The New Sudoku Players' Forum

by **tarek** » Sun Sep 21, 2008 11:26 am

g.r.emlin is the best to do all of this ....

g.r.emlin can verify q1,q2,Sx9 & Sxt ... SE121 rating has to be left for the poster's honesty.

If g.r.emlin is not up for it (for whatever devilish reasons

) Then I'm ready to do the same job.

My suggestion:

*Top 10 of each category in both line & graphic format
*categories are q1,q2,Sx9,Sxt,SE121
* verify q1,q2,Sx9,Sxt but not SE121 (verify SE131 if possible)
* SE121 & other q1,q2,Sx9,Sxty have to be provided by poster or that entry is disqualified

there has to be a database of posted puzzles (an updated q2 taxonomy list is the best) ... failing that .... I would use my own database (if organising this falls to me, that include famous puzzle lists to date )

tarek

by **gsf** » Sun Sep 21, 2008 12:35 pm

tarek wrote:g.r.emlin is the best to do all of this ....

g.r.emlin can verify q1,q2,Sx9 & Sxt ... SE121 rating has to be left for the poster's honesty.

If g.r.emlin is not up for it (for whatever devilish reasons ) Then I'm ready to do the same job.

My suggestion:

*Top 10 of each category in both line & graphic format
*categories are q1,q2,Sx9,Sxt,SE121
* verify q1,q2,Sx9,Sxt but not SE121 (verify SE131 if possible)
* SE121 & other q1,q2,Sx9,Sxty have to be provided by poster or that entry is disqualified

there has to be a database of posted puzzles (an updated q2 taxonomy list is the best) ... failing that .... I would use my own database (if organising this falls to me, that include famous puzzle lists to date )

sounds like a good start
might take 2 weeks to get the pieces together

by **tarek** » Tue Sep 23, 2008 9:30 am

The following is modified from ravel's post on how to rate puzzle.

Puzzle.txt Should have all puzzles needed for rating

Sudoku.exe & Suexratt.exe should be downloaded

a single batch file can be used for rating the puzzles according to q1,q2,Sx9 & Sx9 as follows (windows):

Code: Select all: q1: sudoku -q1 puzzles.txt > q1_ratings.txt q2: sudoku -q2 puzzles.txt > q2_ratings.txt Sx9 & Sxt: suexratt puzzles.txt 1000 2 > suex_ratings.txt

I tend to increase the number that follows suexratt to 10000 for more accuracy with puzzles that have extreme ratings.

Output Example for PB .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...:
q1: .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... # 99485 FNBP C21.m/M3.389.1366
q2: .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... # 99551 FNBP C21.m/M3.389.1366
Sx9,Sxt (1000 2): rating: 5154 , 2102 , .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...
Sx9,Sxt (10000 2): rating: 5105 , 2105 , .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...

tarek

by **coloin** » Wed Sep 24, 2008 12:02 pm

To assist others in making hard puzzles perhaps a simple command line for gsfs program woulkd be useful

Making puzzles using a {-2+2}
sudoku -go{-2+2} origpuzzles.txt >newpuzzles.txt

at 21 clues 75 puzzles can give 750000 other puzzles [overnight]

This could be initially quickly rated with sudoku -qFN [set to print minimal puzzles with rating over 90000 .....[?command for this]

Isomorph puzzles from a file of previously found puzzles need to be purged and removed at this stage. [command for this ?]

I use boxer text editor to remove #ratings [to be accepted by sxratt] and paste the q2 and sxratt ratings into excel.

I actually use havards rather neat "sudoku architect" software for the making of minimal puzzles and purging for known isomorphs - I will try to contact him to see if there is a general release of this software. [since this is what it was made for !]

C

by **vrencianz** » Fri Sep 26, 2008 9:38 am

I have a generator program here http://code.google.com/p/dance-sudoku/ and generated few hard ones (rating 11, few of yours have 14)

..7.2.3......14...1.5........629..73....6....92..786........9.1...68......2.5.7..
..2.....8...7..32.8....9...72.6.....6..247..1.....1.76...1....7.89..6...2.....5..

I am interested about your opinion about these puzzles.

by **champagne** » Fri Sep 26, 2008 10:25 am

vrencianz wrote:I have a generator program here [url]
I am interested about your opinion about these puzzles.

unhappily, no good news

the first one is good for beginners, the second one could be proposed to skilled players.

