The hardest sudokus

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

Postby gsf » Thu Apr 05, 2007 2:02 am

daj95376 wrote:Since there weren't any further comments, I assumed there wasn't any interest and dropped the idea.

too many ideas at once
the solver I posted over the weekend has a format to list the #templates per clue with optional sorting
Code: Select all
%+#r#.P

sorts them ascending separated by .
use - for descending or omit for counts by value 1..9
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Postby coloin » Sat Apr 21, 2007 12:23 am

Sorry - but i do wish I could use your program........

Just curious................What was the result for "Easter Monster" ?
Code: Select all
1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1

Thanks
C
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Postby gsf » Sat Apr 21, 2007 2:41 am

coloin wrote:Sorry - but i do wish I could use your program........
Just curious................What was the result for "Easter Monster" ?
Code: Select all
1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1


Code: Select all
8.18.18.32.39.41.41.130.148

what kind of trouble with my solver?
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Postby coloin » Sun Apr 22, 2007 6:06 pm

Thanks for the daj rating !.......unfortunatly not spectacularly different.

No the slight problem I have with your program is the windows.net frame which it requires.......thats all .

I read somewhere that a puzzle tended to be difficult if it didnt have a clue value. Unfortunatly this precludes many of our 16 clue bases.

However I did find this one - much better than all the others I looked at.
Code: Select all
 1.......6.2.7...5...3...4...8..2........65......8.3.7...4...3...5...8.2.6.......1  Suexr 778, SE 10.5

It possibly would have higher over all daj counts

Edit
Code: Select all
6.9.16.16.22.22.31.31.2632


the missing clue value is high.......but the others are low. Quite possibly this does not tell us much !

C
Last edited by coloin on Mon Apr 23, 2007 4:26 am, edited 1 time in total.
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Postby gsf » Sun Apr 22, 2007 8:12 pm

coloin wrote:No the slight problem I have with your program is the windows.net frame which it requires.......thats all .

I don't use .net -- its compiled for native windows command line (i.e., the CMD.EXE prompt)
could you try again and send the exact error message text
thanks
coloin wrote:I read somewhere that a puzzle tended to be difficult if it didnt have a clue value. Unfortunatly this precludes many of our 16 clue bases.

"didnt have a clue value" -- what does this mean?
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Postby daj95376 » Sun Apr 22, 2007 8:25 pm

coloin: Ruud's solver uses Windows.Net

gsf: One value is not present among the clues
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Postby gsf » Sun Apr 22, 2007 10:33 pm

daj95376 wrote:coloin: Ruud's solver uses Windows.Net

gsf: One value is not present among the clues

thanks

in general with my solver if you don't care how it derives solution(s) use
Code: Select all
-d -qFN

this enables the fastest depth first singles only backtrack search
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Postby tarek » Mon Jun 11, 2007 7:43 pm

It turns out that The backdoor size 3 under the FN constraints does not correlate with difficulty as we would have hoped....

would that still be the case with a backdoor size 2-3 but with the complete arsenal of constraints (forgive me gsf, I lost track of the constraints in your solver)

The reason why I'm suggesting this is that techniques following FN are not always difficult. but A BACKDOOR SIZE 2 UNDER Sudocue techniques for instance, can correlate with extreme difficulty.

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Postby gsf » Wed Jun 13, 2007 1:11 pm

tarek wrote:It turns out that The backdoor size 3 under the FN constraints does not correlate with difficulty as we would have hoped....

would that still be the case with a backdoor size 2-3 but with the complete arsenal of constraints (forgive me gsf, I lost track of the constraints in your solver)

the known M3 (singles backdoor size 3) puzzles all have FNB (singles+box-line/locked-candidates) backdoor size 2
except the Easter Monster which has FNBT2 (singles+box-line/locked-candidates+naked-pairs) backdoor size 2
so it doesn't take much more technique strength to weaken the backdoors
The reason why I'm suggesting this is that techniques following FN are not always difficult. but A BACKDOOR SIZE 2 UNDER Sudocue techniques for instance, can correlate with extreme difficulty.

with the kitchen sink all puzzles in the q1 taxonomy catalog (this includes the hardest from the player's forum) have backdoor size 1 or 0

the q1 taxonomy has a range of q1 ratings from 1 through 99408 (JPF's Easter Monster)
q1>3000 requires guessing in my solver, but there are lower ones that do so also, e.g. q1==71

I had hoped that the q1 ratings for puzzles not requiring guessing would provide insight
into the constraints that solve the puzzles, but that doesn't seem to be the case
my solver doesn't do uniqueness/als constraints -- maybe that skews the observation

recall the the q1 rating uses naked/hidden singles (and box/line for the very hardest) in singleton and pairwise propositions to rate puzzles
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Postby tarek » Fri Jun 15, 2007 8:37 am

hmmm,

Not sure where to go next from here:(

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Postby daj95376 » Fri Jun 15, 2007 4:14 pm

tarek wrote:hmmm,

Not sure where to go next from here:(

tarek

You might want to review these entries.

