hardest 6x6?

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

Re: hardest 6x6?

Postby tarek » Thu Jan 03, 2019 3:46 pm

My last venture (possibly :D ) into one-trick-pony land:
Code: Select all
.3..6...5..4.4....2....13......1.2..   ED=7.1/7.1/7.1
2....6....2....3...3....1...5..4.1..   ED=3.0/3.0/3.0
42..1......2......1....4..35...5....   ED=6.8/6.6/2.6

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Re: hardest 6x6?

Postby Mathimagics » Thu Jan 03, 2019 5:26 pm

In the land of the Mostly Weak, the one-trick-pony is king! 8-)
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Re: hardest 6x6?

Postby tarek » Sat Jan 05, 2019 7:48 am

Random generation can bring out some of the hardest but will not be as concise as Mathimagics enumeration.

The 1st TW is most likely in the AllTW list but I also found a few PW puzzles so I'm pretty sure Mathimagics bigger file will have some nice puzzle there.

Code: Select all
....1..5.2...14...6.....24...3..3... ED=8.3/2.0/2.0
31...4..4....6..1..2.5...3...1...... ED=8.3/1.2/1.2
2....5..4..11......2..3.6..2........ ED=7.6/1.2/1.2


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Re: hardest 6x6?

Postby Mathimagics » Sat Jan 05, 2019 8:38 am

Hi tarek,

I haven't actually got a separate extraction of PW(1-5) puzzles that would include those 3 examples (I just counted them), but can produce one if you wish to search it?
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Re: hardest 6x6?

Postby tarek » Sat Jan 05, 2019 12:13 pm

Thanks Mathimagics,

No need. I had enough time on this one for the moment. I managed to tweak a few things in my solver/generator which was satisfying. I suspect the PW batch to be fairly large & therefore would take a considerable time to rate!!!

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Re: hardest 6x6?

Postby 999_Springs » Fri Jan 11, 2019 6:24 pm

hey guys, just caught up on this topic. was in the middle of a complicated house move and still don't have internet set up at my new place, i can browse these forums fine with mobile data but every time i try to post it logs me out whenever i click submit post and then everything i've written is lost. it's so frustrating

1to9only you are amazing. that was an incredibly quick turnaround time to modify SE to work on 6x6s and those are some great results. well done!

the next step would be to take a look at the pw puzzles with only a few singles at the start to see if there are any higher rated ones 8.4+ - i'm optimistic as there are so many more of them

I'm also surprised that the ratings list contains no 3.6 naked triplets or 3.8 swordfish in it, those would make some nice puzzles for manual solvers

mathimagics: well done on enumerating all possible 6x6 puzzles in your previous posts, that's impressive work too

Mathimagics wrote:.
Sudoku 6x6 is "Sudoku for kids"?

Apparently not - unless the kid is pretty smart … :?

if you allow pencilmark grids in sudokus like tarek is interested in, you can get even smaller ones like this

Code: Select all
12  .   | .   .
.   124 | .   34
--------+---------
.   .   | 14  .
23  .   | .   .
SE 8.3/8.3/7.1

.   134 | .   34
12  .   | .   .
--------+---------
234 134 | 234 .
.   .   | .   23
SE 7.3/7.3/6.6
although at this puzzle size it is questionable if se is a good measure of rating stuff like this since a lot of ratings aren't possible e.g. 7.4-8.1 are almost certainly not possible for any move

edit: singles backdoor size 1 doesn't necessarily mean 1 trick pony because the backdoor could be a candidate that isn't part of a strong link so it needs multiple eliminations to make that placement. but with puzzle sizes this small, it's certainly going to be much easier to find nice short solution paths for them without long chains
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Re: hardest 6x6?

Postby Mathimagics » Sat Jan 12, 2019 3:19 am

.
Well, if anybody wants to get down and dirty, I can always extract those PW 1-3 or 4 for you to play with …

Hmm, Sukaku 6x6 is interesting, but how do you rate them? 8-)

A further thought, we might find harder 6x6 puzzles for SudokuP, but then we'd have a new rating problem
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Re: hardest 6x6?