Both are at thousand miles of the target.

champagne

by **StrmCkr** » Fri Sep 26, 2008 8:51 pm

Code: Select all: rating 11, few of yours have 14

how are you rating them compared to ours? to say few are 14s?

reading your page
are you analizing vers a brute force algorithem of Dancing links (algorithm x.) ? and justifing ease with that.

vrs a constraint logic based solver.
which is where our ratings are based.

we use a colage of programs Soduko Explainer, GSF, and others to list a few. SE is a fairly skilled at rating program given what is currently avialable.

both the puzzles have reletivly no hard steps required to solve?
which makes them not difficult or rated with a high SE index.

they are no where near the scale or caliber to the puzzles many of us are displaying.

by **vrencianz** » Mon Sep 29, 2008 9:19 am

Thank you for your answers and tips.

(I realized that this isn't the right forum topic to ask these kind of questions. Next time I'll find a better one.)

by **Obi-Wahn** » Mon Oct 06, 2008 2:51 pm

This weekend I felt like looking into Sudokus again and checked coloin's latest list.
There were a bunch of toughies that scored 1 Jelly but colx006 was outstanding with 6 Jellies and 19 Swords, which gets it the fourth place in my list behind the three Star scoring puzzles.

Code: Select all: colx006 1.......6.5.7...8...3...4.....5.8.9.....3.....8.92....6.....3...7...5.2...4.....1 SE121 = 11.8

IIRC this is the second highest SE121 rating so far, only one tenth short of the Golden Nugget.

By altering the central box I managed to generate another hard one with 5 Jellies and 14 Swords for fifth place.

Code: Select all: OW081006 1 . .|. . .|. . 6 . 5 .|7 . .|. 8 . . . 3|. . .|4 . . -----+-----+----- . . .|2 . 8|. 9 . . . .|. 1 .|. . . . 8 .|9 5 .|. . . -----+-----+----- 6 . .|. . .|3 . . . 7 .|. . 5|. 2 . . . 4|. . .|. . 1 SE121 = 11.7

Did I miss any other SE121 ratings between the Easter Monster's 11.6 and the Golden Nugget's 11.9?

[edit] Actually I did miss my own post, where I stated that coloin_04/13-1600 and coloin_04/13-1414 reached SE121 = 11.8

I found another 2 puzzles with multiple Jellies:

Code: Select all: OW081007 1 . .|. . .|. . 7 . 4 .|6 . .|. 8 . . . 3|. . .|5 . . -----+-----+----- . 8 .|9 . .|. . . . . .|. 1 6|. . . . . .|4 . 2|. 9 . -----+-----+----- . . 5|. . .|3 . . . 6 .|. . 4|. 2 . 7 . .|. . .|. . 1 2 Jellies & 11 Swords, SE121 = 11.4 OW081008 1 . .|. . .|. . 5 . 9 .|2 . .|. 4 . . . 3|. . .|7 . . -----+-----+----- . 8 .|9 . 6|. . . . . .|. 5 .|. . . . . .|8 4 .|. 9 . -----+-----+----- . . 5|. . .|3 . . . 6 .|. . 4|. 2 . 7 . .|. . .|. . 1 7 Jellies & 23 Swords! SE121 = 11.5

Searching through tarek's Pearly 6000 I found another one:

Code: Select all: tarek_Pearly_#3298 . . .|. . .|. . 4 . 1 .|. . 3|. 9 . 6 . .|. 9 .|8 . . -----+-----+----- . . .|3 . 5|. . . . . 7|1 . .|. . . . 3 .|. . 2|. 1 . -----+-----+----- . . 4|. . .|7 . . . 9 .|5 . .|. 2 . 8 . .|. . .|. . 6 2 Jellies & 12 Swords, SE121 = 11.3

Greetz, Obi

by **tarek** » Thu Oct 09, 2008 11:23 am

Thanks Obi-Wahn for your update ...

here are the puzzles from the patterns game (game 14 onwards) that had an ER >= 10.5 showing their ER/EP/ED

