...43..1.......14...3.4..8.2...2....3.21...3...4..9....3.......5
.6...2....1..7..2...43..1......314.....4..8.2...2....3.21...3...4..9....3.......5
.6...2....1..7..2...43..1....2..14...3.4..8..........3.21...3...4..9....3...2...5
.6...2....1..7..2...43..1....2..14...3.4..8.....2....3.21...3...4..9....3.......5
.6...2....1..7..2...43..1....2.314.....4..8..........3.21...3...4..9....3...2...5
.6...2....1..7..2...43..1....2.314.....4..8.....2....3.21...3...4..9....3.......5
.6...2....1..7..2.2.43..1....2..14...3.4..8..........3..1...3...4..9....3...2...5
.6...2....1..7..2.2.43..1....2.314.....4..8..........3..1...3...4..9....3...2...5
.6...2....13.7..2...43..1......314.....4..8.2...2......21...3...4..9....3.......5
.6...2....13.7..2...43..1......314.....4..8.2...2......21...3...4..93...........5
.6...2....13.7..2...43..1....2.314.....4..8............21...3...4..9....3...2...5
.6...2....13.7..2...43..1....2.314.....4..8............21...3...4..93.......2...5
.6...2....13.7..2...43..1....2.314.....4..8.....2......21...3...4..9....3.......5
.6...2....13.7..2...43..1....2.314.....4..8.....2......21...3...4..93...........5
.6...2....13.7..2.2.43..1....2.314.....4..8.............1...3...4..9....3...2...5
.6...2....13.7..2.2.43..1....2.314.....4..8.............1...3...4..93.......2...5
.6...2.3.....7..2...43..1.......14...3.4..8.2...2...13.21.......4..9....3.......5
.6...2.3.....7..2...43..1....2..14...3.4..8.........13.21.......4..9....3...2...5
.6...2.3.....7..2...43..1....2..14...3.4..8.....2...13.21.......4..9....3.......5
.6...2.3.....7..2.2.43..1....2..14...3.4..8.........13..1.......4..9....3...2...5
.6...2.3...3.7..2...4...1......314..1..4..8.2...2......21...3...4..93...........5
.6...2.3...3.7..2...4...1....2.314..1..4..8............21...3...4..93.......2...5
.6...2.3...3.7..2...4...1....2.314..1..4..8.....2......21...3...4..93...........5
.6...2.3...3.7..2.2.4...1....2.314..1..4..8.............1...3...4..93.......2...5
.6...2.3..1..7..2...43..1.......14...3.4..8.2...2....3.21.......4..9....3.......5
.6...2.3..1..7..2...43..1......314.....4..8.2...2......21...3...4..9....3.......5
.6...2.3..1..7..2...43..1......314.....4..8.2...2....3.21.......4..9....3.......5
.6...2.3..1..7..2...43..1....2..14...3.4..8..........3.21.......4..9....3...2...5
.6...2.3..1..7..2...43..1....2..14...3.4..8.....2....3.21.......4..9....3.......5
.6...2.3..1..7..2...43..1....2.314.....4..8............21...3...4..9....3...2...5
.6...2.3..1..7..2...43..1....2.314.....4..8..........3.21.......4..9....3...2...5
.6...2.3..1..7..2...43..1....2.314.....4..8.....2......21...3...4..9....3.......5
.6...2.3..1..7..2...43..1....2.314.....4..8.....2....3.21.......4..9....3.......5
.6...2.3..1..7..2.2.43..1....2..14...3.4..8..........3..1.......4..9....3...2...5
.6...2.3..1..7..2.2.43..1....2.314.....4..8.............1...3...4..9....3...2...5
.6...2.3..1..7..2.2.43..1....2.314.....4..8..........3..1.......4..9....3...2...5
.6...2.3..13.7..2...4...1......314.....4..8.2...2......21...3...4..93...........5
.6...2.3..13.7..2...4...1....2.314.....4..8............21...3...4..93.......2...5
.6...2.3..13.7..2...4...1....2.314.....4..8.....2......21...3...4..93...........5
.6...2.3..13.7..2.2.4...1....2.314.....4..8.............1...3...4..93.......2...5


and as far as i could check, these are correct.

here below, the list of minimal with the highest number of clues I got in the first (partial) run;

Hidden Text: Show
Code: Select all
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;37
.6......4.13.74.2.2.43..1......314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8..4..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13....8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..1..4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314...3.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.31...13.4..8.24..2...13.21.4.3...4..932.13..1...45;36
.6......4.13.74.2.2.43..1....2.31...13.4..8.24..2...13.21.4.3...4..932.13...2..45;36
.6........13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2..14..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...1..21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2..3..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74...2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.7..2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.1..74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4..3.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.3.4..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..9.2.13..12...5;36
.6.....3..13.7..2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6.....3..1..74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6.....3...3.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..1....5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13...2...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.1...12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.2...2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..93..13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2....3.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3......932.13..1...45;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3......932.13...2..45;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21...3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.2..4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13..1.4.3...4..932.13..12...5;36
.6.....3..13.74...2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12...5;36
.6......4.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932..3..12...5;36



With such a number of minimal derived puzzles, the process should be selective for such seed.

