The New Sudoku Players' Forum

by **hendrik_monard** » Thu Aug 10, 2023 10:31 am

I have been away from this forum for some years. I am wondering, is there an updated list of all the puzzles found, like the lists that champagne used to provide? Or else, what is the latest list?.

In November 2021, mith published a database of new puzzles since the last published database by Champagne (ph_2010). Later, mainly in the first quarter of 2022, a number of additional lists were posted in this thread by mith and by me. Later I posted 3 large lists respectively in May 2022, September 2022 and May 2023. As it seems that for the time being nobody is taking care of maintaining a common overview of all these inputs, I was thinking of assembling them in a structured database for the benefit of all to check novelty of new puzzles.
This database could have the following properties and requirements:
- limitation to SER range 11.9-11.6 (all additional puzzles posted after November 2021 were already limited to this range);
- each puzzle has a unique solution and contains no redundant clues;
- new proposed puzzles should be accompanied by their SER rating (3 components);
The line layout of this database could be as follows:
Field 1: minlex isomorph of the puzzle
Field 2: if different from field 1: the original puzzle on which SER has been calculated, otherwise empty
Fields 3, 4 and 5: the three SER components
Field 6: clue count
Field 7: credits
Field 8: Date of posting in this thread (YYMMDD)
The fields as usual, separated by a semicolon. An empty field would read as ;;
As one of the lists in mith’s database of November 2021 contains all puzzles in the range 11.9-11.6, including those of ph_2010, it could be an option to include them in the 'new' database.

Before engaging in such an operation, I would welcome reactions from all interested members on any of the elements mentioned above. If someone would already have worked out something along these lines, I would be glad to contribute instead.

BTW, I examined the SER 11.9 and 11.8 rated expanded puzzles in mith's T&E(3) database and found 336 new minimals. They are listed in the following hidden file:

Hidden Text: Show

I was wondering if they would belong in the database we are dealing with in this thread. There could be a problem with the expanded 11.7s and 11.6s as many of them, while having a high clue count, also have a relative large number of (individually) redundant clues, with the possibility of generating excessive numbers of new minimals. I am interested to read reactions on this issue as well.

Hendrik

Website · by **denis_berthier** » Thu Aug 10, 2023 11:18 am

Hi Hendrik

hendrik_monard wrote:...
I was thinking of assembling them in a structured database for the benefit of all to check novelty of new puzzles.

From your historical note, you're forgetting an event that has completely changed the search for hard puzzles: the discovery of Loki by mith and my remark that it was in T&E(3), which led to the replacement of SER by T&E-depth as the new filter.

One should also consider a new method independently introduced by mith: the expansion of puzzles by Singles, which allows a very large extension to previous vicinity search for minimals. The counterpart of Singles expansion is the multiplication of minimal puzzles with the same Singles expansion. FAPP such puzzles are identical. The result is, when such techniques are used, a database of min-expands is much more interesting in practice than a database of minimals . And whenever you want to study such puzzles, it avoids much redundant work. (OK, you need the two when working on the extension of the database.) From the 336 new minimals you mentioned, how many min-expands do you get?

It also appeared that SER is unable to make the difference between a puzzle in T&E(2) and one in T&E(3) - as it was unable to make the difference between T&E(1) and T&E(2).

AFAIK, mith IS maintaining the T&E(3) database including your T&E(3) puzzles - maybe with some delay (you know better than me about this). I've shown that all the known puzzles in T&E(3) are indeed in T&E(W2, 2) and have the tridagon pattern. All this makes these puzzles quite special. AFAIK, mith is preparing a new update of the T&E(3) database but honestly, I'm not expecting anything new in the way we'll be able to solve these puzzles.

AFAIK also, nobody has been maintaining the ph2010 database based on SER, which contained only T&E(2) puzzles (where is mith's update of it you're mentioning?). It would probably be useful to maintain it (excluding the T&E(3) part). It would be interesting to see what happens if expansion by Singles is applied to it.

It is noticeable that we know much more about puzzles in T&E(1) or T&E(3) than about those in T&E(2). That's why I don't think it would be a good idea to restrict puzzles in the T&E(2) database to very high SER. IMO, what we need today is indeed the contrary: a database of puzzles in T&E(2), developed according to clear principles - possibly starting from 0 instead of from the existing ph2010.

