The hardest sudokus

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

The hardest sudokus

Postby ravel » Sun May 28, 2006 8:09 pm

[Edit 2007-04-15]
As i mentioned below, i stopped to update this page in January. If you are interested in recent results, please look at JPF's list and the following contributions in this thread. (See also gsf's list there.) You can find my own top ratings for these puzzles here, but its no secret, that i am not fully satisfied with them (i think, if long subnets are needed for a "short" solution, this should be rated higher). Nevertheless i do not intend to upgrade my program in the next months. My last top list can be found here.
If you are interested, howto get the ratings of Sudoku Explainer (ER), gsf's pogram and suexrat, look here.

*******
Sudoku ratings are never good enough, not even for easy puzzles (i often spot a hidden pair before a naked single, but but no one rates the pair easier).
Ratings of very hard puzzles normally depend on, what techniques a solver program has implemented and in which order they are applied.
My method is rather simple and has many weaknesses, but gave some rather good results. Only having implemented a few techniques, it tries to find a minimum number of "brute force" steps, i.e. an elimination by contradiction (after "trying" a number). This can be (equivalent to) an xy-wing or coloring or (mostly) a monster chain (more detailed here). Shorter solutions may exist, also with my basic techniques. So the only thing i can say for sure is, that all puzzles below can be solved with the given number of monster chains using singles, tuples, box interactions, x-wings and UR type 1. All other puzzles i scanned, could be solved with at most 7 brute force steps.

[Edit 2006-10-16:]
Much has happened in the 5 months since i started this thread. 2 new (public) ratings become popular (ER and gsfr, additional to suexrat9) and many new toughies have been found. The list grew from 123 to 322 puzzles and the former number 1 is number 17 now.
Then i realised, that it was rather easy to generate puzzles with more than 3 steps and decided to raise the limit from 4 to 8 (in 6 runs of my program). So the list was reduced to 48 puzzles (5 new ones added) and only 2 of over 100 from the top1465 remained.
From a recent test at most one in a million random puzzles is expected to qualify.

[Edit 2006-11-04:]
The puzzles are getting too hard for my program, Arto's Etana (or Escargot) was the first puzzle, which could not be solved by it (and Sudoku Explainer 1.1 either).

[Edit 2006-12-06:]
These puzzles are too hard for my program to provide a rating. They are ranked after the Sudoku Explainer rating ER [in brackets the gsf rating]:

[Edit 2006-12-17:]
Time to stop to update this list, before dml will send hundreds of new toughies i would have to enter:) So this is my final list in this thread. First i show the hardest 29 puzzles order by ER and (for those with same ER) gsf rating. Th ER is between 10.7 (first 5 puzzles) to 10.5.
Then a list with puzzles beyond RMS follows in same order, a top list for gsf ratings, a top list for gsf ratings without using backdoors (-X option) and the list with RMS ratings, where the puzzles can be found in the list at the end by the line number.

[Edit 2006-12-21:] Removed isomorphic puzzles.
[Edit 2006-12-22:] Reorganized the RMS rated list. And added this puzzle (posted yesterday) here at the top, which is the first one, that could not be rated by gsf's program with the multicoloring proposition
But please note, that i do not intend to update the hardest list here in the future. Until a new thread for this is started, please watch the postings here.

0: Ocean: Christmas present for gsf
Code: Select all
 +-------+-------+-------+
 | . . . | . . 1 | . 2 . |
 | 3 . . | . 4 . | 5 . . |
 | . . . | 6 . . | . . 7 |
 +-------+-------+-------+
 | . . 2 | . . . | . . 6 |
 | . 5 . | . 3 . | . 8 . |
 | 4 . . | . . . | 9 . . |
 +-------+-------+-------+
 | 9 . . | . . 2 | . . . |
 | . 8 . | . 5 . | 4 . . |
 | . . 1 | 7 . . | . . . |
 +-------+-------+-------+


Code: Select all
1: dml11
 +-------+-------+-------+
 | 1 . . | . 5 . | . . . |
 | . . 6 | . . 9 | . . . |
 | . 8 . | 2 . . | . . 4 |
 +-------+-------+-------+
 | . 4 . | . 3 . | . . 8 |
 | . . 7 | . . . | . 6 . |
 | 9 . . | . . . | 1 . . |
 +-------+-------+-------+
 | . 3 . | 8 . . | . . 2 |
 | . . . | . . 4 | . 5 . |
 | . . . | . 1 . | 7 . . |
 +-------+-------+-------+
Solution by gurth here, isomorphic dml155 here
Code: Select all
2: dml12
 +-------+-------+-------+
 | . . 3 | 9 . . | . . . |
 | . 4 . | . 7 . | . . 1 |
 | 6 . . | . . 2 | . . . |
 +-------+-------+-------+
 | 8 . . | . . . | . . 2 |
 | . 7 . | . 5 . | . 3 . |
 | . . 9 | . . . | 4 . . |
 +-------+-------+-------+
 | 2 . . | . . 1 | . . 8 |
 | . . . | . 4 . | . 5 . |
 | . . . | 6 . . | 9 . . |
 +-------+-------+-------+
3: dml15
 +-------+-------+-------+
 | . . 3 | 2 . . | . . . |
 | . 4 . | . 9 . | . . . |
 | 6 . . | . . 8 | . 1 . |
 +-------+-------+-------+
 | 2 . . | . . . | . . 3 |
 | . 1 . | . . 6 | . 4 . |
 | . . 7 | . . . | 5 . . |
 +-------+-------+-------+
 | . . . | . . 1 | . . 2 |
 | . 9 . | . 4 . | . 6 . |
 | . . . | 5 . . | 7 . . |
 +-------+-------+-------+
4: dml6
 +-------+-------+-------+
 | 9 . . | . . 4 | . . . |
 | . 8 . | . 2 . | . 3 . |
 | . . 5 | 7 . . | . . . |
 +-------+-------+-------+
 | . . 1 | . . . | . . 4 |
 | . 6 . | . 8 . | . 7 . |
 | 3 . . | . . . | 5 . . |
 +-------+-------+-------+
 | . . . | . . 5 | . . 1 |
 | . 7 . | . 3 . | . 9 . |
 | . . . | 6 . . | 2 . . |
 +-------+-------+-------+
Solved by gurth here.
Code: Select all
5: dml20
 +-------+-------+-------+
 | 1 . . | . 5 . | . 8 . |
 | . . . | . . 9 | . . 3 |
 | . . . | 2 . . | 4 . . |
 +-------+-------+-------+
 | . . 4 | . . . | 9 . . |
 | . 3 . | . . . | . . 7 |
 | 8 . . | 6 . . | . 5 . |
 +-------+-------+-------+
 | . . 2 | 8 . . | . 6 . |
 | 5 . . | . 1 . | . . . |
 | . 7 . | . . 4 | . . . |
 +-------+-------+-------+
6: dml1
 +-------+-------+-------+
 | 4 . . | . . 9 | . . . |
 | . 3 . | . 1 . | . 2 . |
 | . . 6 | 7 . . | . . . |
 +-------+-------+-------+
 | . . 1 | . . . | . . 4 |
 | . 5 . | 2 . . | . 7 . |
 | 8 . . | . . . | 6 . . |
 +-------+-------+-------+
 | . . . | . . 4 | . . 8 |
 | . 7 . | . 3 . | . 1 . |
 | . . . | 5 . . | 9 . . |
 +-------+-------+-------+
Solved by gurth here.
Code: Select all
7: dml10
 +-------+-------+-------+
 | . . 3 | 1 . . | . . . |
 | . 4 . | . 6 . | . . . |
 | 7 . . | . . 8 | . . 2 |
 +-------+-------+-------+
 | 5 . . | . . 7 | . . 3 |
 | . 1 . | . . . | . 4 . |
 | . . 9 | . . . | 6 . . |
 +-------+-------+-------+
 | . . . | . . 5 | . . 7 |
 | . . . | . 9 . | . 1 . |
 | 2 . . | 3 . . | 8 . . |
 +-------+-------+-------+
8: dml13
 +-------+-------+-------+
 | . . 2 | 1 . . | 7 . . |
 | . 3 . | . 5 . | . . . |
 | 4 . . | . . 6 | . . . |
 +-------+-------+-------+
 | . . 1 | 9 . . | . . 2 |
 | . 8 . | . . . | . 3 . |
 | 7 . . | . . . | 4 . . |
 +-------+-------+-------+
 | . . . | . . 8 | . . 6 |
 | . . . | . 3 . | . 5 . |
 | 9 . . | 4 . . | 1 . . |
 +-------+-------+-------+
9: (184) dml3
 +-------+-------+-------+
 | 8 . . | . . 3 | . . . |
 | . 7 . | . 6 . | . 9 . |
 | . . 4 | 5 . . | . . . |
 +-------+-------+-------+
 | . . 5 | . . . | . . 7 |
 | . 2 . | . . 9 | . 3 . |
 | 1 . . | . . . | 8 . . |
 +-------+-------+-------+
 | . . . | . . 7 | . . 1 |
 | . 3 . | . 2 . | . 6 . |
 | . . . | 4 . . | 5 . . |
 +-------+-------+-------+
Solved by gurth here.
Code: Select all
10: dml16
 +-------+-------+-------+
 | . . 2 | 6 . . | . . . |
 | . 3 . | . 8 . | . . . |
 | 5 . . | . . 9 | 1 . . |
 +-------+-------+-------+
 | . . 6 | . . . | . . 2 |
 | . 8 . | . . . | . 3 . |
 | 7 . . | . . 1 | 4 . . |
 +-------+-------+-------+
 | . . . | . . 4 | . . 5 |
 | . 1 . | . 2 . | . 8 . |
 | . . . | 7 . . | 9 . . |
 +-------+-------+-------+
11: dml4
 +-------+-------+-------+
 | 8 . . | . . 3 | . . . |
 | . 7 . | . 6 . | . 9 . |
 | . . 4 | 5 . . | . . . |
 +-------+-------+-------+
 | . . 2 | . . . | . . 4 |
 | . 3 . | . . 1 | . 7 . |
 | 5 . . | . . . | 8 . . |
 +-------+-------+-------+
 | . . . | . . 9 | . . 1 |
 | . 6 . | . 7 . | . 3 . |
 | . . . | 2 . . | 5 . . |
 +-------+-------+-------+
12: Ocean #5/gold list
 +-------+-------+-------+
 | . . 1 | . . 2 | . . . |
 | . 3 . | . 4 . | . 5 . |
 | 6 . . | 7 . . | 8 . . |
 +-------+-------+-------+
 | . . 6 | . . . | . . 7 |
 | . 1 . | . . . | . 3 . |
 | 9 . . | . . . | 6 . . |
 +-------+-------+-------+
 | . . 7 | . . 1 | . . 8 |
 | . 4 . | . 3 . | . 2 . |
 | . . . | 5 . . | 9 . . |
 +-------+-------+-------+

