## The hardest sudokus (new thread)

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

### Re: The hardest sudokus (new thread)

Mauricio wrote:
champagne wrote:2) try without the given in excess
. either you solve it now and find the given in the solution, the puzzle was not minimal
. or you fail and then you look for something else.
...

Counterexample to point 2
Code: Select all
`.....1..2..3.4..5..6.7..8....1....3..4..9.1..7..1....6..5.7.....8.6...9.2....3..4`
Minimal, not symmetric, remove 1@r6c4 (now multisolution, but symmetric), solve it (assuming uniqueness, wrongly), and you have r6c4=1 in the solution.

Now, if you remove one clue, giving it symmetry, solve it, and if the solution is not consistent with the original puzzle, then you now the clue you erased was not redundant; in other words, redundancy allows you to erase a clue, but IMO it is not easier to know if a clue is redundant than to solve the puzzle.

nice counter example, good to have the expert in symmetry.

is it a contradiction with point 2? I am not sure. and your reaction open some doors
Happily, in the wording, I did not stated that the puzzle was not minimal, so I have may be an escape lane.

Here it is a fact that the solution has a symmetry of given.
No easy way to establish it "forward". It could be that easy moves at the start lead to the symmetry, but in all these puzzles, the first move is very tough to establish.

Trying a kind of "backward" symmetry is still valid.

As you say, if the given in excess does not come, you know you could not erase it and you have to find something else..

If the erased given comes, as the puzzle is assumed to have a unique solution, it must be the solution, but it does not bring the probe that that digit was in excess.

Am I right??