10.7/10.7/09.9 100002003020030040005600000003000002060010070800000900000004800070060050900500001 0040-079-Mauricio
10.7/10.7/09.5 100002030004100500060040001070000040005080006600000300020004900900500003006090070 0051-078-JPF
10.7/01.2/01.2 100200300000040050006003001700000800080060040009000006600300700050090000003008002 0020-205-JPF
10.6/10.6/10.6 100002003020030040005600000003000006060040070800000200000007900090020080600500001 0040-081-Mauricio
10.6/10.6/10.5 100200300000040050006007008300000700090060040002000009700900600050020000003008001 0020-192-JPF
10.6/10.6/10.1 100200300000030040005006007200000600080010090009000008800900200070060000004003005 0020-165-Mauricio
10.6/10.6/10.0 100002030004100500060070001020000080003090007500000300040007600600900003008060090 0051-060-JPF
10.6/10.6/09.8 100200300040050010006001007600800700080060090004002006400900100090020070005003009 0016-141-JPF
10.6/10.6/09.8 010000002304000000050060400000500001002070080000009600008004900000020070600300005 0037-129-Mauricio
10.6/10.6/07.8 100200300000040050004006002600000200070080090005000001200700400090030000008005009 0020-149-JPF
10.6/10.6/06.7 100200300000040050006007001600000100080050070009000008300400200060080000007003009 0020-137-m_b_metcalf
10.6/10.6/03.8 000100000002003004050060070800600500004001002060090040000900000007008003040070080 0022-088-JPF
10.6/10.6/02.6 001002003040000050600070100000803002009000800200706000007010008050000040800600900 0047-129-JPF
10.6/06.7/06.7 010000002304000000050060700000200001001050040000003600007008900000040050200900008 0037-096-gsf
10.6/06.7/03.4 001900000050007600200000030900300010000040000060008007080000004002100060000004500 0041-081-gsf
10.6/01.2/01.2 100002003040050010006700000003000004020080090900000100000004500050090020700800006 0040-039-JPF
10.6/01.2/01.2 001900000050007600200000030300200090000040000060008005080000004002600010000005700 0041-003-Pat
10.6/01.2/01.2 001002003040000050600070100000603008009000200800201000006030009050000040900700800 0047-057-JPF
10.5/10.5/10.5 100002003020040050006700000007000008080050060400000900000009400030080070200600001 0040-148-Mauricio
10.5/10.5/10.4 001002300040000090600700008005200007000000000300006200200003001090000040008500600 0025-089-gsf
10.5/10.5/10.3 100200300000040050006007008300000700070010040009000002200800600050020000008003009 0020-212-JPF
10.5/10.5/10.0 100002003020040050006700000005000008080090040400000700000005800090020060300600001 0040-072-Mauricio
10.5/10.5/09.5 100200300000040050006003007300000800010080090009000001400900200070030000005004006 0020-188-JPF
10.5/10.5/09.5 010000002304000000050060700000200001007080040000009500001004600000010080900500003 0037-107-gsf
10.5/10.5/09.5 001006003040000050200070100000703002003000600800609000008090007050000040100200800 0047-126-gsf
10.5/10.5/09.5 100002030002400500060070002070000050008060003900000800020009300600500004003040010 0051-068-JPF
10.5/10.5/09.4 100200300000010040005003001300000500060070080009000006200500900040060000008001007 0020-174-Mauricio
10.5/10.5/09.4 010000002304000000050060700000200008009030070000004500006005100000090030800100004 0037-062-Mauricio
10.5/10.5/09.4 100002003020040050006500000003000007080070020200000900000009700040080060500600001 0040-034-JPF
10.5/10.5/08.3 001002003040000050300060100000703008002000900800906000003070001050000040900200700 0047-088-Mauricio
10.5/10.4/06.7 100200300000040050005006007200000800030010020009000005700600400080030000004007009 0020-085-JPF
10.5/06.7/03.4 001900000050007600200000030900300010000040000060008005080000004002100060000004700 0041-080-gsf
10.5/01.2/01.2 010020300450000000006000007000300800200040050000007009300100040000050600007008000 0031-090-JPF
10.5/01.2/01.2 000001200030040050600700000100080700070409030009070004000004006050090040008200000 0034-106-JPF
10.5/01.2/01.2 001002003040000010500010600000703002003000500800506000005070009090000040700900800 0047-055-JPF

tarek

by **Pat** » Fri Oct 10, 2008 3:04 am

game 41 also had these puzzles posted by Mauricio ( he did not provide ratings ) --

10.7-10.7-10.4 ..12......3...45..4......6.6..1...7.....8.....9...3..8.5......4..27...1......89..