.

by **champagne** » Thu Aug 10, 2023 12:46 pm

hendrik_monard wrote:I was wondering if they would belong in the database we are dealing with in this thread. There could be a problem with the expanded 11.7s and 11.6s as many of them, while having a high clue count, also have a relative large number of (individually) redundant clues, with the possibility of generating excessive numbers of new minimals. I am interested to read reactions on this issue as well.

Hendrik

Hi Hendrik,

This thread was supposed to collect puzzles having a chance to be "the hardest" although we have no definition of it.
Using SER as filter to select a puzzle to put in the data base of potential hardest, collecting non minimal puzzles was a non sens.
SER ER qualify the hardest step. SER ER is not changed and SER:EP SER:ED are growing when redundant clues are released.

For long, puzzles where a logic has been found reducing significantly the SER rating have been considered as having no chance to be the hardest.
The same happened from the very beginning for the Thor Hammer. Mith came with the solving rule discarding these puzzles from the hardest hunt.

The T&E(3) is another story and should be studied in a specific thread.

It remains that the data base is also the collection of puzzles resisting to the very old SER rating. The thor Hammer is surely one of the hardest pattern to break for SER. Collecting such minimal puzzles is in line with the past

by **hendrik_monard** » Thu Aug 10, 2023 1:49 pm

denis_berthier wrote:........ the discovery of Loki by mith and my remark that it was in T&E(3), which led to the replacement of SER by T&E-depth as the new filter.

The discovery of T&E(3) puzzles was surely an important event. Nevertheless, comparing SER and T&E(3) as mutually exclusive filters goes too far IMO. T&E(3) doesn't make SER obsolete. What to say about T&E(3) puzzles in mith’s list with SER 4.5?

AFAIK also, nobody has been maintaining the ph2010 database based on SER, which contained only T&E(2) puzzles (where is mith's update of it you're mentioning?)

Mith posted an update of ph_2010 here: http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-900.html#p312113
(2 posts 3 Nov 2021)

From the 336 new minimals you mentioned, how many min-expands do you get?

Unfortunately, this is a question that I can’t answer.

There are however a few questions I would like to ask:
- how can one detect whether a minimal puzzle is T&E(3) or not?
- Is there a tool available?
- do minimal puzzles, derived from non minimal T&E(3) puzzles, always remain in T&E(3)?

Website · by **denis_berthier** » Thu Aug 10, 2023 2:43 pm

hendrik_monard wrote:
denis_berthier wrote:........ the discovery of Loki by mith and my remark that it was in T&E(3), which led to the replacement of SER by T&E-depth as the new filter.

The discovery of T&E(3) puzzles was surely an important event. Nevertheless, comparing SER and T&E(3) as mutually exclusive filters goes too far IMO. T&E(3) doesn't make SER obsolete. What to say about T&E(3) puzzles in mith’s list with SER 4.5?

SER mixes everything. These puzzles have URs. Compute their SER without uniqueness and see what it becomes.
SER and T&E-depth are not exclusive. Even after applying the tridagon rules, what remains may have the whole range of SERs.

hendrik_monard wrote:
denis_berthier wrote:AFAIK also, nobody has been maintaining the ph2010 database based on SER, which contained only T&E(2) puzzles (where is mith's update of it you're mentioning?)

Mith posted an update of ph_2010 here: http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-900.html#p312113
(2 posts 3 Nov 2021)

OK, thanks

hendrik_monard wrote:
denis_berthier wrote:From the 336 new minimals you mentioned, how many min-expands do you get?

Unfortunately, this is a question that I can’t answer.

But that's the type of questions you'll have to deal with if you use expansion by Singles.

hendrik_monard wrote:There are however a few questions I would like to ask:
- how can one detect whether a minimal puzzle is T&E(3) or not?

This has nothing to do with minimality. Merely apply the T&E(2) or T&E(3) procedure.

hendrik_monard wrote:- Is there a tool available?

SudoRules allows to do it. Unfortunately, it's quite slow.

hendrik_monard wrote:- do minimal puzzles, derived from non minimal T&E(3) puzzles, always remain in T&E(3)?

Of course, yes; if derived means derived by eliminating candidates. T&E-depth is intrinsic, invariant under isomorphisms and contravariant wrt the inclusion relation.
.

by **mith** » Thu Aug 10, 2023 4:26 pm

hendrik_monard wrote:- Is there a tool available?

