http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539.html
In the former thread the last post is now one year old, and the thread has been very far from the player view on many points. The main one is the use of “uniqueness”. In this thread, uniqueness is assumed. Next post tells you why.
The player’s view (not easy to define) remains my motivation to work in this field.
Having free time and still some brain potential to work with my computer (now passed 83), I did several things recently that can help to summarize all the recent work done by active members as coloin, , hendrik monard ,marek Stefanik, mith, Paquita ….
I also needed my own updated base to see what was new in my recent results on the vicinity search, so I must anyway make with my tools a full update of what I have seen. It will likely be available in two weeks. Many options are open to share the results.
In the search for puzzles of potential interest, to avoid redundancy, the use of a canonical morph of a puzzle is unavoidable. It will be the case here. To be posted for a blind resolution, such puzzles should be morphed to a kind of “random morph”. I use as canonical the puzzle morphed to the min lexical solution grid.
Complaints posted cyclically by players refer to the mass of puzzles with no special interest. On the other hand, defining what is of interest for a player is not easy and changes with each player.
For the vicinity search, main source of new puzzles, the minimal puzzle remains the best seed, but this is not necessary the morph to keep in a player database. With the TH pattern, many minimal puzzles have the same PM “after…”. Also, in most publications, the players start with a PM “after ….”
IMO, it makes sense to store hard puzzles “after…”. This excludes, in fact, al puzzles below the “after” and will reduce significantly the size of the file when the TH is there.
The cutoff can be long discussed, but I would be, for hard puzzles, in favor of a cutoff leading to puzzles having no assignment possible using a relatively high rule as “all bi-values”. Such puzzles would show a {sudoku explainer Ed rating} over 2.3 and possibly up to 8.0
In my quick solver, knowing that this filter must be applied to millions of puzzles, the limit is more what I can do in some milliseconds at most. In my current quick filter, the UR/UL cleaning is still missing.
The issue of puzzles having an identified easy solution through exotic patterns is different.
In my first data base, I had flags telling which “Exotic pattern(s)” had been seen (if any).
Such flags give the opportunity to newcomers to select such puzzles to work on a specific pattern. This is IMO better than to try to reduce the list killing puzzles “easy to solve for a skilled player having the clue”
This requires somebody setting the flags using a solver. I did it in the past, but my old solver is not at all up to date to do it today, and I am too old to just think of taking over the burden. BTW, each player can have its own file based on published puzzles of the database.
I have also a small problem with the flow of puzzles posted in the last 2 years. Just gathering, canonizing, filtering redundancy is a huge task. Keeping track of the first appearance is just not possible. Also, as long as puzzles are not posted in the canonical morph, the updating of the database with the “owner” of the puzzle is usually not feasible. Moreover, if only puzzles shown “after..” are stored, the source will usually be multiple (this is the target).
The hardest sudoku 3 (player view)
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The hardest sudoku 3 (player view)
by champagne » Thu Oct 09, 2025 7:09 am
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UNIQUENESS view.
by champagne » Thu Oct 09, 2025 7:12 am
Assuming that a puzzle has a unique solution was source of many discussions.
It is clear that a puzzle with multiple solutions is not a sudoku. It can not be solved without guesses showing all possible solutions (or the first one).
For a solver, it’s known for decades that a UR, easy to spot, can not appear with four bi values and that with 3 bi values, the fourth cell can be cleaned from the 2 digits.
Building a file of “potential hard” puzzles where this pattern can solve the puzzle is just stupid.
Same if the pattern can reduce the puzzle to “not to hard”;
So, selecting “potential hard puzzles” without this filter is not in the scope of this thread (at least for me).
What is valid for the simplest UR can be extended to other patterns. Some are easy to spot, some are not.
In Serate/Skfr the uniqueness is applied to URs with a minimum of 2 bi-value cells in row or column and to Uls with a similar pattern.
The uniqueness appears also in the last phase of the resolution (BUGs) but here, the hard steps are over.
We have other “uniqueness” rules as for example a puzzle with a symmetry of given. IMO this one is not easy to consider as a basic filter. The symmetry is not so easy to spot if the puzzle is not in the right morph, but this is an open point.
So far, the general filter in use is the set of rules in Sudoku Explainer (on my side). Any other set of rules could be used with more uniqueness patterns.
It is clear that a puzzle with multiple solutions is not a sudoku. It can not be solved without guesses showing all possible solutions (or the first one).