Solved by gurth here.
Code: Select all
13: dml19
 +-------+-------+-------+
 | . . 2 | 4 . . | . . 6 |
 | . 3 . | . 1 . | . . . |
 | 5 . . | . . 8 | . . . |
 +-------+-------+-------+
 | . . 7 | . . . | . . 2 |
 | . 1 . | . . . | . 3 . |
 | 9 . . | 6 . . | 4 . . |
 +-------+-------+-------+
 | . . . | . . 7 | . . 1 |
 | . . . | . 9 . | . 8 . |
 | 4 . . | 2 . . | 5 . . |
 +-------+-------+-------+
14: dml22
 +-------+-------+-------+
 | . . 3 | 5 . . | 1 . . |
 | . 4 . | . 8 . | . . . |
 | 6 . . | . . 9 | . . . |
 +-------+-------+-------+
 | 8 . . | . . . | . . 2 |
 | . 5 . | 7 . . | . 3 . |
 | . . 1 | . . . | 4 . . |
 +-------+-------+-------+
 | . . . | . . 6 | . . 9 |
 | . . . | . 2 . | . 8 . |
 | . 7 . | 1 . . | 5 . . |
 +-------+-------+-------+
15: dml161
 +-------+-------+-------+
 | 1 . . | 3 . . | . . . |
 | . 2 . | . 9 . | 4 . . |
 | . . 5 | . . 7 | . . . |
 +-------+-------+-------+
 | 8 . . | . . . | 1 . . |
 | . 4 . | . . . | . 2 . |
 | . . 7 | . 6 . | . . 3 |
 +-------+-------+-------+
 | . . . | 4 . . | 8 . . |
 | . . . | . 2 . | . 9 . |
 | . . 6 | . . 5 | . . 7 |
 +-------+-------+-------+
16: dml26
 +-------+-------+-------+
 | . . 2 | 9 . . | . . . |
 | . 3 . | . 8 . | . . . |
 | 4 . . | . . 1 | . 5 . |
 +-------+-------+-------+
 | . . 9 | . 7 . | . . 2 |
 | . 1 . | . . . | . 3 . |
 | 6 . . | . . . | 4 . . |
 +-------+-------+-------+
 | . . . | . . 3 | . . 1 |
 | . . . | . 6 . | . 8 . |
 | . . 7 | 2 . . | 9 . . |
 +-------+-------+-------+
17: dml31
 +-------+-------+-------+
 | . 2 . | . . . | 6 . . |
 | 4 . . | . 8 . | . . 7 |
 | . . 9 | . . . | . 1 . |
 +-------+-------+-------+
 | . . 5 | . . 6 | . . . |
 | 3 . . | . 4 . | 9 . . |
 | . 1 . | 2 . . | . . . |
 +-------+-------+-------+
 | . . . | 7 . . | . . 4 |
 | . . . | . . 1 | . 5 . |
 | 8 . . | . 9 . | 3 . . |
 +-------+-------+-------+
18: dml33
 +-------+-------+-------+
 | . . 3 | 7 . . | . . . |
 | . 4 . | . 8 . | . 2 . |
 | 6 . . | . . 1 | . . . |
 +-------+-------+-------+
 | 5 . . | . . . | . . 3 |
 | . 2 . | 9 . . | . 4 . |
 | . . 1 | . . . | 6 . . |
 +-------+-------+-------+
 | . . . | . . 6 | . . 5 |
 | . . . | . 2 . | . 9 . |
 | . 7 . | 4 . . | 8 . . |
 +-------+-------+-------+
19: dml34
 +-------+-------+-------+
 | . . 3 | 9 . . | 1 . . |
 | . 4 . | . 7 . | . . . |
 | 6 . . | . . 2 | . . . |
 +-------+-------+-------+
 | 8 . . | . . . | . . 3 |
 | . 2 . | . 5 . | . 4 . |
 | . . 1 | . . . | 6 . . |
 +-------+-------+-------+
 | . . . | . . 6 | . . 2 |
 | . 5 . | . 8 . | . 7 . |
 | . . . | 3 . . | 9 . . |
 +-------+-------+-------+
20: dml35
 +-------+-------+-------+
 | . . 2 | 9 . . | . . 1 |
 | . 3 . | . 4 . | . . . |
 | 5 . . | . . 6 | . . . |
 +-------+-------+-------+
 | . . 8 | . . . | . . 2 |
 | . 4 . | . . . | . 3 . |
 | 9 . . | 7 . . | 5 . . |
 +-------+-------+-------+
 | 6 . . | . . 1 | . . 9 |
 | . . . | . 3 . | . 4 . |
 | . . . | 2 . . | 7 . . |
 +-------+-------+-------+
21: dml44
 +-------+-------+-------+
 | . . 3 | 2 . . | . . . |
 | . 4 . | . 5 . | . . . |
 | 7 . . | . . 8 | . 1 . |
 +-------+-------+-------+
 | 9 . . | . . . | . . 3 |
 | . 6 . | . 7 . | . 4 . |
 | . . 2 | . . . | 5 . . |
 +-------+-------+-------+
 | . . . | . . 3 | . . 9 |
 | 8 . . | . 4 . | . 6 . |
 | . . . | 1 . . | 2 . . |
 +-------+-------+-------+
22: dml46
 +-------+-------+-------+
 | . . 3 | 2 . . | . . . |
 | . 4 . | . 9 . | . 1 . |
 | 6 . . | . . 7 | . . . |
 +-------+-------+-------+
 | 8 . . | . . . | . . 3 |
 | . 1 . | . . 6 | . 4 . |
 | . . 2 | . . . | 5 . . |
 +-------+-------+-------+
 | . . . | . . 1 | . . 7 |
 | . 9 . | . 4 . | . 6 . |
 | . . . | 5 . . | 8 . . |
 +-------+-------+-------+
23: dml50
 +-------+-------+-------+
 | . 2 . | 4 . . | . . . |
 | . . 6 | . 8 . | 1 . . |
 | 7 . . | . . 3 | . . . |
 +-------+-------+-------+
 | . . . | . 6 . | 3 . . |
 | . . . | 2 . . | . . 5 |
 | . 9 . | . . 7 | . 4 . |
 +-------+-------+-------+
 | 3 . . | . . . | 8 . . |
 | . . 1 | . . . | . 9 . |
 | . 4 . | 5 . . | . . 2 |
 +-------+-------+-------+
24: Ocean #6/gold list
 +-------+-------+-------+
 | . . 1 | . . 2 | . . . |
 | . 3 . | . 4 . | . 5 . |
 | 6 . . | 7 . . | 8 . . |
 +-------+-------+-------+
 | . . 8 | . . . | . . 7 |
 | . 1 . | . . . | . 4 . |
 | 9 . . | . . . | 5 . . |
 +-------+-------+-------+
 | . . 4 | . . 1 | . . 8 |
 | . 2 . | . 3 . | . 1 . |
 | . . . | 6 . . | 9 . . |
 +-------+-------+-------+
25: dml52
 +-------+-------+-------+
 | . . 2 | 9 . . | . . . |
 | . 3 . | . 7 . | . . . |
 | 5 . . | . . 4 | 1 . . |
 +-------+-------+-------+
 | . . 8 | . . . | . . 2 |
 | . 9 . | . . . | . 3 . |
 | 6 . . | 5 . . | 4 . . |
 +-------+-------+-------+
 | . . . | . . 3 | . . 8 |
 | . . . | . 6 . | . 7 . |
 | 1 . . | 2 . . | 5 . . |
 +-------+-------+-------+
26: Ocean #2/gold list
 +-------+-------+-------+
 | . . 1 | . . 2 | . . . |
 | . 3 . | . 4 . | . 5 . |
 | 5 . . | 6 . . | 7 . . |
 +-------+-------+-------+
 | . . 7 | . . . | . . 6 |
 | . 1 . | . . . | . 2 . |
 | 8 . . | . . . | 4 . . |
 +-------+-------+-------+
 | . . 6 | . . 1 | . . 9 |
 | . 4 . | . 3 . | . 1 . |
 | . . . | 7 . . | 8 . . |
 +-------+-------+-------+
27: Ocean #3/gold list
 +-------+-------+-------+
 | . . 1 | . . 2 | . . . |
 | . 3 . | . 4 . | . 5 . |
 | 5 . . | 6 . . | 7 . . |
 +-------+-------+-------+
 | . . 7 | . . . | . . 6 |
 | . 1 . | . . . | . 3 . |
 | 8 . . | . . . | 9 . . |
 +-------+-------+-------+
 | . . 9 | . . 3 | . . 2 |
 | . 2 . | . 1 . | . 4 . |
 | . . . | 7 . . | 8 . . |
 +-------+-------+-------+
28: Tarek Mitrale
 +-------+-------+-------+
 | 4 . . | . . . | 3 . . |
 | . 1 . | 5 . . | . 2 . |
 | . . 6 | . 8 . | . . 9 |
 +-------+-------+-------+
 | . 2 . | . . . | . 5 . |
 | . . 7 | . 9 . | . . 8 |
 | . . . | . . 4 | 6 . . |
 +-------+-------+-------+
 | 3 . . | . . 7 | . . . |
 | . 5 . | 1 . . | . . . |
 | . . 8 | . 6 . | . . . |
 +-------+-------+-------+
29: Ocean Anemone
 +-------+-------+-------+
 | . . 1 | . . 2 | . . . |
 | . 3 . | . 4 . | . 5 . |
 | 5 . . | 6 . . | 3 . . |
 +-------+-------+-------+
 | . . 7 | . . . | . . 6 |
 | . 8 . | . . . | . 4 . |
 | 2 . . | . . . | 1 . . |
 +-------+-------+-------+
 | . . 6 | . . 9 | . . 7 |
 | . 4 . | . 7 . | . 8 . |
 | . . . | 5 . . | 9 . . |
 +-------+-------+-------+
Solved by gurth here.