Postby 999_Springs » Sat Jan 12, 2019 1:12 pm

sure, go for it :) although i'm sure that if you posted those then 1to9only would get there first with a full rating scan, leaving me with nothing to do, just like tarek! i'd be interested to know what comes up

pencilmark 6x6s would be way harder i'm sure, since if even 4x4s can get to se 8.3 i wonder what 6x6s will bring, but they will be tough to rate (maybe easier than the pencilmark 9x9s ? - i remember 1to9only was running into some kind of overflow issue with the pencilmark 9x9s which won't happen here with not many cells remaining) - and even harder to generate as there is no way you can do an exhaustive search :P i'll leave that one to someone else then

and finally, if you get the first 8.2/6.6/6.6 from the file:
Code: Select all
..3..6
...23.
..1.4.
.4.3..
.12...
5..1..
which remains SE 8.2 after the first placement r1c3=3 - and satisfies gurth's symmetry theorem which is nice

turns out you can embed (the complement of) this puzzle into a 9x9 grid by shoving 7,8,9's into random places just like i was doing earlier in the first post - but this time you actually get a valid puzzle:
Code: Select all
..3..7689
...89.237
789236154
..8.4.791
.7.9..348
941378526
.97...812
8..1..975
512789463 SE 8.2, 57 clues
and with 57 clues, this smashes the previous record for SE 8.2 in the "maximum clues per se rating" thread! i'm sure there are others out there like this - it seems a very strange way to go about generating hard 9x9s with lots of clues, but if it works it works :)

edit: here's another one using the same method
Code: Select all
1.3.75689
.869..715
957186234
..97.8543
......897
874359126
.98..7461
......978
761894352 SE 7.8, 58 clues
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Re: hardest 6x6?

Postby eleven » Sat Jan 12, 2019 3:58 pm

999_Springs wrote: ... and finally, if you get the first 8.2/6.6/6.6 from the file:
Code: Select all
..3..6
...23.
..1.4.
.4.3..
.12...
5..1..
which remains SE 8.2 after the first placement r1c3=3 - and satisfies gurth's symmetry theorem which is nice

... which makes it easy:
if r35c4 is not 56, but 4, then also r2c3=4, and r1c5,r2c6=15 => -5r1c4,-6r6c3
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Sudoku6 PW Data

Postby Mathimagics » Sun Jan 13, 2019 10:30 am

I have attached the grids for PW1 and PW2 types.

The files for PW3 and PW4 when zipped exceed 256Kb so they can't be posted here. If anybody would like these PM me giving an email address that I can send them to. I think any rating gems will most likely be found in these first 2 files.

[EDIT] These files (and the TW file) are inaccurate. See the update below.
Attachments
Sudoku6-PW2.zip
(240.35 KiB) Downloaded 15 times
Sudoku6-PW1.zip
(165.75 KiB) Downloaded 16 times
Last edited by Mathimagics on Sun Apr 21, 2019 7:41 pm, edited 1 time in total.
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Re: hardest 6x6?

Postby 1to9only » Sun Jan 13, 2019 7:45 pm

The stats for the last 2 posted files:

- the highest rated grids:
Code: Select all
....5.4....3...5.1....4.3.2.1..6..3. ED=8.4/1.2/1.2
....5.4....3...5.1...34.3.2.1..6.... ED=8.4/1.2/1.2
.2......61..2.4....1.....4.6.5.6..3. ED=8.4/1.2/1.2
.2......61..2.4...61.....4.6.5....3. ED=8.4/1.2/1.2
.2.4....6.....4...61......2..5..123. ED=8.4/1.2/1.2
.2.4....6...2.4...61.........5..123. ED=8.4/1.2/1.2
1...5......3.....1...34...2..556...4 ED=8.4/1.2/1.2
1...5......3...5.1...34...2...56...4 ED=8.4/1.2/1.2

- the breakdown by difficulty ratings:
Code: Select all
        Sudoku6-PW1.txt                                 Sudoku6-PW2.txt