For a solver, it’s known for decades that a UR, easy to spot, can not appear with four bi values and that with 3 bi values, the fourth cell can be cleaned from the 2 digits.
Building a file of “potential hard” puzzles where this pattern can solve the puzzle is just stupid.
Same if the pattern can reduce the puzzle to “not to hard”;
So, selecting “potential hard puzzles” without this filter is not in the scope of this thread (at least for me).
What is valid for the simplest UR can be extended to other patterns. Some are easy to spot, some are not.
In Serate/Skfr the uniqueness is applied to URs with a minimum of 2 bi-value cells in row or column and to Uls with a similar pattern.
The uniqueness appears also in the last phase of the resolution (BUGs) but here, the hard steps are over.
We have other “uniqueness” rules as for example a puzzle with a symmetry of given. IMO this one is not easy to consider as a basic filter. The symmetry is not so easy to spot if the puzzle is not in the right morph, but this is an open point.
So far, the general filter in use is the set of rules in Sudoku Explainer (on my side). Any other set of rules could be used with more uniqueness patterns.
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Re: The hardest sudoku 3 (player view)
by champagne » Thu Oct 09, 2025 7:18 am
What happened in the recent years (among others), and what did I find as new puzzles
On a player view, the major point has been the discovery of the TH pattern, but many other new solving ways have been explored.
Also, many vicinity processes have been discussed,
And millions of new puzzles have been produced in various morphs making it difficult to see if a puzzle is new or not.
I had already morphed mith’s file and my old “PH” file to the canonical morph and re rated all, using SKFR, So, the big task has been to pick up all puzzles seen here and there or got by other ways.
Surely, some puzzles have been lost, but I had at the end 1 180 459 canonical puzzles not in the 2 previous files, mostly rating >=11.5, some minimal, some not.
The second step has been to find all “minimal” and to check again what was new against the 2 files.
I have now 4 267 978 new minimal puzzles in hand. As most of them have a skfr rating >11.5; re rating this file will take several days. As the suppliers use often skfr or serate as pre filter, only a small number of them will be cleaned with the cutoff of 10.5. As a side effect, the skfr rating seems to be mainly in the 4/5 seconds per puzzle, a high value for millions of puzzles.
I’ll keep, for my own use, the entire file. For this thread, I intend to use a first level of expansion made of
Singles
Claiming pointing (sudoku explainer definition)
Locked in unit (hidden or naked).
Note: I have a quick filter for fishes, but with eliminations over serate 7.0
And the UR eliminations are part of the global skfr rating but will come in due time for cases where the puzzle after URs remains at a high rating..
On a player view, the major point has been the discovery of the TH pattern, but many other new solving ways have been explored.
Also, many vicinity processes have been discussed,
And millions of new puzzles have been produced in various morphs making it difficult to see if a puzzle is new or not.
I had already morphed mith’s file and my old “PH” file to the canonical morph and re rated all, using SKFR, So, the big task has been to pick up all puzzles seen here and there or got by other ways.
Surely, some puzzles have been lost, but I had at the end 1 180 459 canonical puzzles not in the 2 previous files, mostly rating >=11.5, some minimal, some not.
The second step has been to find all “minimal” and to check again what was new against the 2 files.
I have now 4 267 978 new minimal puzzles in hand. As most of them have a skfr rating >11.5; re rating this file will take several days. As the suppliers use often skfr or serate as pre filter, only a small number of them will be cleaned with the cutoff of 10.5. As a side effect, the skfr rating seems to be mainly in the 4/5 seconds per puzzle, a high value for millions of puzzles.
I’ll keep, for my own use, the entire file. For this thread, I intend to use a first level of expansion made of
Singles
Claiming pointing (sudoku explainer definition)
Locked in unit (hidden or naked).
Note: I have a quick filter for fishes, but with eliminations over serate 7.0
And the UR eliminations are part of the global skfr rating but will come in due time for cases where the puzzle after URs remains at a high rating..
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TH story
by champagne » Fri Oct 10, 2025 10:13 am
Waiting for the re rating of the big file, I wanted to track the TH history
All this is in the former thread, but hidden in 120 pages.
The TH was first described by “marek Stefanik” Wed Jul 14, 2021 2:51 am
As he wrote in another place, this followed plenty of puzzles having both high number of clues and high ratings, all of them with a similar pattern.