This is the listed of puzzles beyond RMS ranked by ER/gsfr:

10.7 99993 100013 100050000006009000080200004040030008007000060900000100030800002000004050000010700 dml11
10.7 99984 099994 003900000040070001600002000800000002070050030009000400200001008000040050000600900 dml12
10.7 99964 099974 003200000040090000600008010200000003010006040007000500000001002090040060000500700 dml15
10.7 99955 099965 900004000080020030005700000001000004060080070300000500000005001070030090000600200 dml6
10.7 99954 099994 100050080000009003000200400004000900030000007800600050002800060500010000070004000 dml20
10.6 99995 100015 400009000030010020006700000001000004050200070800000600000004008070030010000500900 dml1
10.6 99994 100004 003100000040060000700008002500007003010000040009000600000005007000090010200300800 dml10
10.6 99984 100004 002100700030050000400006000001900002080000030700000400000008006000030050900400100 dml13
10.6 99972 099982 800003000070060090004500000005000007020009030100000800000007001030020060000400500 dml3
10.6 99963 100003 002600000030080000500009100006000002080000030700001400000004005010020080000700900 dml16
10.6 99961 099971 800003000070060090004500000002000004030001070500000800000009001060070030000200500 dml4
10.6 99960 099970 001002000030040050600700800006000007010000030900000600007001008040030020000500900 Ocean #5/gold list
10.6 99954 099995 002400006030010000500008000007000002010000030900600400000007001000090080400200500 dml19
10.6 99954 099964 003500100040080000600009000800000002050700030001000400000006009000020080070100500 dml22
10.6 99953 099993 100300000020090400005007000800000100040000020007060003000400800000020090006005007 dml161
10.6 99943 099963 002900000030080000400001050009070002010000030600000400000003001000060080007200900 dml26
10.6 99934 099974 020000600400080007009000010005006000300040900010200000000700004000001050800090300 dml31
10.6 99932 099995 003700000040080020600001000500000003020900040001000600000006005000020090070400800 dml33
10.6 99931 099982 003900100040070000600002000800000003020050040001000600000006002050080070000300900 dml34
10.6 99931 099941 002900001030040000500006000008000002040000030900700500600001009000030040000200700 dml35
10.6 99922 099975 003200000040050000700008010900000003060070040002000500000003009800040060000100200 dml44
10.6 99921 099998 003200000040090010600007000800000003010006040002000500000001007090040060000500800 dml46
10.6 99910 099920 020400000006080100700003000000060300000200005090007040300000800001000090040500002 dml50
10.6 99909 099919 001002000030040050600700800008000007010000040900000500004001008020030010000600900 Ocean #6/gold list
10.6 99902 099993 002900000030070000500004100008000002090000030600500400000003008000060070100200500 dml52
10.6 99859 099859 001002000030040050500600700007000006010000020800000400006001009040030010000700800 Ocean #2/gold list
10.6 99527 099963 001002000030040050500600700007000006010000030800000900009003002020010040000700800 Ocean #3/gold list
10.6 99337 099981 400000300010500020006080009020000050007090008000004600300007000050100000008060000 Tarek Mitrale
10.6 99325 099985 001002000030040050500600300007000006080000040200000100006009007040070080000500900 Ocean Anemone
10.5 99983 099983 800003000070060090004500000005000004090002070100000800000009003020010060000700500 dml2
10.5 99971 099971 100900000020050000004006003600000100080000020003070004900100800000030050000004006 dml157
10.5 99958 099958 002100000030080000500006400007000001090000020600005300000009008000020070400300600 dml18
10.5 99957 099987 400009000050010030006700000007000008030000010900002400000008007010050060000400200 dml5
10.5 99954 099984 100006000020070030005900000009005001070000020600000400300001006000040070000200800 dml21
10.5 99945 099975 100006080050700000009030000007000050030000002600001400000040900800005060000200007 dml25
10.5 99943 099953 003000009400000100080002060200008400005300000060070000010004800000090070000500003 dml27
10.5 99942 099977 003400600050009000700020000200008070000030001000500900004000020800010003060000500 dml28
10.5 99940 100001 000400600000080003009002010001005040030000800600000007040900020800070000005001000 dml30
10.5 99933 100003 100009000020070000004500030008000001030400020900000500000001007000060040005300800 dml32
10.5 99928 100008 002900000030040010500006000008700002010000030400000500000002006000080040009300700 dml37
10.5 99927 099977 002600100030080000500009000006500002070000030100000400000003009000070080400100600 dml38
10.5 99925 099955 002600000030080000500009010004000002070010030900000500000005006100070090000200400 dml40
10.5 99924 099976 020400009006080000700003000004000700500060030010000002300005800000900004000010060 dml41
10.5 99920 099920 100009005020080000003400000009000001080070020600000300000005008000010070040600900 dml47
10.5 99920 099920 100007090030020008009600500005300900010080002600004000300000010040000007007000300 ArtoI's AI Etana(Escargot
10.5 99918 099921 100007000020080000004300500005400001080000020900000300000005007000020060003100900 dml48
10.5 99909 099909 002900000030040100500006000009000002060005030800000400000008006000030070001200900 dml51
10.5 99851 099984 001002000030040050600700800006000007010000020900000500003001006040050030000800900 Ocean #4/gold list
10.5 99839 099869 100007000040050020006800000005090003020000040700000100000003005090040060000100800 dml9
10.4 99961 099961 002900000030080000400005001001004002070000030600000500005002006000070080000300900 dml17
10.4 99960 099980 060900003500004020000080400800000050003000700090000001001050000070300009900002040 Tarek Gyroscope #1
10.4 99951 099951 800003000070060090004500000005000004060007080200000100000008002030090060000100500 dml7
10.4 99948 099958 900004000050080070001200000002600009030000040700000500000009002080050030000700600 dml8
10.4 99922 099962 100007000020030500004900000008006001090000020700000300000001008030050060000400700 dml45
10.4 99911 099921 020050009006100000700003000030090050000600100000008002005000700090020004800000060 dml49
10.4 99900 099900 100009000020060000003500400005000001060080020700000300080001009000020060000400700 dml53
10.4 99900 099900 003700010040080000500009000600000003020100040007000500000400007000060020800005900 dml54
10.4 99687 099859 001002000030040010500600700007000006010000030800000900002007001040050020000900800 Ocean #1/gold list
10.3 99850 099871 100900050000080400030000006400002100050040000000300007500700090060030200008009001 Mauricio #12
10.3 99839 099869 001002000030040050600700800008000007010000030900000500002001006040050020000600900 Ocean Extreme Jade puzzle
10.1 99848 099858 700009200050080000006400007001000006040000030900000700800002500000060070003100004 Tarek Fluid Drive #43
10.1 99820 099840 000400020600090008007005100400001200050040030006700000004900050100080400030000002 Mauricio #13


The top 23 ranked by gsf (>99950)

99995 10.6 100015 400009000030010020006700000001000004050200070800000600000004008070030010000500900 dml1
99994 10.6 100004 003100000040060000700008002500007003010000040009000600000005007000090010200300800 dml10
99993 10.7 100013 100050000006009000080200004040030008007000060900000100030800002000004050000010700 dml11
99984 10.7 099994 003900000040070001600002000800000002070050030009000400200001008000040050000600900 dml12
99984 10.6 100004 002100700030050000400006000001900002080000030700000400000008006000030050900400100 dml13
99983 10.5 099983 800003000070060090004500000005000004090002070100000800000009003020010060000700500 dml2
99972 10.6 099982 800003000070060090004500000005000007020009030100000800000007001030020060000400500 dml3
99971 10.5 099971 100900000020050000004006003600000100080000020003070004900100800000030050000004006 dml157
99964 10.7 099974 003200000040090000600008010200000003010006040007000500000001002090040060000500700 dml15
99963 10.6 100003 002600000030080000500009100006000002080000030700001400000004005010020080000700900 dml16
99961 10.6 099971 800003000070060090004500000002000004030001070500000800000009001060070030000200500 dml4
99961 10.4 099961 002900000030080000400005001001004002070000030600000500005002006000070080000300900 dml17
99960 10.6 099970 001002000030040050600700800006000007010000030900000600007001008040030020000500900 Ocean #5/gold list
99960 10.4 099980 060900003500004020000080400800000050003000700090000001001050000070300009900002040 Tarek Gyroscope #1
99958 10.5 099958 002100000030080000500006400007000001090000020600005300000009008000020070400300600 dml18
99957 10.5 099987 400009000050010030006700000007000008030000010900002400000008007010050060000400200 dml5
99955 10.7 099965 900004000080020030005700000001000004060080070300000500000005001070030090000600200 dml6
99954 10.7 099994 100050080000009003000200400004000900030000007800600050002800060500010000070004000 dml20
99954 10.6 099995 002400006030010000500008000007000002010000030900600400000007001000090080400200500 dml19
99954 10.6 099964 003500100040080000600009000800000002050700030001000400000006009000020080070100500 dml22
99954 10.5 099984 100006000020070030005900000009005001070000020600000400300001006000040070000200800 dml21
99953 10.6 099993 100300000020090400005007000800000100040000020007060003000400800000020090006005007 dml161
99951 10.4 099951 800003000070060090004500000005000004060007080200000100000008002030090060000100500 dml7


The top 9 for gsfr -X (no backdoors used):

100015 10.6 99995 400009000030010020006700000001000004050200070800000600000004008070030010000500900 dml1
100013 10.7 99993 100050000006009000080200004040030008007000060900000100030800002000004050000010700 dml11
100008 10.5 99928 002900000030040010500006000008700002010000030400000500000002006000080040009300700 dml37
100007 10.5 99927 003050000400009000080100060010000070005000002900004300070060090000200001000003800 dml39
100004 10.6 99994 003100000040060000700008002500007003010000040009000600000005007000090010200300800 dml10
100004 10.6 99984 002100700030050000400006000001900002080000030700000400000008006000030050900400100 dml13
100003 10.6 99963 002600000030080000500009100006000002080000030700001400000004005010020080000700900 dml16
100003 10.5 99933 100009000020070000004500030008000001030400020900000500000001007000060040005300800 dml32
100001 10.5 99940 000400600000080003009002010001005040030000800600000007040900020800070000005001000 dml30


This is the list of puzzles that could be rated ranked by RMS and ER:

