# Potential Hardest Sudokus¶

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 01 May 2019) is ph_1901.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_1901.zip

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.