The list of potential hardest sudokus is maintained by user champagne on forum.enjoysudoku.com who announces new version in the thread The hardest sudokus (new thread) The last archive (as of 2020-09-21) is ph_1910.zip in Google Drive: downloads sudoku.
Archive history:
Verbatim copy:
I prepared a new update of the data base
as for all new files , that update is in my "google drive space" with the name ph_1910.zip
the link to that storage place is [url=https://drive.google.com/folderview?id=0B5lH6mGXxWzXTDFRMnVTbGNlZU0&usp=sharing]here[/url]
The file contains now 3 049 068 puzzles (2 135 371 in the former release dated May 2019)
This huge increas reflects mainly the contribution of Paquita a silent member of the forum.
Other puzzles are coming directly or indirectly ("robbie") from the pattern games
With 944 585 puzzles supplied, Paquita is the second contributor to the data base, but, as she only sumitted puzzles rating 11.x, she can be seen as the main supplier of high ratings.
the count per clue in the data base is now the following
clues Count
20 79
21 11091
22 89568
23 366334
24 758922
25 593558
26 853490
27 302100
28 69787
I added the count for 27-28 clues having now a significant number of such puzzles
The count per er is the following
er count
11.9 9
11.8 59
11.7 124
11.6 373
11.5 996
11.4 2342
11.3 13670
11.2 26023
11.1 178539
11 927353
The changes in the highest entries are mainly dues to paquita additions
and the combined table is the following
20 21 22 23 24 25 26 27 28
11.9 1 5 3
11.8 1 16 30 11 1
11.7 31 53 12 18 9 1
11.6 1 39 62 69 123 69 10
11.5 48 115 199 324 258 52
11.4 133 336 543 659 491 177 3
11.3 1 641 1255 2680 3709 3182 2117 85
11.2 6 997 2769 5791 7635 4386 4336 78 24
11.1 12 1314 5746 19834 35447 36227 43739 26182 9202
11 3 859 5727 26027 59613 131207 364448 275622 60559
24 4079 16098 55169 107529 175829 414880 301970 69785
to compare to the previous one
20 21 22 23 24 25 26
11.9 1 5 3
11.8 1 16 30 10 1
11.7 31 52 12 17 8 1
11.6 1 39 60 60 102 58 9
11.5 48 110 192 292 211 48
11.4 132 329 485 570 407 154
11.3 1 634 1213 2500 3311 2564 1853
11.2 6 996 2748 5707 7404 3913 4119
11.1 12 1292 5470 19048 30750 23049 14278
21 3189 10017 28017 42447 30210 20462
Some evidence here that paquita explored heavily the >24 clues area
Verbatim copy:
I prepared a new update of the data base
as for all new files , that update is in my "google drive space" with the name ph_1901.zip
the link to that storage place is [url=https://drive.google.com/folderview?id=0B5lH6mGXxWzXTDFRMnVTbGNlZU0&usp=sharing]here[/url]
The file contains now 2 105 149 puzzles (2 048 264 in the former release done one month ago)
The main reasons for this new release after one month are the following:
a) By chance, doing a test on the brute force, I discovered that an old lot was processed with a text delimiter causing a wrong canonical form.
I discarded the corresponding records and added the proper records. Meantime, some morphs of the old puzzles had been added, so the redundant puzzles disappeared.
b) paquita, the new supplier came with puzzles rating on the high side, it was interesting to publish them before my 3 months interruption of this task.
And I added some puzzles with 26 clues, the artea where I searched recently.
Due to the redundant discarded puzzles, the tables below can show surprising values.
the count per clue in the data base is now the following
clues Count
20 79
21 10961 +1
22 87995 -281
23 390377 -3274
24 699589 -5135
25 435017 -10702
26 480919 +76306
here it is clear that the redundant puzzles were mainly in the 24/25 clues area
The count per er is the following
er count
11.9 9
11.8 54
11.7 119 +3
11.6 286 +34
11.5 703 +89
11.4 1630 +125
11.3 9353 +446
The changes in the highest entries are mainly dues to paquita additions and partly offset by the redundancy cleaning
and the combined table is the following
clues 20 21 22 23 24 25 26
11.9 1 5 3
11.8 1 15 29 9
11.7 31 51 11 17 8 1
11.6 1 38 53 55 95 36 8
11.5 46 104 171 209 127 46
11.4 130 308 404 406 234 148
11.3 1 630 1128 2222 2512 1245 1615
11.2 6 991 2706 5497 6682 2908 3987
11.1 12 1267 5100 16413 23095 11606 12123
21 3149 9484 24785 33016 16164 17928
Verbatim copy:
This is the update of the file of potential hardest as of December 24 2015
additions are coming partly from the games (including dobrichev's extra lists" ,
and from the generation done on myside, inte the 22-25 clues areas
Nothing was done on my side in the 26 clues area
The file contains now 1 637 062 puzzles (1 583 095 in august)
the count per clue in the data base is the following
20 77
21 10794
22 87082
23 341310
24 541278
25 376668
26 225713
The count per er is the following
10.7 54535
10.6 253111
10.5 544977
10.4 110878
10.3 104157
11.9 9 9
11.8 53 53
11.7 113 113
11.6 187 186
11.5 549 545
11.4 1359 1353
11.3 7986 7910
11.2 19950 19754
11.1 60361 59951
11 79312 78461
10.9 193236 190523
10.8 159825 156589
10.7 55537 54535
10.6 261251 253111
10.5 572593 544977
10.4 116829 110878
10.3 107912 104157
the cutoff gives
10.7-10.5 pearl
10.4 mini 10.4/10.4/10.3
10.3 diamond
As we can see, the highest new entry is a 11.6
Interesting is the distribution of highest ratings per clue.