      8 ED=8.4          ED=8.4/1.2/1.2
     50 ED=8.3          ED=8.3/2.0/2.0               70 ED=8.3          ED=8.3/1.5/1.5
      1 ED=8.2          ED=8.2/1.2/1.2
                                                      5 ED=7.8          ED=7.8/1.2/1.2
     12 ED=7.7          ED=7.7/1.2/1.2                9 ED=7.7          ED=7.7/1.2/1.2
     26 ED=7.6          ED=7.6/1.5/1.5               29 ED=7.6          ED=7.6/1.2/1.2
      1 ED=7.5          ED=7.5/1.2/1.2
     10 ED=7.3          ED=7.3/1.5/1.5               18 ED=7.3          ED=7.3/2.0/2.0
   2749 ED=7.2          ED=7.2/2.0/2.0             2820 ED=7.2          ED=7.2/2.0/2.0
   6824 ED=7.1          ED=7.1/2.0/2.0             8660 ED=7.1          ED=7.1/2.0/2.0
     39 ED=7.0          ED=7.0/2.0/2.0               98 ED=7.0          ED=7.0/2.0/2.0
     85 ED=6.9          ED=6.9/2.0/2.0              105 ED=6.9          ED=6.9/2.0/2.0
    357 ED=6.8          ED=6.8/2.0/2.0              529 ED=6.8          ED=6.8/2.0/2.0
    420 ED=6.7          ED=6.7/2.0/2.0              570 ED=6.7          ED=6.7/2.0/2.0
   8509 ED=6.6          ED=6.6/2.0/2.0            14973 ED=6.6          ED=6.6/2.0/2.0
     52 ED=6.5          ED=6.5/1.5/1.5              120 ED=6.5          ED=6.5/1.5/1.5
     62 ED=6.2          ED=6.2/2.0/2.0               60 ED=6.2          ED=6.2/2.0/2.0
                                                      1 ED=5.8          ED=5.8/1.5/1.5
     81 ED=5.7          ED=5.7/2.0/2.0              161 ED=5.7          ED=5.7/2.0/2.0
    535 ED=5.6          ED=5.6/2.0/2.0              923 ED=5.6          ED=5.6/2.0/2.0
     48 ED=4.6          ED=4.6/2.0/2.0              133 ED=4.6          ED=4.6/2.0/2.0
    622 ED=4.5          ED=4.5/2.0/2.0              931 ED=4.5          ED=4.5/2.0/2.0
    269 ED=4.4          ED=4.4/2.0/2.0              651 ED=4.4          ED=4.4/2.0/2.0
   6718 ED=4.2          ED=4.2/2.0/2.0            10120 ED=4.2          ED=4.2/2.0/2.0
      4 ED=3.8          ED=3.8/1.2/1.2                3 ED=3.8          ED=3.8/1.2/1.2
      8 ED=3.6          ED=3.6/1.2/1.2
     40 ED=3.4          ED=3.4/2.0/2.0               30 ED=3.4          ED=3.4/2.0/2.0
    151 ED=3.2          ED=3.2/2.0/2.0              208 ED=3.2          ED=3.2/2.0/2.0
    257 ED=3.0          ED=3.0/2.0/2.0              218 ED=3.0          ED=3.0/2.0/2.0
    122 ED=2.8          ED=2.8/2.0/2.0               79 ED=2.8          ED=2.8/2.0/2.0
   1023 ED=2.6          ED=2.6/2.0/2.0             1622 ED=2.6          ED=2.6/2.0/2.0
    130 ED=2.5          ED=2.5/2.0/2.0              205 ED=2.5          ED=2.5/2.0/2.0
   1521 ED=2.0          ED=2.0/2.0/2.0             2170 ED=2.0          ED=2.0/2.0/2.0
    193 ED=1.7          ED=1.7/1.7/1.7              405 ED=1.7          ED=1.7/1.5/1.5
  -----                 --------------            -----                 --------------
  30297                 highest rating            45926                 highest rating

Some 3.6 naked triplets and 3.8 swordfishes in there, even 1x 5.8 BUG type 3 and 1x 7.5 ATE (Aligned Triplet Exclusion)!
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Re: hardest 6x6?

Postby Mathimagics » Tue Jan 15, 2019 6:17 am

Is an explusion an exclusive explosion (like a North Korean nuclear test) or an explosive exclusion (like Lance Armstrong getting kicked out of cycling) ? 8-)

[EDIT] Hey, you ruined my joke by fixing that typo :cry:
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Re: hardest 6x6?

Postby 999_Springs » Sun Jan 20, 2019 7:31 pm

very nice work, mathimagics and 1to9only! I'll look into this and maybe the higher pw+n puzzles and stuff further when i get internet properly set up at my new place, but that 8.4 looks delicious :D (are they essentially different or the same puzzle after the singles?) correctly guessed there was a better one out there

Also yeah i spotted that typo too

edit:
Mathimagics wrote:.
Perhaps the 3 cases of NC=8 and FM = 1,3,4 are worth a look?

