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what is the hardest known suduko ?
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JPF

Joined: 05 Dec 2005
Posts: 29
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Location: Paris

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PostPosted: Fri Jun 08, 2007 10:00 pm    Post subject: Reply with quote

rickhev1 wrote:
Here is the hardest sudoku I have encountered. It is by JPF and is rated 11.4 by SE. Mike Metcalf's above is the next hardest one I know of.


Thanks rickhev1.

If you want to know more about hard sudokus you must have a look at some threads :

The hardest sudokus
How regular is to generate sudoku with difficulty 9+ SE?

You can also find a list made by gsf with different rating systems here.

In April, I posted this puzzle, known as the Easter Monster (SE=11.4) and gsfr=99408 :

Code:

 1 . . | . . . | . . 2
 . 9 . | 4 . . | . 5 .
 . . 6 | . . . | 7 . .
-------+-------+-------
 . 5 . | 9 . 3 | . . .
 . . . | . 7 . | . . .
 . . . | 8 5 . | . 4 .
-------+-------+-------
 7 . . | . . . | 6 . .
 . 3 . | . . 9 | . 8 .
 . . 2 | . . . | . . 1


JPF
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latian

Joined: 08 Jan 2008
Posts: 5
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PostPosted: Tue Jan 08, 2008 2:46 pm    Post subject: Re: soduko solver Reply with quote

humbertoldi wrote:

The logical methods implemented are rather simple (no X-Wing, pairs and other fancy stuff). If these methods alone are not sufficient, the program solves by (recursive) guessing.

There are many available solvers.
Pure "recursive guessing" works, but this is not the point here.
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dodo

Joined: 11 Jul 2005
Posts: 5
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PostPosted: Sun Feb 17, 2008 12:01 pm    Post subject: Reply with quote

A local newspaper published (perhaps by mistake) the following:
Code:
1.4|.5.|.8.
3.8|.6.|2..
.9.|8..|..7
-----------
6..|5..|..4
..2|.4.|7..
7..|..1|..3
-----------
4..|..6|.9.
..7|.9.|1.8
.5.|.3.|4.6

After a few steps I arrived at
Code:
124|.5.|689
378|.6.|2..
596|8..|3.7
-----------
6..|5..|..4
..2|.4.|7..
745|..1|..3
-----------
4..|..6|592
267|495|138
.5.|.3.|476

but neither me nor the Simple Sudoku program can proceed further.
Backtrack shows this as "the" solution (I believe there is no other, but I'm not sure):
Code:
124|753|689
378|964|251
596|812|347
-----------
639|527|814
812|349|765
745|681|923
-----------
483|176|592
267|495|138
951|238|476

Any hint of solving it without backtracking?
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tarek

Joined: 31 Dec 2005
Posts: 153
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Location: London, UK

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PostPosted: Sun Feb 17, 2008 12:16 pm    Post subject: Reply with quote

dodo wrote:
Any hint of solving it without backtracking?

Code:
*--------------------------------------------------------*
| 1     2     4    | 37    5     37   | 6     8     9    |
| 3     7     8    |%19    6    #49   | 2     145   15   |
| 5     9     6    | 8     12   #24   | 3     14    7    |
|------------------+------------------+------------------|
| 6     138   139  | 5     278   23789| 89    12    4    |
| 89    138   2    | 369   4     389  | 7     156   15   |
| 7     4     5    | 269   28    1    | 89    26    3    |
|------------------+------------------+------------------|
| 4     138   13   | 17    178   6    | 5     9     2    |
| 2     6     7    | 4     9     5    | 1     3     8    |
| 89    5     19   |%12    3    -28   | 4     7     6    |
*--------------------------------------------------------*
Eliminating 2 from r9c6(ALS-XZ A=129(%) in r29c4 B=249(#) in r23c6 x=9 z=2)

if the most difficult sudoku is a 10, this would be a .001

tarek
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tarek

Joined: 31 Dec 2005
Posts: 153
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PostPosted: Sun Feb 17, 2008 3:18 pm    Post subject: Reply with quote

I just noticed that this thread needs an update.........

I will be posting a list of puzzles with its original poster shortly.

This list on one side has the solver program & on the other the puzzle which rates highst according to it....

My thoughts for the moment are : gsf's sudoku q1 option, Sudoku explainer 1.2.1, SuexratX & probably ravel's minimal steps (RMS), there have been contributions from Obi-Wahn, Champagne & others with their solvers. this could be added to the list.

tarek
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daj95376

Joined: 05 Feb 2006
Posts: 349
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PostPosted: Sun Feb 17, 2008 7:57 pm    Post subject: Reply with quote

There is a Unique Rectangle Type 4 for candidates 15 => [r25c8]<>1, but it doesn't help

There is a W-Wing/Semi-Remote Naked Pair/Y-Wing Styles between cells [r6c5],[r9c6] with strong link [r3c5]=2=[r3c6] that results in three eliminations in 8, the PM cracks at this point