And it took one more year before the discovery of “Loki” with a very high rating.
Loki had another property, it was T&E3, the first puzzle with this property.
From that point, the search moved long to a T&E3 filter and mith published a file of more than 4 million puzzles with this property.
More interesting for the history is what happened before.
Mith made a deep analysis of the ph2010 file
by mith » Sat May 18, 2024 11:07 pm
The entire list (which includes puzzles I would consider degenerate, but which you would not) is here:
https://drive.google.com/file/d/1Bz91WnIT_ppRX1wVPfQQGJsjl2kE_1t9/view
From this list,
The oldest set of puzzles with the TH seen by mith are dated December 2012 January 2013, all posted by mladen dobrichev with minimal puzzles of 31 32 clues, an area not much explored at that time. Here is the full list seen by mith
Six years later, when I started some search with 26 clues, these four puzzles came.
98.76.5..7....5.8...5......6..4....8.4.........7..64......2.9....9..7.45..81.96..;10.80;1.20;1.20;GP;2018_12_01;2157175;26;*
9..76.5..7....5.8...5......6..4....8.4.......8.7..64......2.9....9..7.45..81.96..;10.90;1.20;1.20;GP;2019_01_07;2269259;26;*
98.76.5..7....5.8...5......6..4....8.4.........7..64......2.9....9.3..45..81.96..;10.80;1.20;1.20;GP;2019_01_07;2287241;26;*
98.76.5..7....5.8...5......69.4....8.4.........7..64......2.9.......7.45..81.96..;10.80;1.20;1.20;GP;2019_01_07;2287252;26;*
I don’t know if these puzzles have been a seed for “Paquita”, but in the following months “Paquita” produced plenty of puzzles, many of them rating SE >=11.0
Mith likely produced puzzles in parallel, they are recorded in ph2010 as October 2020.
So, the pattern was likely already identified by “marek Stefanik” and “mith” in 2019.
All this is in the former thread, but hidden in 120 pages.
The TH was first described by “marek Stefanik” Wed Jul 14, 2021 2:51 am
- Code: Select all
Very interesting puzzles, make me wonder what kind of magic would one have to use to prove this contradiction using truths and links (it's in every single one of these 30+-clue puzzles and I'm slowly going insane thinking about it :D).
Code: Select all
123 . . | . . 123
. 123 . | . 123 .
. . 123 | 123 . .
––––––––––––––+––––––––––––––
. . 123 | 123 . .
. 123 . | . . 123
123 . . | . 123 .
As he wrote in another place, this followed plenty of puzzles having both high number of clues and high ratings, all of them with a similar pattern.
And it took one more year before the discovery of “Loki” with a very high rating.
Loki had another property, it was T&E3, the first puzzle with this property.
From that point, the search moved long to a T&E3 filter and mith published a file of more than 4 million puzzles with this property.
More interesting for the history is what happened before.
Mith made a deep analysis of the ph2010 file
by mith » Sat May 18, 2024 11:07 pm
The entire list (which includes puzzles I would consider degenerate, but which you would not) is here:
https://drive.google.com/file/d/1Bz91WnIT_ppRX1wVPfQQGJsjl2kE_1t9/view
From this list,
The oldest set of puzzles with the TH seen by mith are dated December 2012 January 2013, all posted by mladen dobrichev with minimal puzzles of 31 32 clues, an area not much explored at that time. Here is the full list seen by mith
Hidden Text: Show
Six years later, when I started some search with 26 clues, these four puzzles came.
98.76.5..7....5.8...5......6..4....8.4.........7..64......2.9....9..7.45..81.96..;10.80;1.20;1.20;GP;2018_12_01;2157175;26;*
9..76.5..7....5.8...5......6..4....8.4.......8.7..64......2.9....9..7.45..81.96..;10.90;1.20;1.20;GP;2019_01_07;2269259;26;*
98.76.5..7....5.8...5......6..4....8.4.........7..64......2.9....9.3..45..81.96..;10.80;1.20;1.20;GP;2019_01_07;2287241;26;*
98.76.5..7....5.8...5......69.4....8.4.........7..64......2.9.......7.45..81.96..;10.80;1.20;1.20;GP;2019_01_07;2287252;26;*
I don’t know if these puzzles have been a seed for “Paquita”, but in the following months “Paquita” produced plenty of puzzles, many of them rating SE >=11.0
Mith likely produced puzzles in parallel, they are recorded in ph2010 as October 2020.