The tool I use is found here: https://github.com/dclamage/SudokuClassicMinLex (scroll down for Singles Depth)

IIRC it takes something like a tenth of a second if it's in T&E(2), and 1-2s if it's not (this could likely be reduced if it stopped once T&E(2) is exhausted, but it continues until it gets the solution to prove it is in T&E(3)).

---

hendrik_monard wrote:BTW, I examined the SER 11.9 and 11.8 rated expanded puzzles in mith's T&E(3) database and found 336 new minimals. They are listed in the following hidden file

I haven't provided this for download, but I do generate all minimals in the depth 3 search (in fact, the neighborhood searching is done on these, in addition to some other scripts running on the expanded forms). I just haven't been running SER on the minimals (since they should rate the same as their expanded form, absent uniqueness considerations). Recently, I have been prioritizing generating from the 11.8+ puzzles in the database, so currently there are 630 expanded forms which have been rated 11.8 or 11.9 (7, which is unchanged since I restarted the scripts), and ~900 minimals from these. I'll publish an update once this has stabilized.

At some point I would still like to collect what I have in the old (ph2010 based) databases and publish them, it just hasn't been a priority (especially with over 4 million depth 3 minimals not SER rated).

Website · by **denis_berthier** » Sat Aug 12, 2023 7:05 am

mith wrote:... over 4 million depth 3 minimals not SER rated).

Hi mith
The last published version of your database (the version I used for my detailed classification results wrt to the W+OR5W rating) had 847,778 T&E(3) minimals and 158,276 min-expands - about 5.4 minimals for each min-expand.
With now 4,000,000+ T&E(3) minimals, 5-fold increase in size, how many min-expands do you have?
.

by **Paquita** » Sun Aug 13, 2023 12:58 pm

Mith and Hendrik did a wonderful job. I tried to collect all their puzzles before I started my script, so I hope there are no duplicates in my contribution.
As for the current topic, how a database should be set up and what criteria to use for rating, I can't add much. I still work with SER rating and I will have to study the alternatives first.
My batch is minimal puzzles only.
Some 11.8 :