23 10.0 001002000030040050500600700007000006010000080900000200002001004080030010000900500 Ocean #7/gold list
23 10.0 001002000030040050500600700007000006040000080900000200002001003080030010000700500 Ocean #8/gold list
22 10.6 900001800060030000002500007009000006050000020400000300300008100000040080007900005 Tarek Fluid Drive #8
20 09.8 600001900080030000001700002002000007050000010400000300300009600000040080008200005 Tarek Fluid Drive #1
20 09.4 001000200030000040400050006000102000060070030000809000300000005050040060008000900 Ocean 1#vert.symm
19 09.9 000000070060010004003400200800003050002900700040080009020060007000100900700008060 ArtoI AI Killer Application
19 09.9 100000900000040060050800002080700009600030010000009200040000000002005700300060008 ravel #1 of 0.3 mio from pattern test
18 10.0 001002000030040050500600700007000008010000030900000600008003001040010020000500900 Ocean #9/gold list
18 10.0 100900700020060000003005008400003080000600002007050900300000001090500000008020040 Mauricio #11
18 09.4 000300020000040600000001007600008001050090000009200030020000000400006008003700050 Tarek #2/Daemonicus
17 10.0 000001002010020030400500000004000006070030010800000900500008000000010070006400500 Ocean #1/M21/D21
17 10.0 400700000020009080005010003600100090030006002001050800000060008009000030700001400 Mauricio #9
17 09.9 001002000030040050600700800005000001090000040800000300004001002000050060000900700 Ocean M21 #1/2
17 09.5 001002000030040050600700800005000009060000040700000300009003001040050000000800700 Ocean M21 #2/2
16 10.0 001002000030040050500600700007000006010000080900000200003007001080010040000500900 Ocean Coral
16 10.0 300008700050020000009600001006000003040000090700000200500007100000080030001900004 Tarek Fluid Drive #12
16 09.9 600009800050030000002500007007000009010000020400000300300008600000040080009700001 Tarek Fluid Drive #2
16 09.9 001400006040050020900006300400000700050000080006000009008700003000080010300009400 Mauricio #10
15 10.0 000600700020050080003001009900002010050060000008400003400800090000006800002010007 Mauricio #5
15 09.9 100005600060030000002900007007000009080000020400000300300009100000040060005700008 Tarek Fluid Drive #3
15 09.9 200007600050010000003800009008000005040000030700000100500006900000070020009300004 Tarek Fluid Drive #18
15 09.9 200005800000040030010700005050100009400080060000009300060000000007001900800020003 ravel #2 of 0.3 mio from pattern test
15 09.8 001000200030040050600000007000103000080000030000604000200000006040050080007000100 Ocean's BB
15 09.4 001000002030040000500600300004007001000080030900200600000008009070020040200100800 Ocean #11/18
15 09.4 001002000020030000400100500006000001030000070800000600002009004070080030600500800 Ocean Mjolnir #6
14 10.0 001002000030040050500600700007000006080000040900000100004008003020030080000700900 Ocean #10/gold list
14 10.0 001002000030040050500600700008000006010000020900000500002001004070030010000800600 Ocean #11/gold list
14 09.9 900006700040030000007100004008000006020010080600004900100002008050070020000300600 JPF #1/100b
14 09.9 001002000020030040400500600006000005010000020700000800008001006030040090000800700 Ocean #12/gold list
14 09.8 000001002030040050600700000005000004080020090700000300100004000000050080009600700 Ocean #14/M21/D21
14 09.5 001002000020030000400500600006000007010000080900000500007008003030090010500700400 Ocean Mjolnir #1
14 09.4 000001002030020040500600000003000007010080020400700500600004000000060010007300900 Ocean #1/M22/D22
14 09.4 006003000090010080300500000003009001020030050500800900007004005030090020400000700 JPF # 16/163
13 09.9 700003900090050000008600001001000002020000080500000300900004700000030050006100004 Tarek Fluid Drive #41
13 09.8 700006100050080000002900003003000004080000060200000700600001800000020050009300001 Tarek Fluid Drive #33
13 09.5 001002003020040010500600700006000004080000090300000200003001009090060020700800500 Ocean #1/empty box
13 09.4 300009400070010000009500002008000006050000090400000100600004300000060020002800005 Tarek Fluid Drive #23
13 09.4 900006800010030000006500007007000009050000060800000300100008900000040020002700005 Tarek Fluid Drive #30
13 09.4 001002000030040000500100600007000003040000080900000100002003006080050040100700900 Ocean Mjolnir #3
12 09.9 001002003020040010500600000000007001030080020400500600005009002070000080300000900 Ocean #7/18
12 09.8 700008500040090000002600001001000003080000020900000400500003700000040050006100008 Tarek Fluid Drive #39
12 09.7 100000002020030040005000600000307000040010030000805000008000500030020090600000001 Ocean #1/4 ER9.7
12 09.5 000001002030040050600200000005000007070030040200000600100008000000070090004600800 Ocean #11/M21/D21
12 09.5 001002000020030040400500600006000005030000070800000100002005009070010030000900800 Ocean #9/empty box
12 09.5 300005400020070000005600009009000008060000010500000300700004200000030080008100006 Tarek Fluid Drive #14
12 09.4 000500700020060040006001003900200400030000010007003008100700600050040070009008000 tso #7/31
12 09.4 000001002030020040500600000007000003010040080600000500900006000000070030008500900 Ocean #8/M21/D21
12 09.4 200006800060070000009100004003000005010000030600000700700008200000090080005400001 Tarek Fluid Drive #9
12 09.4 400005700060020000009300008008000005010000090700000600100002400000060030005800001 Tarek Fluid Drive #13
12 09.4 001002000030040000500600700007000008020000090100000500003008004040010060600500100 Ocean Mjolnir #5
12 09.3 001002003020040010500600200000007000080010020400500600005009008070000040800000900 Ocean #16/18
11 10.4 001002000030040050004700800006000007010000030900000600007001008040030020060500900 RW - variation of Ocean #5/gold list
11 09.9 001000002030040000500600300007008001060010030100900800005009004080050070200100900 Ocean #3/3
11 09.5 000001000010020030400500100006007003080030010200900400009000002070080060800300500 Ocean #1/3
11 09.5 000001002030040050600700000005000004070080030200000600100006000000050070003900800 Ocean #13/M21/D21
11 09.5 001002000030040050500600700007000008040000090600000100003008002090060040000100500 Ocean #11/empty box
11 09.5 001000200030000040500060007000108000040070050000209000600000005070080060002000900 Ocean #3vert/symm.
11 09.5 100004600060030000007500009009000002050000070400000300300008100000040020008200005 Tarek Fluid Drive #5
11 09.5 600007400080010000009300006002000005030000020100000700800004600000070010005900003 Tarek Fluid Drive #40
11 09.5 001002000030040000500100600007000008090000040200000100003006005040090080100700200 Ocean Mjolnir #2
11 09.4 000600090000030500000007008300008007040090000001200060090000000500002003006400010 Tarek #16/Daemonicus