So, the pattern was likely already identified by “marek Stefanik” and “mith” in 2019.
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puzzles to store "ATER..."
by champagne » Sun Oct 12, 2025 7:52 am
Puzzle “after”
I made a test in "best conditions", starting from three solution grids in mith’s file having a total of 17882 puzzles rating skfr >= 10.5
I expanded the puzzles {singles, locked in .. and locked sets in units}.
I got then 52 different puzzles, but as I have already seen in coloin’s results, some puzzles are subsets of other puzzles.
Here is the status for the solution grid rank 5090094309.
The first step delivers four puzzles
Easy here to see that 2 puzzles are super sets of the 2 others.
Keeping the four has no sense on a player view, so we have to clean the file.
Keeping supersets could lead to less puzzles, but with the risk to kill the highest ratings,
so I did the cleaning keeping only subsets and finished with 19 puzzles (from 17882)
For sure, the ratio 17882 to 19 is due to the selection of solution grids with many puzzles, but with this limited set of rules used in the expand phase, we should get a reasonable size for the file for players
I made a test in "best conditions", starting from three solution grids in mith’s file having a total of 17882 puzzles rating skfr >= 10.5
I expanded the puzzles {singles, locked in .. and locked sets in units}.
I got then 52 different puzzles, but as I have already seen in coloin’s results, some puzzles are subsets of other puzzles.
Here is the status for the solution grid rank 5090094309.
The first step delivers four puzzles
- Code: Select all
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4;37
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4;38
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4;38
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495...2..78.4;39
Easy here to see that 2 puzzles are super sets of the 2 others.
Keeping the four has no sense on a player view, so we have to clean the file.
Keeping supersets could lead to less puzzles, but with the risk to kill the highest ratings,
so I did the cleaning keeping only subsets and finished with 19 puzzles (from 17882)
Hidden Text: Show
For sure, the ratio 17882 to 19 is due to the selection of solution grids with many puzzles, but with this limited set of rules used in the expand phase, we should get a reasonable size for the file for players
Last edited by champagne on Sun Oct 12, 2025 2:23 pm, edited 1 time in total.
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Re: The hardest sudoku 3 (player view)
by coloin » Sun Oct 12, 2025 11:35 am
Were the 17882 puzzles all minimal ?
Those 19 puzzles have 2718 minimal puzzles [only]
But they do expand back up to 19. So that in itself is a good reduction.
These 3 max expands [summating the clues manually]
have 12730 minimals [only] and they expand back up to 47 puzzles...
expanding more
have 21650 minimals ....and they expand back up to 48 puzzles
Those 19 puzzles have 2718 minimal puzzles [only]
But they do expand back up to 19. So that in itself is a good reduction.
These 3 max expands [summating the clues manually]
- Code: Select all
...4.6.8.4...8...66...27.54239...8..7468.2...815...6.2.62.485.7..4....28...2.546. ED=10.6/10.6/2.6
.2..567...5.18.2.6...7.2..528.5.7...319...57.574....6.......85.8.2.756.1..58.1.27 ED=10.9/1.0/1.0
1......894.7.89...689....4529.74.5.8...9.842.84..25.97..48...72..82.495......78.4 ED=10.2/1.2/1.2
have 12730 minimals [only] and they expand back up to 47 puzzles...
expanding more
- Code: Select all
...4.6.8.4...8...66...27.54239...8..7468.2...815...6.2.62.485.7..4....28...2.546. ED=10.6/10.6/2.6
.2..567...5.18.2.6...7.2..52865.7...319...57.574....6.......85.8.2.756.1..58.1.27 ED=10.9/10.9/2.6
1..4...894.7.89...689....4529.74.5.8...9.842.84..25.97..48...72..82.495......78.4 ED=10.2/10.2/8.2
have 21650 minimals ....and they expand back up to 48 puzzles
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Re: The hardest sudoku 3 (player view)
by coloin » Sun Oct 12, 2025 12:12 pm
repeating with [ SE without uniqueness]
gave 15752 minimals which re-expanded back up to 45 puzzles....