Code: Select all: 987.........65.............8.493.2..27........932...8472...38.93....247..4......3 ED=11.8/1.2/1.2 98.76.5..7.4.5..6..........6.794....5...87.....86.5.....9.....8....9432......64.. ED=11.8/1.2/1.2 987.........65.............8.493.2..72........932...843....247.2....38.9.4......3 ED=11.8/1.2/1.2 987.........65.............8.493.2..72........932...84.4.....23.....347......28.9 ED=11.8/1.2/1.2 98.76.5..7.5.......46.59...89.....7.....8...3....4.2...7.6.4.5....89.........5.6. ED=11.8/1.2/1.2 98.76.5..7.5..8....46.59...89.....7.....4.3..........2.7.6.4.5....89.........5.6. ED=11.8/1.2/1.2 98.76.5..7.5.......46.58...89.....7.....9...3....4.2...7.6.4.5....98.........5.6. ED=11.8/1.2/1.2 98.76.5..7.5..9....46.58...89.....7.....4.3..........2.7.6.4.5....98.........5.6. ED=11.8/1.2/1.2 987.........96.8.......5...84........93.72.8...2...3...7.4...98.3.2..7.4......23. ED=11.8/1.2/1.2 98.76....7.54......46..98..6......32.7............5.8..9.58..4....9.6.......47..8 ED=11.8/1.2/1.2 98.76.5..7.5....6...4......6..98....5.84.7....7..56..4.9..........8...39....9..2. ED=11.8/1.2/1.2 98.76.5..7.5.48....46..9....6.....3...4...62............74.6..8...95........87.9. ED=11.8/1.2/1.2 98.76.5..7.5.48....46..9....974.6.8.....87..9....5.....6......3..4...6.2......... ED=11.8/1.2/1.2 98.76.5..7.4.5..6..........6.794....5...8......86.5.....9.....8....764.......432. ED=11.8/1.2/1.2 9876.........958.......4...8.32..69.2..3..7...76......7.9...26.32..6..87.6....3.. ED=11.8/1.2/1.2 9876.........958.......4...8.32..69.2..3.67...76......7.9...26.32.....87.6....3.. ED=11.8/1.2/1.2 9876.........958.......4...7.9...36..6....2...32....8767.......2.83..69...32.67.. ED=11.8/1.2/1.2 9876.........958.......4...7.9...36..6....2...32.6..8767.......2.83..69...32..7.. ED=11.8/1.2/1.2 9876.........958.......4...86....3...23....87..9...26.67.......3.82..69...23.67.. ED=11.8/1.2/1.2 9876.........958.......4...86....3...23.6..87..9...26.67.......3.82..69...23..7.. ED=11.8/1.2/1.2 9876.........958.......4...83.2..69.2..3..7....6......79....26.3.2.6..87.68...3.. ED=11.8/1.2/1.2 9876.........958.......4...83.2..69.2..3.67....6......79....26.3.2....87.68...3.. ED=11.8/1.2/1.2 9876.........958.......4...8.32..69.2..3..7.8.76......7.9...26.32..6...7.68...3.. ED=11.8/1.2/1.2 9876.........958.......4...8.32..69.2..3.67.8.76......7.9...26.32......7.68...3.. ED=11.8/1.2/1.2 987.........65.............8.493.2..72........932...842....347..4......3.....28.9 ED=11.8/1.2/1.2 9876........59.........4...83........927.68....6....2..7..3.9.8.2.....73......26. ED=11.8/1.2/1.2 9876.........958.......4...86....3...23....7...9...2.667.......3.82..6.9..23.678. ED=11.8/1.2/1.2 9876.........958.......4...86....3...23.6..7...9...2.667.......3.82..6.9..23..78. ED=11.8/1.2/1.2 9876.........958.......4...83.2..69.2..3..7.8..6......79....26.3.2.6...7.68...3.. ED=11.8/1.2/1.2 9876.........958.......4...83.2..69.2..3.67.8..6......79....26.3.2.....7.68...3.. ED=11.8/1.2/1.2 98765.......4..........3...8..7..2...9....67..6.2...586...2.89.2...6.5.7.5....... ED=11.8/1.2/1.2 98765.......4..........3...8.62..75.7..8....2..9.....66...2..972...6.8.5..5...... ED=11.8/1.2/1.2 98765.......4..........3...8.6.2.97.2...6..58..5......7..8...2.6..2..5.7..9....6. ED=11.8/1.2/1.2 98765.......4..........3...8..7..2...9....67..6.2...586...2.5.72...6.89..5....... ED=11.8/1.2/1.2 98765.......4..........3...8.62..75.7..8....2..9.....66...2.8.52...6..97..5...... ED=11.8/1.2/1.2

and 11.7

Hidden Text: Show

by **Paquita** » Sun Aug 13, 2023 1:17 pm

And 11.6

Hidden Text: Show

by **Paquita** » Sun Aug 13, 2023 1:18 pm

11.6 continued

Hidden Text: Show

by **Paquita** » Sun Aug 13, 2023 1:19 pm

some more 11.6

Hidden Text: Show

by **Paquita** » Sun Aug 13, 2023 2:32 pm

Denis, I wanted to check out your Constraint Resolution Theories (2011), there is a link on SudokuX Minlexer's Github page, but that Research Gate page no longer exists.
I hope that paper can add to my understandig of the topic. Is it available elsewhere?

Website · by **denis_berthier** » Sun Aug 13, 2023 4:09 pm

Paquita wrote:Denis, I wanted to check out your Constraint Resolution Theories (2011), there is a link on SudokuX Minlexer's Github page, but that Research Gate page no longer exists.
I hope that paper can add to my understandig of the topic. Is it available elsewhere?

All my publications are available on GitHub: https://www.researchgate.net/profile/Denis-Berthier. I've noticed this morning that access was restricted to ResearchGate members but I've corrected this, so that you should now be able to see it. For some reason of their own, they don't appear in any sensible order, so that you have to scan the whole list.

More specifically, [CRT] is available here: https://www.researchgate.net/publication/280301602_Constraint_Resolution_Theories.
Instead of that book, I would however recommend to read a more recent one: https://www.researchgate.net/publication/356313228_Pattern-Based_Constraint_Satisfaction_and_Logic_Puzzles_Third_Edition. The abstract theory in the first two parts is unchanged (except for a few improvements in the writing) but you have a lot of examples and more recent classification results for Sudoku and toy have more examples: Kakuro....

