The New Sudoku Players' Forum

[Eioru]

many of them are produced by Ocean and gsf

10.0 puzzles
.....1..2.1..2..3.4..5.......4.....6.7..3..1.8.....9..5....8.......1..7...64..5..
...1...2..1..3.4....5.....67......6....4..1....8..6..73...4......6..5..8.9.2.....
...1..2....3.4.....2...5..6..4.7..3..8....1..6.......5..7.9..4.9..4..........25..
..1.....2.3...14......5..6.5...6..7...2..8....4.3........9....66...7..9...4...1..
.1....2.......3..45...2..1.2...6..5...7..8....9.3..........48....49....36......2.
.1..2.........3..4..45...6..2..7.1....8.....36......5....4....59....2....7..9.2..
.1..2.........34..5..6...1...3..78...6.1.........3...7..4..83...2.....9.6.......5
1.....2......3...4..45...3..6...21.....7...4.2.......8.1..6......74...5.8....9...
1.....2...3......4..56...7..8...3...2...1...8...7...5...79...6..1..8.........79..
1...2..3......14...5......6.7.6....8.....3.1...8...6....2.3.....6.5....79....4...

9.9 puzzles
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....6..9....2.......4..7...35..8..
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....9..9....2.......4..7...35..8..
..1.....2.3..4....5..6..3....7..8..1.6..1..3.1..9..8....5..9..4.8..5..7.2..1..9..
..1..2..3.2..4..1.5..6..........7..1.3..8..2.4..5..6....5..9..2.7.....8.3.....9..
.1..2...3......41........5...56......2..4...78....9...6....3....4..1...2..95.....
1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...5..3..4.7.......1
1.......2.3..4..5...6...7.....1.3....4..8..9....4.5.....7...1...8..3..4.2.......6
1.......2.3..4..5...6...7.....1.3....8..7..4....4.6.....2...6...5..3..8.9.......1
1.......2.3..4..5...6...7.....1.4....8..7..4....5.8.....7...6...5..3..8.2.......1

[gsf]

many of them are produced by Ocean and gsf

10.0 puzzles
.....1..2.1..2..3.4..5.......4.....6.7..3..1.8.....9..5....8.......1..7...64..5..
...

the 10 10.0 puzzles are the same up to isomorphism

and these are the only puzzles that don't appear in ocean's 55 hardest (up to isomorphism)

Code: Select all

..1..2..3.2..4..1.5..6..........7..1.3..8..2.4..5..6....5..9..2.7.....8.3.....9..
..1.....2.3..4....5..6..3....7..8..1.6..1..3.1..9..8....5..9..4.8..5..7.2..1..9..
.1..2...3......41........5...56......2..4...78....9...6....3....4..1...2..95.....


[ravel]

Kalimera, back again.
Thanks for all the contributions in my absence.

I am very honored by the idea of writing a booklet about hardest sudokus, but there are two main arguments against such a project in the moment.
The one is, that i am very short of time and this will not change until the end of the year.
The other is, that still there are coming in new hardies going to the top of the list each month and this will not change as long as Ocean is working for this thread
So i think, it is too early for a compendium/annotation of this thread, but of course i would appreciate, if anybody wants to start something in this direction.

I am still hoping that a better rating program will be made available for all.
My program seems to work without serious bugs, but it is written quickly out of a simple solving/creation program, so the source (maybe 2/3 of it should be thrown out and the rest optimized) and also a binary (it is very slow, the hardest need hours to calculate the steps) is a shame for a programmer, so i dont dare to publish it.

For the new puzzles i ran my program for Eioru's sudoku from 9/3, which can be solved with 2 steps, also Gurths pearl with ER 8.9 needed less than 4 steps.
JPF's two puzzles are not totally finished yet [Edit: 4 and 3 steps]

Oceans puzzles will need my program at least the next 2 nights (the puzzles with ratings above 9 or 14 steps in the first run are checked again with up to 5 or 9 other versions or selection orders).

[ravel]

Updated the list again.

[Edit: thanx to gsf: What i denoted as ER-9.9 #1 and #5, are the same, so i had to renumber 289 to 269. I also corrected the wrong copy of puzzle 241]
The step counts for Oceans puzzles are:
ER-9.9: 9,7,5,7
ER-9.8: 7,6,9,3,4,7
ER-9.7: 12,9,6,6
ER-9.6: 4,6,5,8
ER-9.5: 5,3,4,4,6
9.7-rated with new pattern: 8
9.7-rated from the "rare shape" thread: 5


JPF's 9.4-rated had 4 steps.

I should note that the ratings are not really fair for the puzzles, that had high steps in the first run. E.g. i got 20 steps for the 3rd 9.9 puzzle first, but in the 5th run it fell down to 7 steps, whereas the 3rd puzzle of the 9.8-rated had 9 steps (less than 10) in the first run, so i did not start another run to save time.

[gsf]

I am still hoping that a better rating program will be made available for all.
My program seems to work without serious bugs, but it is written quickly out of a simple solving/creation program, so the source (maybe 2/3 of it should be thrown out and the rest optimized) and also a binary (it is very slow, the hardest need hours to calculate the steps) is a shame for a programmer, so i dont dare to publish it.

I posted alternative characterizations and ratings here
for ocean's 54 -- I just posted ratings for the complete 289 there

my solver rates all 289 in 22sec on a 1Ghz pentium
it splits the solution into steps but takes into account all moves available at each step (instead of just the hardest)
the rating applies multiple constraint orders, from "easy" to "hard", and stops
at the first in the order that solves each puzzle

[Ocean]

Updated the list again.