11 09.4 400009700050080000002600001001000006070000090200000300300007400000020030006800005 Tarek Fluid Drive #16
11 09.4 300006800070090000002100004004000009010000020800000500900008300000050060003700001 Tarek Fluid Drive #34
11 09.4 009070000050200060800004100100008700002000003060000040000050004000600090000001800 Tarek Pincer 1
11 09.3 000001002020030040500600000007000008090040020600800500900008000000090030006700100 Ocean #5/D22
11 09.2 005000009020030040000600800004900001000040060700008900003001008070060090500200600 JPF #70/100
11 09.2 001002000020030000300400500004000001060000070800000300002006007070080060400500900 Ocean Mjolnir #11
10 09.9 000100020000030600000004003300006004050020000001700080010000000600009008002500070 Tarek #18/Daemonicus
10 09.9 700002900050060000008900004004000003090000050100000200600001800000020070003400009 Tarek Fluid Drive #32
10 09.8 700000400020070080003008009000500300060020090001007006000300900030040060009001005 top1465 #77 "the toughest known"
10 09.8 001002003020040000500600200007008001030000020100900600009007004080000050000100700 Ocean #6/18
10 09.8 100000500020060080003004007200008001060900000008030050700001006040700200000080070 Mauricio #3
10 09.8 000600500002080040500007002010060090005300100300001008006004030040900007800030000 Mauricio #6
10 09.8 020070600400008000000200001900060400007800009030004020300005800000100050008030004 Mauricio #7
10 09.6 100200300000030000004001005600700100000000080008009004700600200000010000005008009 Eioru #3/14
10 09.6 700009800090030040005600001006000009040000030200000100100008700050040010007200005 Tarek #1/Group 1
10 09.5 001002003020040010300500600005000004070000080900000500000001009080050070600700300 Ocean #6/empty box
10 09.5 200004700040090000008500001001000005030000060700000900900007200000040080006100009 Tarek Fluid Drive #19
10 09.4 200004700040090000008500001001000005030000060700000900900007200000040080006100009 Tarek Fluid Drive #15
10 09.4 000001002030040050100600000005000007080030040600000100900006000000050070004200900 Ocean #9/M21/D21
10 09.4 900004300040030020005900001007000004020000010800000600600003100050040070009800005 Tarek #3/Group 2
10 09.4 009002007070090020300400900005000001000060080200801700006009000030080050100200400 JPF #3/55
10 09.4 100009700060030040007400006002300000040010090500000400800005001000070030000600200 JPF #4/100b
10 09.4 800006000020050070005100004009500000030070040100008200400000701000040050002600008 JPF #13/100b
10 09.4 002004005030060000000700600000009001090050030400200800001005002050040090700800000 JPF # 9/163
10 09.4 400008300060090040008100006003800004050060090600003200100000005070080030004700000 JPF # 13/163
10 09.4 000002003020040010500100600007000004010000080300000200005003002080070090600200500 Ocean #4/empty box
10 09.4 001002003000040010500600700003000004060000080900000200005007002080030070700200500 Ocean #5/empty box
10 09.4 001002000020030040500600700007000006030000080900000100002006004080040030000100900 Ocean #10/empty box
10 09.4 600004900080030000005100002002000007010000050400000800300008600000040070007200009 Tarek Fluid Drive #6
10 09.4 000100080000030600000006002500002004080090000001400030020000000600007005003800090 Tarek #17/Daemonicus
10 09.4 100400500020010080003007001900000006060002050007000300800000090040800005001006200 Mauricio #4
10 09.3 000300500050010030007004001200000400060090000001006002800700200090080050005009007 top1465 #89
10 09.3 000004700000030060000200009005000001090080030300007600100006004070090020002300100 JPF # 55/163
10 09.3 400008500080030000001900002008100005030060020000004700900007000050000060002500004 JPF # 57/163
10 09.3 400009300080060000005200007003000008020000050900000600600002100000090040001800002 Tarek Fluid Drive #28
10 09.3 000009400000080010000500006009700005010000080300002000600000300080010090005200007 Tarek Aries
10 09.2 000007100020060090001900008009700000030020060000004800400003200010070000008400705 JPF # 108/163
10 09.2 100050000000200030004000600090003000600070005000100070001000200030009000000060001 Nick70 #848 of all 19's with this pattern
09 09.9 000001002010030040500600000004000001070080030200000900900002000000040070003500800 Ocean #3/M21/D21
09 09.9 001002000030040050500600100007000006080000090400000300006007002090030080000100400 Ocean #13/gold list
09 09.9 400008100050090000006700005003000007020000030900000800500001400000080090007600002 Tarek Fluid Drive #22
09 09.8 100900070050007009000040600000003800200600005004050060001008006090100700800020010 Mauricio #1
09 09.6 001000200030040050600000007000105000040000080000904000700000006050030040002000100 Ocean #49/50
09 09.5 900006800050030000001700009002000007070000020400000300300008900000040060005200001 Tarek Fluid Drive #4
09 09.5 003050004400700030080003200010000090007001800800200007040006000900030500002900006 Mauricio #8
09 09.4 000001002010030040500600000004000001070080030600000800200006000000050070003900500 Ocean #5/M21/D21
09 09.4 000007600040030080002500003007000002030000070900000100600008900070040060009100005 Tarek #1/Group 2
09 09.4 600001900080030000001700002002000007050000010400000300300009400000040080008200005 Tarek/JPF same with a mutable digit
09 09.4 000006000060090010100500700003002009020060030700300800009007008070040000500000300 JPF # 11/163
09 09.4 001000200030000040500060007000108000070030050000209000400000003060040070009000800 Ocean 22#vert.symm.
09 09.4 800006700050030000001400005009000002030000060400000100600007800000040050002900003 Tarek Fluid Drive #7
09 09.4 000003090000010057000500862000000009060000080302000700005204000180070000400008000 JFP #1/two empty boxes/diagonal
09 09.4 000300090000070100000006007200007006040080000009500030090000000600002001003400050 Tarek #14/Daemonicus
09 09.4 800002100020060000004900007007000003090000050200000600600001800000040010003500009 Tarek Fluid Drive #10
09 09.4 300009500040010000001600008008000006090000040200000900500004300000070020007800005 Tarek Fluid Drive #17
09 09.4 300004200040070000001600009009000005080000010400000700700005300000020080008100006 Tarek Fluid Drive #26
09 09.4 500007900060030000008500002002000001070000060900000400300009700000040010001200005 Tarek Fluid Drive #27
09 09.3 006003004040070000500900200000802005000040010800700000008009003010000050200500800 JPF #54/100
09 09.3 007009002040020000800600500009507006000000040100006900001000005050030020700900800 JPF #15/55
09 09.3 800007900040010060000500000006000002020030070900002800700003100010080000005100304 JPF # 34/163
09 09.3 000400090000060300000002007600001002080030000009500040050000000200007006004800010 Tarek #8/Daemonicus