Code: Select all
001002300040030050500100006007000000060000080200000100009001004030050060000900700 JPF #2/100b
001002300040030050500100006007000000060000080200000100009001004030050060000900700 Ocean #14/empty box

200004700040090000008500001001000005030000060700000900900007200000040080006100009 Tarek Fluid Drive #15
200004700040090000008500001001000005030000060700000900900007200000040080006100009 Tarek Fluid Drive #19
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Postby Ocean » Fri Jun 15, 2007 6:43 pm

gsf wrote:
tarek wrote:It turns out that The backdoor size 3 under the FN constraints does not correlate with difficulty as we would have hoped....

would that still be the case with a backdoor size 2-3 but with the complete arsenal of constraints (forgive me gsf, I lost track of the constraints in your solver)

the known M3 (singles backdoor size 3) puzzles all have FNB (singles+box-line/locked-candidates) backdoor size 2
except the Easter Monster which has FNBT2 (singles+box-line/locked-candidates+naked-pairs) backdoor size 2
so it doesn't take much more technique strength to weaken the backdoors

These are the 14 M3-puzzles known so far (labeled as in the q1 taxonomy catalog):

100000002090400050006000700050903000000070000000850040700000600030009080002000001,Easter-Monster
900000005040300060002000100080740000000020000000806070100000900030007040005000002,ULTRA0300
700000004020600010005000800030910000000050000000203090800000700060009020004000005,ULTRA0301
100000089000009102000000400007600000030040000900002005004070000500008010060300000,tarek-4/08
100000002003400050060000700000890040000306000009040000020000100700000006005080030,jpf-04/14/08
500000003020600010008000900040701000000030000000420070900000500010007020003000008,ULTRA0302
100000002003400050060000700000050040000301000008940000020000100700000006005090030,jpf-04-10
100000006020500040003000700040850000000010000000024080007000300050009020600000001,coloin
100000006020500040003000700040890000000204000000015080007000300050009020600000001,coloin-05/11/01
001000200030000040500030006000107000040000080000902000300000008060050030002000700,ocean-2007-05-29-1
300000200000540000000600000102003000000000064800000000090700050000000108050060000,gfroyle-2007-05-30-4
080090000300000060000300040000010005002000900007000800650000100000207000000004000,gfroyle-2007-05-30-3
000020580040300000010000000000600071500000200000400000200059000000000306700000000,gfroyle-2007-05-30-2
000500001308000000400003000000610000900000800000050000060700020010000300000000490,gfroyle-2007-05-30-1

The gsf's q1-ratings split in two different groups, [00795-01723] and [95600-99408].
Explainer ratings are {3.6, 4.4, 5.7, 6.6, 9.4, 11.0, 11.1, 11.2, 11.3, 11.4}.

tarek wrote:hmmm,

Not sure where to go next from here

Is there any correlation at all between backdoor size and difficulty? What about number of backdoor cells/pairs? Will backdoor size 3 + something extra imply a hard puzzle? What about backdoor size 2 + something extra?
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Postby tarek » Thu Nov 08, 2007 2:17 am

some records to break (not the q1 rating though)....
SE 11.5, Sx9 3400+, SS backdoor size 2

Code: Select all
Golden Nugget
.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7.....
 . . . | . . . | . 3 9 
 . . . | . . 1 | . . 5 
 . . 3 | . 5 . | 8 . . 
-------+-------+------
 . . 8 | . 9 . | . . 6 
 . 7 . | . . 2 | . . . 
 1 . . | 4 . . | . . . 
-------+-------+------
 . . 9 | . 8 . | . 5 . 
 . 2 . | . . . | 6 . . 
 4 . . | 7 . . | . . .

Enjoy solving

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Postby RW » Thu Nov 08, 2007 3:33 pm

Nice one tarek! Interesting that it is not created in the same way as the most recent toughies in the "9+" thread, and it isn't fully diagonal. It actually breaks many "rules" that have been made up for creating tough puzzles. Apart from not being diagonal, there's also several given digits repeated in band 1 and stack 3.

As we've had the christmas present, the new year's present and the Easter Monster, I was expecting some new monster puzzle to appear around halloween. They tend to come close to holidays...:D

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Postby coloin » Thu Nov 08, 2007 3:40 pm

Fantastic "Golden Nugget"
11.5......Suexrat9 3400 +
Well done, How did you make it ?

Awaiting the swords and jelly count !!!!

I actually have more M3 puzzles !

C
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