champagne
champagne
2017 Supporter

Posts: 6250
Joined: 02 August 2007
Location: France Brittany

### Re: The hardest sudokus (new thread)

Champagne,

i have made a new filter now. Can you find a hard one in this sample ?
Hidden Text: Show
.2.45....4....92....6.2...........383...9.5...7...3.1.5..9..3...8......6..1....7.
..3..6..9.5.1.....8...7.........436...4...9.....62...4.1.8.......6..2..37...6..5.
1...56.....7..9..6.6.7...4..4.6..3....5..7...9...1........7.82.......4...8.2....3
.2...6.894....9..3..97..5....4.7.9..8......2..3......4..1..76...4..........51....
...4...8...7..92......3...526...1.....19......7....1..5......4.71.8....3..6..29..
..34......5...9...6...2.1..2...6...1.4.5...6...6..3.....9...6.7......8.28...7..1.
.....6......18.2.66..32.....7.....5...9...4..8....2..33....1..8..5...9......4.37.
..3..67...5.1....66...2..4..8....9..3.18.......5.....8.....4.2..3.9....1....7.6..
1...5...9.56........92......1..6...7.....4.2....8..3....1.7...67......4..6...387.
.....678....1....6.6..7.4...7...1..4..5.2....9...3....3.....5...1...7..8..29...4.
...4.67....7....2.....7...5..6.4.5...9.6.1...8..3.....3..9...5..1......8..4.6.2..
..3..6.8....1..2.66...7...5..4......3....4.9..98.2.....3...8.6.8.....1.7...5.....
..3..6.8....1..2......7...4..9..8.6..3..4...1.7.2.....3....5..8..5...6..98.....5.
1...5...9......12...8...5...3.8.....5...6..9...4..7....7.6.4...6...2.9....53....6
1...5...9......12...8...5...3...7...8...6..9...48....2.7...4....8.3....66...2.9..
1..4.6....5.1.9.....6.2..1..8..4...5..9..2.4.7.....3..3.....8....42...6.........7
......7.94....9.3..8....4.5..18......6..2....7....53..5....7..3.7.6.......2.1..7.
..3.....94....92...9..7..1....56.9......1...8.6...7.5..1.7...9...2.....38.....4..
..3..6..9.5.1.....8...7.........43....4...92....62...4.1.8.......6..2..37...6..5.
...4...8...7..92......3...526...1.....19......7....1..5...9..4..9.8....3..6..29..
1...5...9..7...2...69..3.4....8..9.....91..7.9....5..83..5....1..2...6...4.......
.2.4....9..7...23.6.....5........69..9...4..2..5.9..7.3....8......2.1....1..4...8
1.......9..67...2..8...3.....76...4.36..1.....9..78.....5...2.....5..6.4.....7.5.
....56.8...71....6....27.....6..1..53......6..4.6..9....5.1...2.9....3..8......4.
...4.6..9..7.8..6......35..2...1....8......1...16.7.....2.6..9....9..3...9...5..4
1.....7.9.5.1......69....1.....4.8.7.....3..29..7...5.....2.4....4..8..36......7.
..3..6.8....1..2......7...4..9..8.6.....4.1...7.26......5.....383...5...96.....5.
1....67...571.......9....1..4....3.......89.29..7...6......24..5..6...9.....3...8
...4...8...7..92......3...52...7.1....19.....76...1...5......4...6..29...7.8....3
1.....7..4.7....36....7...42....8...5..9.......4.1.3....1.4.6...4...2.9.8..5.....
...4...8...7..92......3...52...7.1....19.....76...1...5...9..4...6..29.....8....3
....5.7..4...8...3.6.3...1.2....5.3..3.9..1......4.....9.7....1..2....7.8.....69.
...4...8...7..92......3...526...1.9...19.....7.....1..5...9..4...6..29.....8....3
...45....4....92....6.2......9.....83...9.5...75..3.1.5..9..3...8......6..1....7.
..34...8..5......6.....71..24.....9.3..9.......9.4.8....28...4.....6...7.....15.8
..34...8..5......6.....71..24.....9.3..9.......9.4.8....28...4.....64..7.....15..
..34......5...9...6...2...12...1...8.4.5..1....1..3.9...2.....77.....61.....7.8..
..34......5...92..6.9.7.....15....98.....1.2....5..1...9...58....4.6.......3...7.
..34......5...92..6...7.....15.....8.....1.259..5..1...9...58....4.6.......3...7.
..345.....5...92..6...7.....15.....8.....1.259.....1...9...58....4.6.......3...7.
.2.....8..5.1....6..9..71..2....3.......41.....47..3..6..9...2...2.1.9...8......5
.2..5..8......9..17.91.....2..5.8.6..6....8....8.6.4..3.............73...4..2..5.
.2.4....9..7.8..3.6...2.5....69.8....1..4...8.....1...3.....6...6...4..2..5....7.
.2.4...8.4.......68.9..7...2..9...7..7..1.6.......3..5......3....27...4..4...5..1
1....6..9.5.1...3...8...1....1...8...3.....5.9....4..2..2..7.9....24...77...6....
1....67.....18...6.6.73.....1...3..8...5.....5.4....2..3...1..7....9.4..9.2......
1...5...9.56........92......1..6...7.....462.6..8..3....1.7...67......4......38..
1...5...9.56........92......1..6...7.....4.2.6..8..3....1.7...67......4......387.
1...5...9......12...8...5....73....6.8...4..16...2.9...3...7...8...6..9...48.....