The optimized test can speed up significantly the process if number of clues has an upper limit.

champagne

PS: I'll have a look to coloin's list to day
champagne
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Re: The hardest sudokus (new thread)

Postby eleven » Thu Sep 15, 2011 10:51 am

sdk_fan wrote:My method is: try to put a possible value on a box, and then, I continue with putting another value on another box....

And if these values do not lead to a solution - do you try another value then ? If so, your method is simple backtracking - and your program is about 100000 times slower than public programs.
eleven
 
Posts: 1665
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Re: The hardest sudokus (new thread)

Postby champagne » Thu Sep 15, 2011 12:25 pm

Hi,

I updated the data base of potential hardest.
The link is unchanged

here

The data base has mainly been extended in the 23 clues field.

I have in wait state some puzzles that should enter in the lowest part of SE ratings, but I wait for skfr availability.
SE rating consume to many resources.

Addition include as well some puzzles coming from dobritchev twin generation

Analysis of specific properties has been done for 2000 more puzzles, but I didn't work on the others.

champagne
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minimizing puzzles

Postby dobrichev » Thu Sep 15, 2011 9:12 pm

champagne wrote:
dobrichev wrote:Here is one non-minimal puzzle with 999911111 digit distribution.

Code: Select all
.6..12.34.13.74.2.2.43..1....2.314..13.4..8.24..2...13.21.4.3...4..932.13..12..45 10.4/10.4/10.0

...


...
I got the following results

Code: Select all
clues   nb
23   124
24   4622



I am confirming there are 124 23-clues minimals.

According to my tool, this is the distribution of low-clue puzzles with the non-givens fixed
Code: Select all
clues     minimals
23             124
24            2822
25            8146
26            7881
27            3169
28             913
29             112
30               0

[edit: added counts for 27..30-clues puzzles]
[edit 2: some of the counted 24+ puzzles still don't conform the mask, must revise the list]
[edit 3: updating the list, hope now the counts are correct]

MD
Last edited by dobrichev on Mon Sep 26, 2011 8:54 am, edited 1 time in total.
dobrichev
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Re: The hardest sudokus (new thread)

Postby eleven » Wed Sep 21, 2011 2:07 pm

Hi, what i was trying was to find subgrids of extremely hard puzzles, where still eliminations are possible. I dont have any idea so far, how to deduce the eliminations, but it looks easier to find them in the subgrid.

Since my program is very new and probably buggy, my question is, if someone can verify the eliminations in the 2 samples below (the second puzzle is from champagnes list of 18 hardest). Maybe this is possible with XSudo.

Code: Select all
12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;11.90;11.90;2.60;elev;1;5
 *--------------------------------------------------------------------*
 | 1      2       689    | 3     46789  45679  | 45789  4579   458    |
 | 4      389     5      | 2789  12789  179    | 6      1379   138    |
 | 389    7       3689   | 689   14689  14569  | 4589   2      13458  |
 |-----------------------+---------------------+----------------------|
 | 6      589     2789   | 1     2479   479    | 3      457    2458   |
 | 2789   189     4      | 5     3      679    | 278    167    1268   |
 | 2357   135     1237   | 267   2467   8      | 2457   14567  9      |
 |-----------------------+---------------------+----------------------|
 | 23789  3689    23789  | 4     5      3679   | 1      369    236    |
 | 23579  134569  12379  | 679   1679   13679  | 2459   8      23456  |
 | 359    134569  139    | 689   1689   2      | 459    34569  7      |
 *--------------------------------------------------------------------*
23 groups locked, 31 cells locked, 31/110 candidates could be eliminated
 *-------------------------------------------------*
 | .  2       .  | .  .  45679  | .  4579   458    |
 | .  389     .  | .  .  179    | .  1379   138    |
 | .  7       .  | .  .  14569  | .  2      13458  |
 |---------------+--------------+------------------|
 | .  589     .  | .  .  479    | .  457    2458   |
 | .  189     .  | .  .  679    | .  167    1268   |
 | .  135     .  | .  .  8      | .  14567  9      |
 |---------------+--------------+------------------|
 | .  3689    .  | .  .  3679   | .  369    236    |
 | .  134569  .  | .  .  13679  | .  8      23456  |
 | .  134569  .  | .  .  2      | .  34569  7      |
 *-------------------------------------------------*

r1c6<>4, r1c6<>5, r1c6<>7, r1c6<>9, r1c8<>7, r1c8<>9, r1c9<>8, r3c6<>1, r3c6<>4, r3c6<>6, r3c6<>9, r3c9<>4, r3c9<>5, r3c9<>8, r4c6<>7, r4c6<>9, r4c8<>4, r4c9<>4, r5c6<>6, r6c8<>6, r6c8<>7, r7c6<>6, r8c2<>3, r8c2<>9, r8c6<>6, r8c6<>7, r8c6<>9, r8c9<>2, r8c9<>3, r9c2<>9, r9c8<>9