Note also that all my publications related to Sudoku are available in the Publications folder of CSP-Rules: https://github.com/denis-berthier/CSP-Rules-V2.1
.

by **hendrik_monard** » Sun Aug 13, 2023 5:06 pm

Paquita wrote:Mith and Hendrik did a wonderful job. I tried to collect all their puzzles before I started my script, so I hope there are no duplicates in my contribution.
As for the current topic, how a database should be set up and what criteria to use for rating, I can't add much. I still work with SER rating and I will have to study the alternatives first.

Hi Paquita
Impressive list.
All your puzzles are minimal and maxlex.
I checked your lists and found a number of duplicates (see hidden list).
The references behind the puzzle are to be read as follows:
prefix M : in my posts of 23 Feb and 5 April 2022
The others (MM...) were in my post(s) of 15 May 2022
Probably you skipped some as the lists had sometimes to be split.

Hidden Text: Show

Code: Select all: 987......6..95.....4.......3..21.65....5.3..2....96.31...36.59....1...2.....2.1.3 M502 9876.....5.....96..4.......3...5.21....2..6.3...1.3.95...31..2.....6935......21.. M503 98.76.5..7.5..98...64......6..95....54..87....974.....4.....68......4.32........1 M490 98.76.5..7.5.498...64......8.695....4...87....97......6.....45....6...32........1 M491 987......6..95.....4.......3..5.21..2..13..65....96..2...3....1...26..59....1.23. M509 9876.....5.....96..4.......3..2..6.11...5.23......1.95...13..2.....6915......23.. M511 987......6..95.....4.......3..21.65....5.3..2....96.31.3.1...2.....6.59.....2.1.3 M443 987......6..95.....4.......3..21.65....5.3..2....96.31.3.1...2....36.59.....2.1.. M445 9876.....5.....96..4.......3...5.21....2..6.3...1.3.95.3...21......6935.....1..2. M446 9876.....5.....96..4.......3...5.21....2..6.3...1.3.95.3...21.....31..2.....69.5. M444 987......65.94......3........52..1......6.94.....1..25...4.5..1...12.46.....965.2 M489 987......65.94......3........52..1.....56.94.....1..2....4.5..1...12.46.....965.2 M508 9876.....54....96...3........4.2.1......9645......1.2....2..6.4...14..95.....521. M493 9876.....54....96...3........4.2.1.....4.1.2.....96.5....2..6.4...14..95.....521. M504 987......6..95.....4.......3..5.21..2..13..65....96..2.2.3....1....6..59....1.23. M506 987......6..95.....4.......3..5.21..2..13..65....96..2.2.3....1...26..59....1..3. M492 9876.....5.....96..4.......3..2..6.11...5.23......1.95.1...23......6915.....3..2. M494 9876.....5.....96..4.......3..2..6.11...5.23......1.95.1...23.....13..2.....69.5. M505 987......6...........85....4.32.51..2.1.4.3.....3........58.21....4.1.53....324.8 M2551 987......65.94......3......2..4.51.....12..64....96..5..52....1....6..49....1.52. M507 987......65.94......3......2..4.51.....12..64....96..5..52....1...56..49....1..2. M512 9876.....54....96...3......2..1..6.4....5.12......4.95..4..12......6945.....2..1. M513 9876.....54....96...3......2..1..6.4....5.12......4.95..4..12.....42..1.....69.5. M510 987......6...........85....4.32.51..2.1.4.3.....3......2.4.1.53...58.21.....3.4.8 M2553 98.76.5..5....487.........98.9....4.32..46....14.7.......65.79.....8.4.5.......86 MM2785 98.76.5..7.5..4....46.8.9..67.5...98.5.8.........9.......6...32...47.61.......4.9 MM2995 9876.....54.97......3......21..9.76..9...........2...1..976.12....2...37....136.9 MM791 9876.....54.97......3......21..9.76..9.1.........2......976.12....2...37....136.9 MM863 98765....6.........439......7........21...95....1...72...59.21....2.65.7....17.69 MM2845 98765....6.........439......7..2.....21...95....1...7....59.21....2.65.7....17.69 MM2839 98765....6.........439.....2...1.96....59..1....2.68.5.128...59..8.........1..28. MM2849 98765....6.........439.....2...1.96....59..12.....68.5.128...59..8.2.......1...8. MM598 98765....6.........439.....2...1896....59..1....2.68.5.12....59..8.........1..28. MM2844 