10.6-10.6-9.9 ..12......3...45..6......7.2..7...6.....8.....9...3..4.8......9..51...2......73..

by **Obi-Wahn** » Fri Oct 10, 2008 11:29 am

There are no new puzzles requiring a Jelly check in these lists.

I planned to publish a list of all Jelly+ puzzles known to me so far (162). And I tried to build in a new feature into my solver. So far I counted the most complicated checks for the complete solution of a puzzle. Now, I thought I just count the Jelly and Sword checks till the next candidate elimination. This way I can solve a puzzle step by step and get the count for the most complicated candidate elimination, just like Sudoku Explainer. I hoped that this rating (most complicated step instead of the sum for the complete solution) would be better correlated to the SE rating.

When I applied this method to the Golden Nugget something weird happened. For the complete solution my solver only needs 1 Jelly and 20 Sword checks.

Code: Select all: .---------------------.---------------------.---------------------. | 25678 14568 124567| 268 2467 4678 | 1247 3 9 | | 26789 4689 2467 | 23689 23467 1 | 247 2467 5 | | 2679 1469 3 | 269 5 4679 | 8 12467 1247 | :---------------------+---------------------+---------------------: | 235 345 8 | 135 9 357 | 123457 1247 6 | | 3569 7 456 | 13568 136 2 | 13459 1489 1348 | | 1 3569 256 | 4 367 35678 | 23579 2789 2378 | :---------------------+---------------------+---------------------: | 367 136 9 | 1236 8 346 | 12347 5 12347 | | 3578 2 157 | 1359 134 3459 | 6 14789 13478 | | 4 13568 156 | 7 1236 3569 | 1239 1289 1238 | '---------------------'---------------------'---------------------'

For the first steps I got the following counts:
1) R7C4<>3, 2 Swords
2) R4C4<>3, 2 Swords
3) R2C1<>7, 1 Jelly, 4 Swords
4) R1C1<>8, 1 Jelly, 4 Swords
5) R7C9<>3, 1 Jelly, 5 Swords
6) R1C3<>6, 1 Jelly, 5 Swords
7) R1C3<>5, 1 Jelly, 6 Swords
8) R2C1<>2, 1 Jelly, 6 Swords
9) R3C2<>9, 1 Jelly, 6 Swords
10) R2C2<>6, 1 Jelly, 7 Swords

Code: Select all: .---------------------.---------------------.---------------------. | 2567 14568 1247 | 268 2467 4678 | 1247 3 9 | | 689 489 2467 | 23689 23467 1 | 247 2467 5 | | 2679 146 3 | 269 5 4679 | 8 12467 1247 | :---------------------+---------------------+---------------------: | 235 345 8 | 15 9 357 | 123457 1247 6 | | 3569 7 456 | 13568 136 2 | 13459 1489 1348 | | 1 3569 256 | 4 367 35678 | 23579 2789 2378 | :---------------------+---------------------+---------------------: | 367 136 9 | 126 8 346 | 12347 5 1247 | | 3578 2 157 | 1359 134 3459 | 6 14789 13478 | | 4 13568 156 | 7 1236 3569 | 1239 1289 1238 | '---------------------'---------------------'---------------------'

So far, so good. And now step 11:
R2C4<>9 and R3C1<>9, 3 Jellies, 12 Swords!

That doesn't make sense. How can a single step be more complicated than the complete solution? Okay, so I thought my step solving function was flawed. But when I started my original solver on the reduced candidate grid, it gave: 4 Jellies & 14 Swords for the complete solution.

So the question is now: how can a puzzle get more complicated for my solver by correctly removing candidates?
I'm quite puzzled ...

Greetz, Obi

by **coloin** » Sat Oct 11, 2008 12:16 pm

Interesting that you have highlighted those new puzzles - which surprisingly arnt in the taxonomy list.

I wish you luck in clarifying your recent solver problems . Maybe this is of help.

Thanks for your analysis of the batch of puzzles.