Code:
+--------------------------------------------------------------------+
|  1      2      4     |  37     5      37    |  6      8      9     |
|  3      7      8     |  19     6      49    |  2      45-1   15    |
|  5      9      6     |  8      12-----24    |  3      14     7     |
|----------------------+----------------------+----------------------|
|  6      138    139   |  5      278    379-8 |  89     12     4     |
|  89     138    2     |  369    4      39-8  |  7      56-1   15    |
|  7      4      5     |  269   *28     1     |  89     26     3     |
|----------------------+----------------------+----------------------|
|  4      138    13    |  17     17-8   6     |  5      9      2     |
|  2      6      7     |  4      9      5     |  1      3      8     |
|  89     5      19    |  12     3     *28    |  4      7      6     |
+--------------------------------------------------------------------+
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hobiwan

Joined: 11 Feb 2008
Posts: 83
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PostPosted: Mon Feb 18, 2008 10:07 am    Post subject: Reply with quote

There are also some XY-Chains, that solve the puzzle, for example:

XY-Chain candidate 9: [r2c4]-1-[r3c5]-2-[r6c5]-8-[r6c7] => [r6c4]<>9, puzzle solved
XY-Chain candidate 1: [r2c4]-9-[r2c6]-4-[r3c6]-2-[r9c6]-8-[r9c1]-9-[r9c3] => [r9c4]<>1, puzzle solved
XY-Chain candidate 8: [r6c5]-2-[r3c5]-1-[r3c8]-4-[r3c6]-2-[r9c6] => [r45c6]<>8, [r7c5]<>8, puzzle solved
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tarek

Joined: 31 Dec 2005
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Location: London, UK

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PostPosted: Thu Feb 21, 2008 7:38 pm    Post subject: Reply with quote

Here is an up-to-date list of the hardest puzzles according to some solver programs......

Additions/corrections are most welcome.


Hardest Sudokus according to various solver programs:

gsf's sudoku q1 (rating) 1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1 JPF Easter Monster 99408
gsf's sudoku q1 (Processing time) ..1..4.......6.3.5...9.....8.....7.3.......285...7.6..3...8...6..92......4...1... tarek tarek071223170000-052 4m19s@2Ghz
Nicolas Juillerat's Sudoku explainer 1.2.1 .......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... tarek golden nugget 11.9
dukuso's suexrat9 .2.4.37.........32........4.4.2...7.8...5.........1...5.....9...3.9....7..1..86.. coloin col-02-08-071 4483
dukuso's suexratt .......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... tarek golden nugget 2141
RMS .....1.2.3...4.5.....6....7..2.....1.8..9..3.4.....8..5....2....9..3.4....67..... Ocean Ocean's New Year's present for RW 24
Obi-Wahn's solver 1.......2.9.4...5...6...7...5.3.4.......6........58.4...2...6...3...9.8.7.......1 coloin coloin-04/13-1414 1 Star - 7 Jellies - 27 Swords
Champagne's solver (Processing time) .......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... tarek golden nugget 96s250

tarek
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witch hunter robin

Joined: 09 Oct 2008
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PostPosted: Thu Oct 09, 2008 2:59 am    Post subject: Reply with quote

Personally I find the 25x25 the most challenging. Yes, I have solved them on my own.
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MacroSudoku

Joined: 06 Nov 2008
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PostPosted: Thu Nov 06, 2008 2:38 pm    Post subject: Reply with quote

Regarding the:

gsf's sudoku q1 (Processing time) ..1..4.......6.3.5...9.....8.....7.3.......285...7.6..3...8...6..92......4...1... tarek tarek071223170000-052 4m19s@2Ghz

My solver takes only 1 015 milliseconds (which is more or less 1 second) to solve it, with a intel celeron M 1.5GHz...

Does it mean that my solver (MacroSudoku) is quicker than the one used to rate the above Sudoku?
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Mauricio

Joined: 22 Mar 2006
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PostPosted: Thu Nov 06, 2008 5:16 pm    Post subject: Reply with quote

Solving and rating are 2 different things.
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tarek

Joined: 31 Dec 2005
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PostPosted: Thu Nov 06, 2008 5:39 pm    Post subject: Reply with quote

MacroSudoku wrote:
My solver takes only 1 015 milliseconds (which is more or less 1 second) to solve it, with a intel celeron M 1.5GHz...

Does it mean that my solver (MacroSudoku) is quicker than the one used to rate the above Sudoku?
That is the quoted figure for q1 (a rating algorithm in gsf's sudoku) Processing time.

tarek
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MacroSudoku

Joined: 06 Nov 2008
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PostPosted: Thu Nov 06, 2008 5:45 pm    Post subject: Reply with quote

Ok, thanks for the info.

But does it mean that my solver is pretty quick (i.e quicker than the one used by tarek), even though I made it with visual basic (which is not really known for its rapidity)?

Also, if my solver use human-solving techniques, why can't we say that solving and rating are related? I mean, the macro and a human would more or less apply the same solving techniques, so it looks to me that they should be related in some way, no?
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MacroSudoku

Joined: 06 Nov 2008
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PostPosted: Thu Nov 06, 2008 5:46 pm    Post subject: Reply with quote

Ok sorry, i've got my answer now... and it seems that our posts were sent at more or less the same time Smile
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ququman

Joined: 30 Jun 2006
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PostPosted: Thu May 14, 2009 2:19 am    Post subject: Reply with quote

I would like to submit a puzzle that is harder than the Easter Monster. I would like your opinions on this puzzle:

090030006
004500000
800001000
020090300
006000002
500000070
000700500
000008010
003060004

Let me know what you think.
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