09 09.3 000700080000060500000004006600001002090020000003800070080000000400005001007900030 Tarek #13/Daemonicus
09 09.3 100008400020030000005700002006000005070000090400000100300004500000080020009600007 Tarek Fluid Drive #21
09 09.2 100005300030020080004100000006900004010030020000008500700000902080000050000200400 JPF #76/100b
08 10.0 002400006080050040900006300400000700050000080006000009001700004000080030200009100 Mauricio #2
08 09.9 000001002010030040500600000004000001070080030200000600900002000000040070003500800 Ocean #2/M21/D21
08 09.8 000001002030040050600200000005000003070080040200000900900004000000050070004100600 Ocean #10/M21/D21
08 09.8 001002003020040050600700800005000004090000070300000200006008000010050090800200600 Ocean #7/empty box
08 09.7 001000200030000040500060007000108000070030050000209000600000005050090060002000800 Ocean 2#vert.symm.
08 09.7 000001002030020040500600000006000005070040080100800900700002000000030010008900600 Ocean #3/M22/D22
08 09.5 001002300040030050500100006007000000060000080200000100009001004030050060000900700 JPF #2/100b
08 09.5 001000200030000040500030006000107000040060050000208000300000009060090030002000700 Ocean 7#vert.symm.
08 09.5 001000200030000040500030006000107000040060050000208000300000009060090030008000100 Ocean 8#vert.symm.
08 09.5 001000200030000040500060007000103000040080050000902000800000006050070080002000900 Ocean 9#vert.symm.
08 09.5 400003700010090000006500008004000002050000060700000300900007100000040080008200005 Tarek Fluid Drive #20
08 09.4 001000002030040000500600700008007000000010030700500600005009004000050080200300900 Ocean #3/18
08 09.4 000001002030020040500600000004000007080030020900000500100009000000040080007500900 Ocean #7/M21/D21
08 09.4 000001002030040050600700000004000008090050030800000600100007000000030090008200400 Ocean #12/M21/D21
08 09.4 100004800070030020006900003005000007020000030600000900900008100000040060001200005 Tarek #2/Group 2
08 09.4 800001700020030050000600009003000004060000020100000800600008000050040030009700005 Tarek #5/Group 2
08 09.4 001009006080060070400700100005003000000040020100502900004006002030010090800200400 JPF #51/100
08 09.4 004003009030050080000000100001800004070060000200701900002009007050010090300500600 JPF #1/55
08 09.4 000007900030060040008500000000100005000040030600009400400001602020000090007200100 JPF # 17/163
08 09.4 800005900040060030006100008001500007080070000900003000500002300060000040008000705 JPF # 15/163
08 09.4 001002000020030040400500300003000005060000070800000100002003009070080060000100800 Ocean #8/empty box
08 09.4 001000200030000040400050006000102000060030070000708000300000005050040030002000800 Ocean 12#vert.symm.
08 09.4 000700030000050800000006004500008006030020000001900040040000000600009005002300070 Tarek #11/Daemonicus
08 09.4 000500090000010600000006008100008004090060000005700030050000000400002001003900070 Tarek #15/Daemonicus
08 09.4 500008200080070000003100009006000004010000030800000700700002500000060020004900001 Tarek Fluid Drive #11
08 09.4 700002600050010000003800009009000005040000030200000100500006700000020040004300008 Tarek Fluid Drive #35
08 09.3 100007000030020050005600002000300007040080030800005900200000301010000000007900406 JPF # 20/163
08 09.3 200000900070040020008100004001300006000010080900006500700003005050070030009200400 JPF # 30/163
08 09.3 006003008300500700000090060008002006400700100050010030004000003500800600090000020 tso #9/31
08 09.3 000100600060030040005008000800600200090000070003002008500900400020070090007005000 tso #25/31
08 09.3 001000002030000010400500300003006001070080030900400500000008009060040020700100800 Ocean #2/3
08 09.3 100006800040030020006900003005000004020000030600000900900008100070040000001700005 Tarek #4/Group 1
08 09.3 200003700000060040009500008007005001080070060500200800100000300070020050004900007 JPF #56/100
08 09.3 005007000060040030100600200008400003090030000300701000004005008010000060200000900 JPF #7/55
08 09.3 500007900090050040001200000004000006060030050100004800700003200030070090005800307 JPF # 32/163
08 09.3 000003800020050000000700004006400001000030090700001300500000900080070030001200006 JPF # 56/163
08 09.3 500000600010080020002400009005200001070000080400009000000003105000070030007500200 JPF # 72/163
08 09.3 000900030000070200000008004600001008040050000003600090010000000800004006009300020 Tarek #7/Daemonicus
08 09.3 001002300040030050500100006007000000060000080200000100009001004030050060000900700 Ocean #14/empty box
08 09.3 200006400060010000009300001008000009040000070700000500500004200000090010002800003 Tarek Fluid Drive #25
08 09.3 100004900090030000008200005005000007060000080900000300300007100000040060006800002 Tarek Fluid Drive #37
08 09.2 000001002020030040500600000003000007080040020600700900800006000000050080005900300 Ocean #2/D22
08 09.2 009005006070030040800600300000108005040000080000006100008009004000000020300500600 JPF #22/55
08 09.2 000007000010090060900600700009400002050030000200800400004005007030000010700300900 JPF #44/55
08 09.2 009005000030000010400800900003504000020000070500600800000003006070010030000900400 JPF #48/55
08 09.2 800000900040060030006100008001500007080070000900003000500002300060000040008600705 JPF #49/100b
08 09.2 500008900010000000004600007009300005000070060200000400400009802050080040003400500 JPF #55/100b
08 09.2 100006900020030000009700002001000006040020050300008400900004105080000000004900600 JPF #58/100b
08 09.2 100005200050060010007200008008100004020000060900000000000008309070040000003500800 JPF #68/100b
08 09.2 500008000030000060009000005000300008010020000600005400400007500020060080007500109 JPF #87/163
08 09.2 500008000030050060009000000000300008010020050600005400400007500020060080007000109 JPF #88/163
08 09.2 500008000030050060009000005000300008010020000600005400400007500020060080007000109 JPF #89/163
08 09.2 200005900090040020003000006007100008040060090000009100600008007000020030005000800 JPF #95/163
08 09.2 100008700090040080005900003006500007040060000700003600600000005000020090000000301 JPF #104/163
08 09.2 001002000030040000500100600006000005020000070800000900009003004040070020100600800 Ocean Mjolnir #10
08 09.1 000700000801006000009005408290000003008003900600200070900000000080009025032060700 ravel 1 out of a million
08 09.1 007005008060010040300600000001006005020080070800500200000009003070000050600200800 JPF # 152/163
08 09.0 100000009007080006000300050000040800700001000096000000008200000500000063060070400 RW #1/7
Last edited by ravel on Wed May 02, 2007 3:27 am, edited 100 times in total.
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Postby RW » Sun May 28, 2006 11:51 pm