Thanks for analyzing the puzzles!
A bit interesting that now also a puzzle with ER 9.8 did not qualify for the list. Seems that puzzles with high ER-rating can have any number of steps. Roughly ten percent below 4 steps, and ten percent 12 steps or more, in the ER-range 9.5 to 9.9. Direct correlation between the two methods seems to be rather small. One of the 23 submitted "X-puzzles" made it to the "top ten" (12 steps now), which is close to the "expected two".

I should note that the ratings are not really fair for the puzzles, that had high steps in the first run. E.g. i got 20 steps for the 3rd 9.9 puzzle first, but in the 5th run it fell down to 7 steps, ...

So, new puzzles may initially get too high rating - and it's expected that some of them will later be downgraded...

[ravel]

So, new puzzles may initially get too high rating - and it's expected that some of them will later be downgraded...

Yes, the problem behind it is that my rating can differ much for isomorphic puzzles - the harder they are the more (which is not the case for gsf's rating and much less for ER).

Also, my rating only takes the best step count it finds. I suppose, a puzzle, where many different ways are possible to solve it in say 5 or 6 steps is easier than one like gsf's leader, where a 5 (brute force) step solution was found, but the next best needed 10 steps.

[gsf]

Also, my rating only takes the best step count it finds. I suppose, a puzzle, where many different ways are possible to solve it in say 5 or 6 steps is easier than one like gsf's leader, where a 5 (brute force) step solution was found, but the next best needed 10 steps.

right, for the ratings I posted, the solver identifies all moves at a position and doesn't
commit until all are identified
this models the inferior step thread step counts
that thread reached a concensus on step that all submitters were eventaully
able to reproduce with their own solvers

that step definition didn't measure the best solutions -- rather it measured
reproducable solutions, even on isomorphic copies

when a solver resorts to propositions (the g word) it can get lucky and hit
a solution earlier with a different sequence of propositions
for all known puzzles, even the hardest can be solved with at most two
(very lucky) propositions

the problem is that luck is hard to quantify and codify
if a puzzle has 1/n solutions that is easy, and (n-1) that are the hardest ever seen,
is it easy or hard?
maybe if n were small, but even with 40 candidate cells with ~3 candidates each,
n would be ~(40*3)**2 or ~10**4

[Eioru]

Code: Select all

6.54.....
...2..3..
.3...1..9
..3.4..8.
.....8..7
81..9.4..
1..8...3.
..6..4...
4...7.2.1

[ravel]

Thanks Eioru, 5 steps.

[tarek]

gsf scoring would mean that screening should become easier.......

A high score from sudoku coupled with a high score from suexrat should do the trick.........

7 steps by ravel's reckoning & 9.3 SE reckoning is outside the top 100 by gsf's reckoning, some serious puzzles out there

I suggest that because of the great number of puzzles generated & due to the effort put in here by ravel, that the posted puzzles SE rating should be checked beforehand by the poster to insure that they are equal or more than a pre defined standerd (I set that for myself now as being my last best SE rating which is 9.3 )

tarek

[claudiarabia]

Code: Select all

. . . 7 . . . 4 .
. . 2 . 1 . 9 . .
. 3 . . . 8 . . 5
. . . 8 . . . 7 .
. . 4 . 9 . 6 . .
. 5 . . . 4 . . 3
1 . . 9 . . . . .
. . 8 . 4 . 2 . .
. 2 . . . 3 . . .   Missoni


Claudia

[ravel]

Tarek,

i hope that gsf's new rating will be a third good indicator for the hardest puzzles. We all know (and recently Ron has pointed it out), that each rating looks at other properties of the sudokus.

I saw that my current leader, Ocean #1/M21/D21, is nr 1 for SE also and nr 2 in gsf's rating, so i think, there can be common agreement, that it is the hardest known in the moment.

For other puzzles there are big rating differences, and i think about removing puzzles from the list, which are low rated either by SE or gsf's rating.


Claudia,

thanx for the puzzle, i will check it on Monday.

[JPF]

Here are 3 puzzles (SE >=9.0)

Code: Select all

000700040006010900030000005000800070004090800050001003100980000008040200020003000
000700040006010900030000005100800070004090000050001003600980000008040200020003008
000700040006010900030000005100800070004090000050001003600980000008040200020003004


JPF

[Eioru]

Code: Select all

 . 2 . | 1 . 6 | . . .
 8 . 6 | . 2 . | . . .
 . 7 . | 3 . . | . . .
-------+-------+-------
 1 . 9 | . . . | . . 4
 . 5 . | . . . | . 7 .
 2 . . | . . . | 9 . 3
-------+-------+-------
 . . . | . . 1 | . 4 .
 . . . | . 5 . | 2 . 8
 . . . | 7 . 9 | . 6 .        ...9.0

 . 2 . | 1 . 3 | . . .
 9 . 8 | . 5 . | . . .
 . 1 . | 4 . . | . . .
-------+-------+-------
 7 . 9 | . . . | . . 5
 . 3 . | . . . | . 4 .
 8 . . | . . . | 6 . 1
-------+-------+-------
 . . . | . . 7 | . 6 .
 . . . | . 6 . | 2 . 3
 . . . | 3 . 2 | . 5 .         ...8.9