1...5..8...7.....6.....34..2..9.1........5.2...5.2.8...4...8..7..6...3..8...9..5.
1...5..8..5...9..6..9.2.5...7.3.......4..23.....54.....6......1..52..9..8......7.
1...5......7..9..6.6.7...4..4.6..3....5..7...9...1........7.82......84...8.2....3
1...5.7....6..9....8......42....3..1....2..37...5..2....46.....5...1.3...9...8..5
1...56.....6...1...8.2....4...3..84..3...49......2...3....4..7.5...7.....4.9....8
1...5...9......12...8...56.2...6..9..3.8.2..1..4..7....7...4...6...2.9.....3.....
1...5..8...7.....6.....34..2..9.1........5.2...5.2.8...4......7..6...3.88...9..5.
..345....4....9..2...1......1..7..9...539....9....42...7......4......6.86....8.2.
.2.4...8.....8...68....71.42..5...9..95.......4..3.........1..7..28...4.....6.3..
.2...6.8.4..18......972..........5...7.6...2.9.......35....7..4...2..3...1..6..7.
1...5...9..7...2...6.....4....83.......9...7.9....5..83..5....1..2..16...41.9....
.....67...5.1.......9.3...4...7..41......56....8.4...3..2...34.8...2....93......2
...45.7....7.8.........7.1.2......9.31......6..5..41...6.2....1..1..85..9......3.
.2...67.........32..9....6...854.....4...3.7.9...1.4....189....5.........9...4..7
1.......9..67...2..8...3..4..76...4..3..1....96...8.....5...2.7.......5....5..4.6
1...5...9.5.....3...9.......1..6...7.....4.2.6..8..3........87.7..3.2.4...1.7...3
.2..5....4....92...89......2..5...633...1...7..4..38...4....3.....6...15....7....
1...5...9.56........92......1..6...7.....4.2....8..3....1.7...67......4.9....387.
1..4..7....7..9..6.8.....5.....1....83..9......5..7.6.3.......5....4..92..2..56..
..3.5.7..4....9....8.2..1..2.....31...6.1...7......65..9.8...6......4.....5.3..7.
.2....7..4....9..3....2.4....1...6..8....3..4...67..1..8...5...5...3..4...98....5
.2...6.8...71.....6.9.3......1.9.......7..3...6...2.5......4..2..6....4..42...8.5
1...5...9......12...8...5..2...6..9..3.8.......4..7....7.6.4.1.6...2.9.....3....6
1...5...9......12...8...5..2...6..9..3.8.2.....4..7....7.6.4...6...2.9.....3....6
..3.5.7..4.7..9....8.7....1.7.8...1.8.5.4....9.........6.2..1.......3..8.......62
..3.5.7..45...9....8.2....52....4..3..5.3..7....8......9....61...6.1...7.......5.
..34...8..5......6.....71..24.....9.3..9.......9...8....28...4.....64..7.....15.8
.2....7.94.......6..93...1...5.3........98.5....5....1.7..4......18...9.6....3..2
1.......9..67...2..8...3.6...76...4.36...1....9...8...6....7.5....5..2....5.....4
..3.5...94....9..2...1......1..7..9...539....9....42...7......4......6.86....8.2.
....5.7..4...8...3.6.3...1.2....5....3.9..1......43....9.7....1..2....7.8.....69.
..34..7...5..8...6.....3....1...4...5.6.1....8..6....1...2..9...6..4...89....7.2.
....56.8...71....6....2.4...9..7....3..5..8....5..1..2.4.7.......6.1...59.....3..
....5....4....92...89....1.2..5.......4..29...3..6..7.3..7...2..4...83.....6....1
...4...8...7..92......3...526...1.....19.....7...2.1..5...9..4...6..29.....8....3
...4...8...7..92......3...526...1.....19.....7...2.1..5...9..4...6..29.....8....3
...4.6..9..7.8..6......35..26..1....8......1...1..7.....2.6..9....9..3...9...5..4
..3..6.8....1..2......7...4..9..8.6.3...4.1...7.2.......58......6.....5.93...58..
..3.5...94....92..8..2............7...1..5..2.6....8...7..12.4.....3.6....25....1
..34......5...9...6...2..1.2...6...7..4.......9...36.........788...7.1...7.5.8..2
.2...67..4.6.....37.8....6.2....84......9..1..8.5.......2..78.....1...9.....3...5
.2...6...4...8.2...89.....1...6....5..4.9.3.......1.7.3.......7.4..3.9....2..5.4.
.2.4....9..7.8.23.6...2.5........6...9...4..2..5....7.3..9........2.1....1..4...8
.2.......4....9..6..9.7.1....17..5..3....5.91.6.....2...8..79.....8....4.3..1....
.2.4...8...7..9.......3...52..6...4...6.....1.4...3.....28...7.7....21..8....59..
1......8..5......3..9..74....4.7.9..8......5..3..4...7..27..6......64.......92..1
1....67....7.8...6.6.3........9......8...7..19...3.5..5...4..2..1...3..7..2...4..
1....67...5..8..3...92...6....5...1..8..9....6....3..73....4.7...2...4........3.1
1....67...57.8..3........4.........3.1...56....6.4..2...1..79..5..9....2.9.8.....
1...5...9..7...2...6.....4....83.9.....9...7.9....5..83..5....1..2..16...4..9....
1...5...9.5.........92......1..6...7.....462.6..8..3....1.7...67......4..6...38..
eleven