Code: Select all
..34...5.....3......1..2.....56.....
.....6.5.1..2..3.......1......6...4.
1.........3........34.2......5.6..4.
4.2
4.2
2.6
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Corrections: TW/PW Table

Postby Mathimagics » Sun Apr 21, 2019 7:35 pm

999_Springs reported a discrepancy in the table I posted above, and I found that there was a bug with the singles-counting process.

The corrected figures are:

Code: Select all
MP table (total minimal puzzles = 72425047)
 +----+-----------+-----------+--------+---------+---------+---------+---------+---------+---------+---------+
 | NC |   Minimal |    Strong | TW(0fm)| PW(1fm) | PW(2fm) | PW(3fm) | PW(4fm) | PW(5fm) | PW(6fm) | PW(7+fm)|
 +----+-----------+-----------+--------+---------+---------+---------+---------+---------+---------+---------+
 |  8 |      2619 |      2447 |      0 |       6 |       0 |       2 |       6 |       2 |       4 |     152 |
 |  9 |    607072 |    576686 |     97 |     432 |     958 |    1263 |    1546 |    1621 |    1408 |   23061 |
 | 10 |  12884906 |  12256735 |   4893 |   14065 |   21115 |   28385 |   34713 |   39759 |   45134 |  440107 |
 | 11 |  35853981 |  34019016 |  24842 |   57964 |   78375 |  108043 |  133235 |  148572 |  172422 | 1111512 |
 | 12 |  20408957 |  19330960 |  18638 |   39077 |   63172 |   94941 |  104120 |  121106 |  121871 |  515072 |
 | 13 |   2601185 |   2472427 |   2377 |    5484 |   10649 |   15953 |   18530 |   17600 |   16770 |   41395 |
 | 14 |     65547 |     62403 |    159 |     265 |     393 |     304 |     291 |     304 |     928 |     500 |
 | 15 |       780 |       780 |      0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |
 +----+-----------+-----------+--------+---------+---------+---------+---------+---------+---------+---------+
 |    |  72425047 |  68721454 |  51006 |  117293 |  174662 |  248891 |  292441 |  328964 |  358537 | 2131799 |
 +----+-----------+-----------+--------+---------+---------+---------+---------+---------+---------+---------+


So there are 3 times as many TW puzzles as reported earlier, and so the file "AllTW.zip" is inaccurate, as are the "PW1", "PW2" etc files.

Apologies for any inconvenience! :oops:

I now have a file with all TW+PW grids (72,425,047 - 68,721,454 = 3,703,593 grids), tagged with the NC and FM counts, which I can mail to anybody on request (PM me with an email address). The zipped file size is 19Mb.
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Re: hardest 6x6?

Postby 999_Springs » Mon Apr 22, 2019 3:08 pm

by filling in all the singles, i can independently confirm that the numbers in mathimagics's table above are right.

here are some more stats:
number of puzzles by clue count before doing singles:
Code: Select all
clue count, puzzles
8  172
9  30386
10 628171
11 1834965
12 1077997
13 128758
14 3144
15 0

number of initial singles:
Code: Select all
initial singles, puzzles
0  51006
1  117293
2  174662
3  248891
4  292441
5  328964
6  358537
7  375708
8  379170
9  380461
10 334882
11 256924
12 206152
13 134041
14 50843
15 12868
16 738
17 12

after filling in all the singles, and discarding duplicates, there were 542257 puzzles in total, out of the original 3703593. here is the count of number of puzzles by clue count, and number of unique puzzles:
Code: Select all
clue count, puzzles, unique puzzles
8  0      0
9  103    103
10 5325   5323
11 39867  38778
12 98986  84895
13 149762 101229
14 213196 98356
15 280265 82129
16 316389 58576
17 365304 35903
18 377135 19622
19 381553 9715
20 429132 4613
21 379550 2075
22 255367 625
23 261761 242
24 95972  59
25 53926  14

i'm in the middle of converting the big pile of 542257 puzzles to 9x9's where possible, and rating them. i'll post when/if i find something good. so far i'm going through the batch in descending order of clue count. found a nice 16-clue SE 8.4...
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