- Code: Select all
...4.6.8.4...8...66...27.54239...8..7468.2...815...6.2.62.485.7..4....28...2.546. ED=11.6/11.6/2.6
.2..567...5.18.2.6...7.2..52865.7...319...57.574....6.......85.8.2.756.1..58.1.27 ED=11.7/11.7/2.6
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=11.7/10.6/3.4
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4 ED=11.7/10.4/2.6
gave 15752 minimals which re-expanded back up to 45 puzzles....
Hidden Text: Show
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Re: The hardest sudoku 3 (player view)
by champagne » Sun Oct 12, 2025 3:32 pm
Hi coloin,
Interesting view on this.
I had a look at the solution grid 5090094309
four expand
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4;5090094309;1k67SheOsCcTW5
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4;5090094309;1k67SheOsCcTa5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4;5090094309;1k67UeeRsCcTW5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495...2..78.4;5090094309;1k67UeeRsCcTa5
two with no subset
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4;5090094309;1k67SheOsCcTW5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4;5090094309;1k67UeeRsCcTW5
mith's file has 3539 puzzles, 3179 rating 105 and 360 rating 108
and the rating of the 4 puzzles is
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4 ED=10.5/4.5/2.6
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495...2..78.4 ED=10.5/4.5/2.6
clearly, the 2 last have a UR step.
The four puzzles return the 3539 minimal puzzles of the source.
The 2 puzzles with no subset return only 1410 minimal puzzles,
Now, my question is :
In a player view, is it worth to see
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
as 2 different puzzles to play??
Interesting view on this.
I had a look at the solution grid 5090094309
four expand
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4;5090094309;1k67SheOsCcTW5
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4;5090094309;1k67SheOsCcTa5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4;5090094309;1k67UeeRsCcTW5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495...2..78.4;5090094309;1k67UeeRsCcTa5
two with no subset
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4;5090094309;1k67SheOsCcTW5
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4;5090094309;1k67UeeRsCcTW5
mith's file has 3539 puzzles, 3179 rating 105 and 360 rating 108
and the rating of the 4 puzzles is
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495......78.4 ED=10.5/4.5/2.6
1......894.7.89...689....4529....5.8...9.842.84..25.97..48...72..82.495...2..78.4 ED=10.5/4.5/2.6
clearly, the 2 last have a UR step.
The four puzzles return the 3539 minimal puzzles of the source.
The 2 puzzles with no subset return only 1410 minimal puzzles,
Now, my question is :
In a player view, is it worth to see
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
as 2 different puzzles to play??
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Re: The hardest sudoku 3 (player view)
by coloin » Sun Oct 12, 2025 9:53 pm
champagne wrote:Now, my question is :
In a player view, is it worth to see
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
as 2 different puzzles to play??
I would say one minimal puzzle from each of the 52 expands is essentially representative. but even one single puzzle per "similar" max expand / solution grid might be enough..?
How to chose which is the most challenging one is hard to say.
The problem is that SE/skfr do not factor in the use of the tridagon elimination ... even when its the simple / non-degenerative elimination.
So these puzzles unfortunately do have an inflated rating ..
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Re: The hardest sudoku 3 (player view)
by champagne » Mon Oct 13, 2025 7:44 am
coloin wrote:
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495......78.4 ED=10.8/10.4/3.4
1......894.7.89...689.....529.74.5.8...9.8...84..25.97..48...72..82.495...2..78.4 ED=10.8/10.8/2.6
but even one single puzzle per "similar" max expand / solution grid might be enough..?
How to chose which is the most challenging one is hard to say.
in a thread starting with "the hardest sudoku", the answer seems easy.
The puzzle with superset clues cannot be harder and coul even have a lower ER rating, so from a player view, the subset is the right choice.
BTW, the intensive use of "maxexpand" has been very good to get new minimals and fruitful vicinity, but is also responsible for all these "similar puzzles" of small interest for the players.
coloin wrote:
The problem is that SE/skfr do not factor in the use of the tridagon elimination ... even when its the simple / non-degenerative elimination.
So these puzzles unfortunately do have an inflated rating ..
I think that I answered to this in the opening posts.
If the file is supposed to contain the "hardest puzzle", it is also a file dedicated to give samples of puzzles with exotic patterns.
One option could be to kill all puzzles "easy after use of the exotic pattern ", but this would loose all knwon samples;
As I wrote, in the PH data base, I kept flags describing the exotic patterns seen.
I still have twice a month requests to access to my google drive, this showing that many silent players want to download the ph file.
BTW, I hoped to have here some comments from players, and this did not come so far.
- champagne
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