Posts: 1800
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

This is a very homogeneous lot. Very close as well of the primary selection I am doing.

I just erased a small number of puzzles I would not have taken.

Most of these puzzles have an EXOCET or a "Quasi EXOCET" pattern.
All are solved using the 2 cells AC2, not more

Sometimes the EXOCET pattern works well, sometimes not, so about 20 of them are still very hard, even using the EXOCET property.

Difficult to predict the SE rating, but from my experience in the pattern game, you have the best chance to find high ratings in the top of the below list.

I would bet for the best ones in the range 10.5 11.5 and not many below 10.0 , but this is in the field I explored. You came with surprising results.

champagne

I think your hardest is in that short list

Hidden Text: Show
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and here is a near complete list sorted to have in the top the highest SE ratings

Hidden Text: Show
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champagne
2017 Supporter

Posts: 6250
Joined: 02 August 2007
Location: France Brittany

### Re: The hardest sudokus (new thread)

Thanks,

the puzzles all have ER >= 11.2 and q2 > 98000, i applied the new filter additionally.
But i know better now, how to select puzzles for you.
eleven

Posts: 1800
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:The puzzles all have ER >= 11.2 and q2 > 98000, i applied the new filter additionally.
But i know better now, how to select puzzles for you.

I have always been testing minimal puzzles for difficulty ... Your search for a "Hardest" non minimal puzzle would be exploring uncharted waters.

tarek

tarek

Posts: 2650
Joined: 05 January 2006

### Re: The hardest sudokus (new thread)

I dont search for non minimal hardest puzzles, i just dont test for minimality in the moment
This can be done later easily, it will not change the basic ER rating in almost all cases, but lower the other two.
eleven

Posts: 1800
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

hi eleven,

From my experience, the right cut off to catch all "hardest puzzles" should be lower than 11.2 my last "hardest" had only a rating 10.8.
10.6 would be I think a good cut off.

champagne
champagne
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### Re: The hardest sudokus (new thread)

champagne wrote:From my experience, the right cut off to catch all "hardest puzzles" should be lower than 11.2 my last "hardest" had only a rating 10.8.
10.6 would be I think a good cut off.

When we were attempting the generation of "Hardest puzzles" 3+ years ago. We used to hit a brick wall with SE at the 10.6 mark. That is why JPF at the time collated the posted puzzles with a 10.6+ rating.

This reminded me of that time in the ancient past when Ocean hit that 10.0 mark for the 1st time . How far back did the goal posts move

tarek

tarek

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### Re: The hardest sudokus (new thread)

tarek wrote:
champagne wrote:From my experience, the right cut off to catch all "hardest puzzles" should be lower than 11.2 my last "hardest" had only a rating 10.8.
10.6 would be I think a good cut off.

When we were attempting the generation of "Hardest puzzles" 3+ years ago. We used to hit a brick wall with SE at the 10.6 mark. That is why JPF at the time collated the posted puzzles with a 10.6+ rating.

This reminded me of that time in the ancient past when Ocean hit that 10.0 mark for the 1st time . How far back did the goal posts move

tarek

We are speaking here of a cut off to analyze puzzles, not for a final publication. But may be we should have that discussion in another thread.

Reversely, frankly I don't believe at all we can rely on SE rating alone to extract hardest puzzles.

I did not publish many puzzles up to now and I have in cache some puzzles that would be eligible with your 11.2 filter, but they have nothing attractive on my view.