Code: Select all: Cloudy Bay # No Jelly, no Sword Bronze Medalian # 5 Swords Silver Plate # 1 Jelly, 10 Swords Platinum Blonde # 1 Sword Tungston Rod # No Jelly, no Sword Golden Nugget # 1 Jelly, 20 Swords DukDiamond1 # 1 Sword DukDiamond2 # 1 Sword WeeKender2 # 1 Sword WeeKender1 # 1 Sword Fata Morgana # 1 Sword Trompe-l'oeil # 2 Swords

The posting of the other puzzle has highlighted an interesting observation however.

The making of these puzzles was derived by using a 16 clue template
- obtaining all the possible ways to complete the puzzle by filling in the central box
- then remove clues from the central box.

16 clue templates commonly had ~ 500,000 grid completions, where a random 16 clue might have 4 million or more.

Now particular 16 clue template that I have found is this one - a slight modification to colx006

Code: Select all: 1.......5.6.2...8...3...7.........4...........8.......7.....3...4...6.2...5.....1

The middle clues [even numbers] in B1379 occur as a single clue in B2468

Code: Select all: +---+---+---+ |1..|...|..5| |.6.|2..|.8.| |..3|...|7..| +---+---+---+ |...|.3.|.4.| |...|.71|...| |.8.|4..|...| +---+---+---+ |7..|...|3..| |.4.|..6|.2.| |..5|...|..1| +---+---+---+ Its easy to give an example of 20 clue SE 9.0/8.6 /1.2

many of the puzzles with this template have a difficult first elimination
Here is the initial pms for this complete puzzle -not many bivalue positions or cells it would appear............

Code: Select all: +----------------------+----------------------+----------------------+ | 1 279 24789 | 36789 4689 34789 | 2469 369 5 | | 459 6 479 | 2 1459 34579 | 149 8 349 | | 24589 259 3 | 15689 145689 4589 | 7 169 2469 | +----------------------+----------------------+----------------------+ | 2569 12579 12679 | 5689 3 2589 | 125689 4 26789 | | 234569 2359 2469 | 5689 7 1 | 25689 3569 23689 | | 23569 8 12679 | 4 2569 259 | 12569 135679 23679 | +----------------------+----------------------+----------------------+ | 7 129 12689 | 1589 124589 24589 | 3 569 4689 | | 389 4 189 | 135789 1589 6 | 589 2 789 | | 23689 239 5 | 3789 2489 234789 | 4689 679 1 | +----------------------+----------------------+----------------------+

These are the "initial" pms for the 16 clue template [no clues in central box]

Code: Select all: +---+---+---+ |1..|...|..5| |.6.|2..|.8.| |..3|...|7..| +---+---+---+ |...|...|.4.| |...|...|...| |.8.|...|...| +---+---+---+ |7..|...|3..| |.4.|..6|.2.| |..5|...|..1| +---+---+---+

Code: Select all: +-------------------------------+-------------------------------+-------------------------------+ | 1 279 24789 | 346789 346789 34789 | 2469 369 5 | | 459 6 479 | 2 134579 134579 | 149 8 349 | | 24589 259 3 | 145689 145689 14589 | 7 169 2469 | +-------------------------------+-------------------------------+-------------------------------+ | 23569 123579 12679 | 1356789 12356789 1235789 | 125689 4 236789 | | 234569 123579 124679 | 13456789 123456789 12345789 | 125689 135679 236789 | | 234569 8 124679 | 1345679 12345679 1234579 | 12569 135679 23679 | +-------------------------------+-------------------------------+-------------------------------+ | 7 129 12689 | 14589 124589 124589 | 3 569 4689 | | 389 4 189 | 135789 135789 6 | 589 2 789 | | 23689 239 5 | 34789 234789 234789 | 4689 679 1 | +-------------------------------+-------------------------------+-------------------------------+

Hovever this template has a very lowly 132274 grid solutions

This means there will be many more valid puzzles with a complete central box.