er 20 21 22 23 24 25 26
11.9 1 5 3
11.8 1 15 29 8
11.7 31 51 9 14 8
11.6 1 38 50 41 43 10 4
11.5 46 100 150 138 83 32
11.4 130 304 385 306 161 73
11.3 1 628 1123 2173 2162 1087 812
11.2 6 990 2708 5468 6066 2921 1736
11.1 12 1263 5090 15977 20468 11613 5938
11 3 802 5060 20686 28563 14436 9751
24 3944 14520 44900 57760 30319 18346
to be compared to the previous one
20 21 22 23 24 25 26
11.9 1 5 3
11.8 1 15 29 8
11.7 31 51 9 14 8
11.6 1 38 50 41 42 10 4
11.5 46 100 150 135 82 32
11.4 130 304 382 304 160 73
11.3 1 628 1122 2145 2131 1071 812
11.2 6 990 2708 5395 5995 2869 1736
11.1 12 1263 5090 15817 20378 11453 5938
11 3 802 5060 20306 28381 14147 9751
24 3944 14522 44256 57380 29800 18346(no search)
the 25 clues column could be highly biased as most of existing puzzles are directly produced out of 24 clues seeds.
2 or 3 cycles using 25 clues as seed could change slighly the scope
Verbatim copy:
This is the update of the file of potential hardest as of Septembet 5th 2014
The file contains now 1 529 600 puzzles (1 264 655 puzzles in april)
264 945 puzzles have been added since April,mainly in the 23-24-26 clues fields.
Nothing new has been done to produce new seeds out of the JExocet patterns.
the count per clue in the data base is the following
20 77
21 10791
22 86867
23 336675
24 508910
25 359513
26 226584
more 183
The count per er is the following
er CompteDeer
11.9 8
11.8 50
11.7 112 /110
11.6 184 /174
11.5 529 /472
11.4 1324
11.3 7737
11.2 19322
11.1 59157
11 77514
10.9 186252
10.8 150552
10.7 53651
10.6 246167
10.5 520375
10.4 105540
10.3 101126
the cutoff gives
10.7-10.5 pearl
10.4 mini 10.4/10.4/10.3
10.3 diamond
As we can see, the highest new entry is a 11.7.
Interesting is the distribution of highest ratings per clue.
er 20 21 22 23 24 25 26
11.9 1 4 3
11.8 1 15 26 8
11.7 31 50 9 14 8
11.6 1 38 50 41 41 10 3
11.5 46 99 149 128 82 25
11.4 130 301 376 288 160 69
11.3 1 627 1108 2112 2039 1069 781
11.2 6 989 2673 5339 5767 2855 1638
11.1 12 1263 4986 15732 20000 11415 5749
11 3 802 5053 20118 27628 14086 9813
24 3942 14350 43887 55905 29685 18078
here is the former table
20 21 22 23 24 25 26
11.9 1 4 3
11.8 1 15 26 8
11.7 31 50 8 13 8
11.6 1 38 50 40 34 10 1
11.5 46 99 138 102 75 12
11.4 130 301 332 251 156 49
11.3 1 627 1102 1763 1818 1055 539
11.2 2 989 2670 4900 5376 2839 1176
11.1 12 1263 4976 13961 18977 11389 3407
11 3 802 5042 17835 25694 14006 6178
20 3942 14320 38988 52265 29538 11362 150435
As we can see, the new 11.7 came in the 23 clues area.
Next investigation will continue also in the 22 23 clues area, but most will be done in the 24-26 clues.
This should not change the tendency seen here with the pic SE ratings in the 22-23 clues area.
As already said, this is partly due to the Sudoku Explainer rating rules,
we have a direct effect of the number of candidates on the rating, not easy to quantify.