(and I don't see a rush to enter new puzzles)

Anyway, I don't want to be a source of trouble and if you think it's better, we open a separate thread

champagne
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### Re: The hardest sudokus (new thread)

champagne wrote:We are speaking here of a cut off to analyze puzzles, not for a final publication. But may be we should have that discussion in another thread.
I was only confirming your suspicions through our attempts back in 2006/2007

champagne wrote:Reversely, frankly I don't believe at all we can rely on SE rating alone to extract hardest puzzles.
I think it was said before that SE ratings >=9.5 are difficult to judge because all available solvers will go to T&E at this stage. q1, q2, Sx9 & Sxt all have flaws ... There is a chance that we are excluding puzzles with SE>=9.5 from the hardest list.

champagne wrote:I did not publish many puzzles up to now and I have in cache some puzzles that would be eligible with your 11.2 filter, but they have nothing attractive on my view..
As far as I'm concerned, this thread is to discuss the "Hardest puzzles" ... Discussions, Posted puzzles & ratings should NOT be limited by the filters I'm employing.

If you suspect that you have the hardest puzzle in a group of puzzles then feel free to post them.

tarek

tarek

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### Re: The hardest sudokus (new thread)

Here is one for the q2 list
Code: Select all
`99450 .2.4.....4....92...98.....4...6....75...1.....4...38..3......6....7....1..4..85.. Green Glasses`

This grid only has 2 strong links (but a low 10.x ER)
Code: Select all
`..3....8.4.........7..3...4...6..8...6.5.2.9...7.1...6.8.9..2..7...6...8.1.....5.+-------------------------+-------------------------+-------------------------+| 12569   259     3       | 1247    24579   145679  | 15679   8       12579   || 4       259     125689  | 1278    25789   156789  | 135679  12367   123579  || 125689  7       125689  | 128     3       15689   | 1569    126     4       |+-------------------------+-------------------------+-------------------------+| 12359   23459   12459   | 6       479     3479    | 8       12347   12357   || 138     6       148     | 5       478     2       | 1347    9       137     || 23589   23459   7       | 348     1       3489    | 345     234     6       |+-------------------------+-------------------------+-------------------------+| 356     8       456     | 9       457     13457   | 2       13467   137     || 7       23459   2459    | 1234    6       1345    | 1349    134     8       || 2369    1       2469    | 23478   2478    3478    | 34679   5       379     |+-------------------------+-------------------------+-------------------------+`

champagne wrote:All are solved using the 2 cells AC2, not more

Still i dont know, what AC2 really is and i did not find a definition in this forum. Can you point me to one please and demonstrate an AC2 move in this grid (#9 in my list), so that we can see, how complex it is ?

Code: Select all
` *----------------------------------------------------------------------* | 1       23478  23478  | 3467   5      678     | 2467   368    9      | | 2348    5      6      | 13479  13489  1789    | 1247   138    12348  | | 348     3478   9      | 2      1348   1678    | 14567  13568  13458  | |-----------------------+-----------------------+----------------------| | 234589  1      23458  | 359    6      259     | 459    589    7      | | 35689   3789   3578   | 13579  139    4       | 1569   2      158    | | 24569   2479   2457   | 8      129    12579   | 3      1569   145    | |-----------------------+-----------------------+----------------------| | 234589  23489  1      | 459    7      2589    | 259    359    6      | | 7       2389   2358   | 1569   1289   125689  | 1259   4      1235   | | 2459    6      245    | 1459   1249   3       | 8      7      125    | *----------------------------------------------------------------------*`

I have uploaded 5000 puzzles to zippy share f3sudoku.zip. They all passed 3 filters, which throw out 90 % of the known hardest including swampy oil and Mauricio's puzzle, but probably dont have a very high ER. Maybe you can find something in this set.
eleven

Posts: 1800
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:Here is one for the q2 list
Code: Select all
`99450 .2.4.....4....92...98.....4...6....75...1.....4...38..3......6....7....1..4..85.. Green Glasses`
Hi eleven,
Good catch ... Unfortunately I think it is a non minimal isomorph of Fata Morgana .... This will happen often when your search widens.