Nice list, wouldn't want to face that in a dark alley at night... What happened to #125 from top1465 that topped your previous list with 11 steps?

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Postby Havard » Mon May 29, 2006 12:58 am

Hi Ravel! Great work compling this list!:)

I rate puzzles by what my solver can solve, and if the solver can't crack it, neither can I...:) 4 puzzles in your list was solved by my solver, and hence I would vote for the exclusion of these from the list:)

the culprits are #77, #85, #104 and #110

Look forward to the day I can solve all these...:)

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Postby daj95376 » Mon May 29, 2006 1:34 am

Ravel,

You may need to update your list. When I ran them through my solver, 38 puzzles were duplicated in 40 entries. Your original post of 162 puzzles became only 122 unique puzzles for me.

Here's a list of the duplicated puzzles.

Code: Select all
......7.1..4....3..85....6.6..9.1....1...7..5....3.2...2...8.5.8.1.29....6..7....
....1...2..3....4..2...56.......78..1.......5..49.......94...1..5....3..8...6....
....2.68.9..3.........6.3...9...6..7.1....8..3.6..8.2......5...4.2.1.9...8.9...7.
...1..2.7....4...5.8...3.....5..7..9.1..5..3.2..9..5.....6...4.1...7....8.2..9...
...3...86..76..1......5...4..6.1....5.4...3.2.9..4.7..2...3.6....1..54..43...9...
...3..5...5..1..3...7..4..12.....4...6..9......1..6..28..7..2...9..8..5...5..9..7
...4..5...7...3.....421..6..3..8.1..8..7....695.3........9....1.6.....2...3..6.84
..23.....85..4....97.5.1...4.....89..2.91...3.....4..6......5.9.....5.1...7.3...8
..3...6.......1.9..7..5.....18....5..2..7.1..6.9....72...83..1....2.....4...673..
..3.4..1....192......3....7..4.6....5...34..2.8.9.........7...67......58.29....3.
..3.5.4..7...6.....5.8...6.5....3..4.1..7..8.2..4....7.4...8.5.....4...9..6.1.2..
.1...7......85.9....3.....4.2..4....75.96....1....8.2...62............3......57.8
.3.....82..2.9......4..67......43....1....5..7..6.5.2..9.2....6..65....9......31.
.32..........2..4.9.7..5....1...3.98...2..6...68.1..2....53....57......3....471..
.4.2....8..1.5..4.2..8..7....8....97...6..3...957............6.7.4.1...2.....31..
.4.3..9...7...5.2.8........6.....352..5....9...4...6.....9....8....42.7..9.16....
.52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9
.6.....7.87.3..59...54..2....9.564.....9...8.2.78.....7....4..2..8...71.........9
.6.....7.9...8...6..3..91....8.95....2.4...6....21.8....5...6..3...4...8.4.....2.
1...5.......2.1.....3.7..6.........962......7.8593.....3..6..8..7....1..5....4.7.
1...9..3...2..3.5.7..8.......3..7...9.........48...6...2..........14..79...7.68..
1..6......7.3.9.4...4.7...2.1.7....9.37...2..5.......6.....59....2.3....78..1....
3..5..1...7.....8...8..4..66..4..9...3..6..5...7..1..48..1..3......2..6...2..9...
3..7...2...8.4...9....5...1..24.....5...3.4.......8.3...46.....9..2.3....1.....67
38.5...29..5.4..3.......5...2.4............8.4.9.8.2...7...6......2.....864.9.3..
5..2..3......8..9...2..4..66..1..9...1.....4...7..3..87..3..4...9..7..2...5..6..9
5..4..8......9..1...2..1..56..3..4...5..7......4.....83..6..7...6.....8...8..2..1
5..7.........3..7...8..5..36..1..4...8..2..9...9..8..1...4..3...6..9..4...2..6..9
5..8..4...8..9..5...7..6..2..4..3..6.3.......9..1........7..8...4..5..1...2..1..4
6.......3.7..8..9...2...5.....3......8..1..7......2.....5...1...9..4..8.3.......2
6......1...7.......5..83.2.....4.3....28.6....7.....5......91....8235.......1...4
6.....3...5..9..8...2..6..98.....7...7..5..4......1..51..3..5...4..2..6...8..7..2
6..1..7......7..8...9..8..37..4..5...3.....2...4..5..81..2..4.........5...6..9...
6..9..4...4..5..3...8..6..55..7..3...7..2......2..5..41..6.........3..8...6..2..1
7.....4...2..7..8...3..8..9...5..3...6..2..9...1..7..6...3..9...3..4..6...9..1..5
7..9....6....6..83.....32..8....9....5.....3...24....1..8...6...6..1...741...5.9.
9..7..1...2..1...7...5..6........56......32..1...5...824..813...1542...6..9.....2
9.4..5...25.6..1..31......8.7...9...4..26......147....7.......2...3..8.6.4.....9.
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Postby ronk » Mon May 29, 2006 1:41 am