The reason for this is :

the "real" pms are this [* represents a "real" elimination]

Code: Select all: +-------------------------------+-------------------------------+-------------------------------+ | 1 279 *4*8* | 346789 346789 34789 | 2*6* 3*9 5 | | *59 6 *79 | 2 13*57* 13*57* | 149 8 349 | | *4*8* 259 3 | 145689 145689 14589 | 7 1*9 2*6* | +-------------------------------+-------------------------------+-------------------------------+ | 23569 1*357* 12679 | 1356789 12356789 1235789 | 125689 4 236789 | | 234569 1*357* 124679 | 13456789 123456789 12345789 | 125689 135*7* 236789 | | 234569 8 124679 | 1345679 12345679 1234579 | 12569 135*7* 23679 | +-------------------------------+-------------------------------+-------------------------------+ | 7 1*9 *26** | 14589 124589 124589 | 3 569 4*8* | | 389 4 189 | 1357** 1357** 6 | 5*9 2 7*9 | | 2*6** *39 5 | 34789 234789 234789 | 4*8* 679 1 | +-------------------------------+-------------------------------+-------------------------------+

This means that this template has got these reductions - and that is without any given clues in the central box!

Achieving any of these reductions even when solving a complete puzzle envolves a a hard SE >9.3 if attempted before simpler methods.

This will be a form of "SK loop" in the puzzles with this template.

Easter Monster has a template which has eliminations - without the central box.

Code: Select all: +-------------------------------+-------------------------------+-------------------------------+ | 1 478 34578 | 356789 356789 35678 | 3489 369 2 | | 238 9 378 | 4 123678 123678 | 138 5 368 | | 23458 248 6 | 123589 123589 12358 | 7 139 3489 | +-------------------------------+-------------------------------+-------------------------------+ | 234689 5 134789 | 1236789 12346789 1234678 | 12389 123679 36789 | | 234689 124678 134789 | 12356789 123456789 12345678 | 123589 123679 356789 | | 23689 12678 13789 | 12356789 12356789 1235678 | 123589 4 356789 | +-------------------------------+-------------------------------+-------------------------------+ | 7 148 14589 | 12358 123458 123458 | 6 239 3459 | | 456 3 145 | 12567 124567 9 | 245 8 457 | | 45689 468 2 | 35678 345678 345678 | 3459 379 1 | +-------------------------------+-------------------------------+-------------------------------+ +-------------------------------+-------------------------------+-------------------------------+ | 1 478 345*8 | 356789 356789 35678 | 3489 369 2 | | 238 9 378 | 4 12*67* 12*67* | 138 5 368 | | *3458 248 6 | 123589 123589 12358 | 7 139 3489 | +-------------------------------+-------------------------------+-------------------------------+ | 234689 5 134789 | 1236789 12346789 1234678 | 12389 12*67* 36789 | | 234689 12*67* 134789 | 12356789 123456789 12345678 | 123589 12*67* 356789 | | 23689 1267* 13789 | 12356789 12356789 1235678 | 123589 4 356789 | +-------------------------------+-------------------------------+-------------------------------+ | 7 148 *4589 | 12358 123458 123458 | 6 239 3459 | | 456 3 145 | 12*67 12**67 9 | 245 8 457 | | 45*89 468 2 | 35678 345678 345678 | 3459 379 1 | +-------------------------------+-------------------------------+-------------------------------+

These are many of the initial elimination clues envolved in the EM SK loop which were commented on by Allan Barker..... here and here in 3D

Golden Nuggett however wouldn't /doesnt have these "real" eliminations revealed if/when the most populated box is cleared.

champagnes solver perhaps finds similar eliminations, and consequently is able to classify these SK loop puzzles [including 04/13-1600 and 04/13-1414] as slightly easier !

C

by **AllanTrojan** » Sat Oct 11, 2008 7:45 pm

I just joined this forum today though I have been reading it for a little while.

Tonight I completed writing a Sudoku program in visual basic
and it seems to have no difficulty in solving the 'hardest' problems
in a few seconds.

I would be grateful if someone could explain to me
what the notations ER/EP/ED mean
and how they are calculated.

Presumably they are explained in this forum in some earlier postings.
A link to these would be appreciated.

by **StrmCkr** » Sat Oct 11, 2008 7:57 pm

Code: Select all: Tonight I completed writing a Sudoku program in visual basic and it seems to have no difficulty in solving the 'hardest' problems in a few seconds.

and what is your solver based on?

they are hardest only becasue logic based or cover set elliminations based solvers find steps that are beyond most human solvers to allocate and complete. requiring emence amount of compution to show and prove any give ellimination befor progreess is made.

a brute force solver ie: "dancing links" etc will crack these in fractions of secods.

our ratings are only from solvers that dont rely on trial and error till completion.

The New Sudoku Players' Forum

The hardest sudokus

from game 41

ER/EP/ED