My tedious task will also check if the puzzles posted here have been posted before ... Your non minimal puzzles have to be minimized then checked
I have already a database with top lists of the past & submissions from coloin to check against but it will require updating with new puzzles submitted here.

tarek

tarek

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### Re: The hardest sudokus (new thread)

Wow, i really found an old one from random puzzles ? What a surpise !
eleven

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### Re: The hardest sudokus (new thread)

eleven wrote:
champagne wrote:All are solved using the 2 cells AC2, not more

Still i dont know, what AC2 really is and i did not find a definition in this forum. Can you point me to one please and demonstrate an AC2 move in this grid (#9 in my list), so that we can see, how complex it is ?

full-tagging-t5624.html

or on my website, but let me answer briefly.

My main process is a search of AIC's and AIC's nets to eliminate candidates.

Code: Select all
`level 1: stong links and weak links generated from rows/columns and boxes including groups.level 2: AHS are added with new strong links and new weak links.level 3: are added rowx/ columns or boxes patterns in which 2 digits are "unknown" to solve it         each possible solution (a couple of digits in 2 groups) is a super-candidate.         These super-candidates are eliminated in the same way as candidates.         2 kinds of new patterns are considered           2 cells 3 digits giving 3 super candidates             AC2 defined as {n cells n-2 known digits 4 free digits} and 6 "super candidates";              the smallest AC2 is made of 2 cells 4 digits and no known digit (group) `

In the last version of my solver (still bugged at the last level but I had no time to fix the bug), I defined a level 3.1 using only the smallest AC2.
. I thought and this is verified that most puzzles would be solved just using these ones
. They are much easier to see for a player.
. Last but no least, EXOCET patterns have such an AC2 as base, and the SK loop is solved just using them.

You can find examples of solutions using AC2 on my website;

champagne
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### Re: The hardest sudokus (new thread)

eleven wrote:Wow, i really found an old one from random puzzles ? What a surprise !

well a while back i was generating 21-clue puzzles and passing them on to champagne - and it was pleasing to see his solver and subsequent rater program advancing.

it seemed I was generating puzzles which just happened to give high ratings with -q2 and sxt/sx9
and these were the best that i got some time ago, just making the crieria.
Code: Select all
`3149 ,    1115 , .......2........49.2.9..7.......8...5...1.6...3.4....7..1..7...87..5.3...4.3.....# 99166 FNBP C21.m/M3.625.8503564 ,    2012 , ..3.......5.4...8.1.......7.9..8........94.6.5.62.............3.6.9...4...7.2.1..# 97003 FNBP C21.m/M2.5.223045008 ,    1212 , ...2....871......9..6.9.5....8.6...5.....23...4....6....9.3..5.4....1........7...# 96665 FNBP C21.m/M2.10.4592`

It was also unclear which puzzles to pick to continue to advance with a {-2+2} process - pick the hard ones or perhaps the not so hard ones ???? It is impossible to know how extensive or complete the trawl was !

The 22-clue search gave many more puzzles per {-2+2} and was more protracted. I think i gave up.

Anyhow

it might be a more direct way of making hard puzzles.......

i made this non-minimal 27 clue puzzle - by hand
probably fairly easy to generate them
the diagonal pattern and the clues in each box are not fixed
Code: Select all
`+---+---+---+|3..|..9|.4.||.2.|.7.|6..||..1|8..|..5|+---+---+---+|..6|3..|..7||.5.|.2.|.8.||4..|..1|9..|+---+---+---+|7..|..6|..1||..8|.5.|3..||.9.|4..|.2.|+---+---+---+`

instead of easy it was a bit hard SE 6.8/6.8/6.8
removing clues - probably going to be harder still - and there will be many puzzles .
Code: Select all
`3....9.4..2..7.6....1.....5..63......5..2....4....19..7....6..1..8.5.3.....4...2.# SE=9.2/9.1/9.0`

If we can generate a non-minimal 27 clue with SE 9.0 - there will be many harder puzzles generated im sure.

C
coloin

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