Code: Select all
..34..7...5...9.2.....1....23.....5...1.6.3..8..........46..........8.9....17.6.. ;5416;elev;11.1;1.2 ;1.2 ;8
 *-------------------------------------------------------------------*
 | 169    12689   3     | 4      258   256     | 7     168   1589    |
 | 1467   5       678   | 378    38    9       | 148   2     13468   |
 | 4679   246789  2789  | 2578   1     23567   | 4589  3468  34589   |
 |----------------------+----------------------+---------------------|
 | 2      3       679   | 789    48    147     | 1489  5     146789  |
 | 4579   479     1     | 25789  6     2457    | 3     478   24789   |
 | 8      4679    5679  | 23579  2345  123457  | 1249  1467  124679  |
 |----------------------+----------------------+---------------------|
 | 1357   1278    4     | 6      9     235     | 1258  1378  123578  |
 | 13567  1267    2567  | 235    2345  8       | 1245  9     123457  |
 | 359    289     2589  | 1      7     2345    | 6     348   23458   |
 *-------------------------------------------------------------------*
23 groups locked, 32 cells locked, 12/108 candidates could be eliminated
 *-----------------------------------------------------------------*
 | .      .     .     | .      .     .       | .     .     .       |
 | 1467   5     678   | 378    38    9       | 148   2     13468   |
 | .      .     .     | .      .     .       | .     .     .       |
 |--------------------+----------------------+---------------------|
 | 2      3     679   | 789    48    147     | 1489  5     146789  |
 | .      .     .     | .      .     .       | .     .     .       |
 | 8      4679  5679  | 23579  2345  123457  | 1249  1467  124679  |
 |--------------------+----------------------+---------------------|
 | .      .     .     | .      .     .       | .     .     .       |
 | 13567  1267  2567  | 235    2345  8       | 1245  9     123457  |
 | .      .     .     | .      .     .       | .     .     .       |
 *-----------------------------------------------------------------*

r2c9<>8, r4c9<>8, r4c9<>9, r6c2<>9, r6c6<>2, r6c6<>5, r6c9<>2, r6c9<>9, r8c1<>5, r8c2<>2, r8c9<>2, r8c9<>5
eleven
 
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Re: The hardest sudokus (new thread)

Postby champagne » Thu Sep 22, 2011 8:04 am

Hi,

I had in my database that non minimal puzzle from mauricio, a very old one.

6....2.5952..4..1...35..2..3..1945...1.658.3...5273..1..4..51...3..2..4575.4....8;11.2;11.2;11.2tax Mauricio's-non-min 37

I looked for minimal sub puzzles and found 240 of them with the following clues

Code: Select all
26   24
27   120
28   96


I'll add them to the data base with family code "GP" and Id "mau 37".

They will be in the next update

champagne
champagne
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Re: The hardest sudokus (new thread)

Postby champagne » Thu Sep 22, 2011 8:32 am

eleven wrote:23 groups locked, 31 cells locked, 31/110 candidates could be eliminated
*-------------------------------------------------*
| . 2 . | . . 45679 | . 4579 458 |
| . 389 . | . . 179 | . 1379 138 |
| . 7 . | . . 14569 | . 2 13458 |
|---------------+--------------+------------------|
| . 589 . | . . 479 | . 457 2458 |
| . 189 . | . . 679 | . 167 1268 |
| . 135 . | . . 8 | . 14567 9 |
|---------------+--------------+------------------|
| . 3689 . | . . 3679 | . 369 236 |
| . 134569 . | . . 13679 | . 8 23456 |
| . 134569 . | . . 2 | . 34569 7 |
*-------------------------------------------------*[/code]
r1c6<>4, r1c6<>5, r1c6<>7, r1c6<>9, r1c8<>7, r1c8<>9, r1c9<>8, r3c6<>1, r3c6<>4, r3c6<>6, r3c6<>9, r3c9<>4, r3c9<>5, r3c9<>8, r4c6<>7, r4c6<>9, r4c8<>4, r4c9<>4, r5c6<>6, r6c8<>6, r6c8<>7, r7c6<>6, r8c2<>3, r8c2<>9, r8c6<>6, r8c6<>7, r8c6<>9, r8c9<>2, r8c9<>3, r9c2<>9, r9c8<>9


If I catch your point, your findings is that in these four columns you must have r1c6=6 r3c6=4 .....

This looks like an XSUDO approach. I guess the XSUDO SLG based on these four columns would give more eliminations.

1) How did you come to that
2) If you don't have XSUDO, I'll try it for you
3) you have to many rookeries, this is not something I am looking for in my solver

champagne
champagne
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Posts: 5753
Joined: 02 August 2007
Location: France Brittany

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