daj95376 wrote:... 38 puzzles were duplicated in 40 entries. Your original post of 162 puzzles became only 122 unique puzzles for me

The 39 grid-formatted puzzles were duplicated in the 123 line-formatted puzzles. Perchance you picked up both.
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Postby daj95376 » Mon May 29, 2006 3:59 am

ronk, thanks for the clarification!

I copied both the above and the one-liners into my input file.

Still, that only explains part of my results. If you examine entries #14 and #23 in the list, you'll find the remaining discrepancy.
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Postby ravel » Mon May 29, 2006 8:45 am

Thanks, RW and daj95376.
I had overlooked #125 (has 7 steps now) and had #326 as duplicate entry.
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Postby Viggo » Mon May 29, 2006 8:10 pm

Thank you for your interesting ratings. I have one question: Do a simple discontinuous Nice Loop count as a step by your solver? I think that a discontinuous Nice Loop is the same an error net with no multiple interferences.

/Viggo
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Postby ravel » Mon May 29, 2006 8:26 pm

Viggo wrote:Thank you for your interesting ratings. I have one question: Do a simple discontinuous Nice Loop count as a step by your solver? I think that a discontinuous Nice Loop is the same an error net with no multiple interferences.

/Viggo

No, as i said, for my solver an elimination that can be made with an xy-wing is counted the same as one, that needs an error net with multiple interferences. It does not check, what causes a contradiction and how many steps are needed for that. So many improvements are possible (both for the solutions and my solver, but i do not intend to invest more time in it at the moment).
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Postby tso » Mon May 29, 2006 11:37 pm

Is anyone finding that the hardest puzzles have anything in common that would either help in constructing them directly or generating them more efficiently or identifying them by inspection? Some templates seem to yeild harder puzzles -- but is that as far as it goes? Any hint there may be some rules of thumb, like "puzzles with 2 or 3 clues in each group are more likely to yeild an ultra hard" ... or something like that?
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Postby daj95376 » Mon May 29, 2006 11:53 pm

If you inspect the top 20 puzzles in the list, you'll find many with bands of clue cells running diagonally across the grid. This doesn't guarantee a difficult puzzle, but it definitely indicates an arrangement that current techniques can't handle very well.
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Postby Ruud » Tue May 30, 2006 2:54 am

I have tested the creation of puzzles with this diagonal pattern. The percentage of difficult puzzles is much higher than average.

These samples are all minimal and require several chains to solve. Interesting to know how they perform compared to other hard puzzles.

Code: Select all
000800400070020080006009003000700000030090040009006005800300700040060020003007006
200000100030000050001008002400100900060050080005002007600900800090070030008001000
000300700030020000009001006000100300080040010002005009900700400050080020000003007
100500400060010020008007000300600700010070090009002000600400900050080030003005006
700500000000010030001009005900800000050090070007004002200900400010050060008002003
400100200080040060005009008100000700040020080003007005200400000090080000008003000
800900700090040020002006009100000500020060010007003002300500400040070090000008001
200000800090080010001002007500200600070040030004001002300600700000030080009008005
200400500040060020001002000900500700080010060005009002700100000030090050008006004
200100300000050000006002005300200400090070050007008003800900700030010060001004008
100900300060010000004006005400700200010020030002009008200400900050000080009008001
200100300010030040004007001700800900080090030000003002900500600070060020001004008
400300500090050010002000009900200600060030020007006004600400200080070030000003005
000900500010070080005002006200700400050020090009006008700800900040030010003007004
600900700000060040003000009800300200020050090006008001200800900040020010008004005


I also have a collection of 3418 non-minimized puzzles with this pattern:

Code: Select all
X . .|X . .|X . .
. X .|. X .|. X .
. . X|. . X|. . X
-----+-----+-----
X . .|X . .|X . .
. X .|. X .|. X .
. . X|. . X|. . X
-----+-----+-----
X . .|X . .|X . .
. X .|. X .|. X .
. . X|. . X|. . X


If anyone would like to check them, drop me an email and I will send them to you. My email is ruud@(my website)

Ruud.
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Postby ravel » Tue May 30, 2006 2:51 pm

Ruud wrote:I have tested the creation of puzzles with this diagonal pattern. The percentage of difficult puzzles is much higher than average.

These samples are all minimal and require several chains to solve. Interesting to know how they perform compared to other hard puzzles.

This pattern is a nightmare's nest !

#11 and #14 needed 6 steps, #7 7 steps and #13 9 steps. I will add them above.

The others had less than 4 steps.
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Postby daj95376 » Tue May 30, 2006 5:07 pm

Ruud,

A nice collection of diagonal puzzles.

Code: Select all
Puzzle #1:

...8..4...7..2..8...6..9..3...7......3..9..4...9..6..58..3..7...4..6..2...3..7..6

r1c8    =  6     Hidden Single
r2c4    =  6     Hidden Single
r3c2    =  8     Hidden Single
r7c2    =  6     Hidden Single
r8c7    =  3     Hidden Single
r7c9    =  4     Hidden Single
r7c8    =  9     Hidden Single
    b9  -  5     Locked Candidate (1)
r69     -  8     X-Wing
  c36   -  4     X-Wing
r4c8    =  1     [r4c8]=3 => [r6]=INVALID
                 Singles
Last edited by daj95376 on Wed Sep 13, 2006 6:13 am, edited 1 time in total.
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Postby Ruud » Tue May 30, 2006 6:40 pm

Here are a few more from this nest:

Code: Select all
000300900040070050005008000300400700060080010004005002200500000050010070006009008
700500000030090020001004007200100500050060090007000003900200100010000050004000008
800700500040080000003004007200300700000090080000000001300500400020060090005001008
800600400030020000002007001600900000040050070009000003100200800080000060007005004
900600500080090040003002006400900700020060050009008000700100300010040020000006000
500900100000010040003008005800400000060080070002005003600000800090000060004007002
100000000030040020005003000700200800040090070003008006200000500000060030006001008
600800200070060040002000001700000900090070060008005000100200300000040020003001005
900100200060000040001007009100300900050080000007009008500200300070040010000000006
400900800030080070000000000500300000020050010009004005700000600080020030002001004
300400600040020080005000009900100200000000050006003000000200400080070030001008005
900400100040010090006000004400600700090020030002008000200900000050030000007001008
100800300030050020004001008700400200040010060005008001000700600080000030002006005


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