98765....6.........439.....2...1896....59..12.....68.5.12....59..8.2.......1...8. MM2841 98765....6.........439.....8..59.2..1...2.69....1.6.85.218..5.9...2..81.......... MM2848 98765....6.........439.....8..59.21....2.65.8....1..69.128..95....1...8.....2.... MM2994 98765....6.........439.....8..59.21....2.65.8....1..69.128..95....1...82......... MM2850 98765....6.........439.....8..59.21.2...1..69.....65.8.128..95....1...8.....2.... MM687 98.76.5..7.5..4....4..8.9..67.5...98...8.........9..5..6....4.9...65..32....7..1. MM692 98.76.5..7.54..6....4.85...8......3.59.....21...9..4.66......5..7..........89..67 MM864 98.76.5..7.59.4....4..8....67.5...98...8.........9..5..6....4.9...65..32....7..1. MM613 98.76.5..7.59.4....4..85...67.....98...8.........9..5..6....4.9...65..32....7..1. MM691 98.76.5..7.5..4....4..8.9..67.5...98.5.8.........9.....6....4.9...6...32...47..1. MM2819 98.76.5..7.59.4....4..8....67.5...98...8.........9..5..6....4.....65..32....7..15 MM614 98.76.5..7.59.4....4..8....67.5...98..98............5..6....4.....65..32....7..15 MM609 98.76.5..7.5..4....4..8.9..67.5...98.5.8.........9.....6....4.....6...32...47..15 MM611 9876.....54..9......3...7..32...6.711.....6.2......93...21.93.6...2...1......7.9. MM402 9876.....54..9......3...7..32.9.6.711.....6.2.......3...21.93.6...2...1......7.9. MM407 9876.....54.79......3......2.....61..1.9.6.27........3..91...72..12..36......7..9 MM409 9876.....54.79......3......2...7.61..1.9.6.27........3..91...72..12..36.........9 MM413 9876.....54.79......3......29....61..1.9.6.27........3..12..36....1...72.....7..9 MM408 9876.....54.79......3......29..7.61..1.9.6.27........3..12..36....1...72........9 MM412 98.76....7.54..6....4.85...8.....93..9.....21...95.4.66......5..7..........89..67 MM3252 98.76....7.59.4....64.5....8.....32..9....1.8...48..756.........7....4.....89.76. MM3001 98.76....7.59.4....64.5....84....32..9....1.8...48...56....7......89.76.......4.. MM789 98.76....7.59.4....64.58...8.....32..9....1.8...4...756.........7....4.....89.76. MM2989 98.76....7.59.4....64.58...84....32..9....1.8...4....56....7......89.76.......4.. MM787 98.76.5..7.54.9....64.8....8.....93.59.....21......4.66.........7.5........89..67 MM720 98.76.5..7.59.4....46.8....67.5...98...8.........9..5.5.....4.....6...32....7.61. MM2993 98.76.5..7.59.4....46.85...67.....98...8.........9..5.5.....4.....6...32....7.61. 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MM688 9876.....54.97......3......21....76..9...........2...1...76.12....2.9.37....136.9 MM788 9876.....54.97......3......21....76..9...........2...1..12.9.37...76..2.....136.9 MM686 9876.....54.97......3......21....76..9.1.........2.......76.12....2.9.37....136.9 MM722 9876.....54.97......3......21....76..9.1.........2......12.9.37...76.12......36.9 MM685 9876.....54.97......3......21..9.76.....2..91...........976..2...12...37....136.. MM600 9876.....54.97......3......21..9.76.....2..91...........976.12....2...37....136.. MM2979 9876.....54.97......3......21..9.76....1.........2..9...976.12....2...37....136.. MM689 9876.....54.97......3......21..9.76....1.........2..9...976.12...12...37.....36.. MM599 9876.....54.97......3......21..9.76..9...........2...1..12...37...76..2.....136.9 MM597 9876.....54.97......3......21..9.76..9.1.........2......12...37...76.12......36.9 MM596 98765....6.........439.....2...1896....59..1......68.5.1.....59..8.2.......1..28. MM399 98765....6.........439.....8..59.2..1...2.69......6.85.2.8..5.9...2..81.....1.... MM400 98765....6.........439.....8..59.2..1...2869....1.6..5.21...5.9...2..81.......... MM2837 98765....6.........439.....8..59.21....2.65......18.69.12...95....1...8.....2.... MM2828 98765....6.........439.....8..59.21....2.65......18.69.12...95....1...82......... MM2838 98765....6.........439.....8..59.21.2...18.69.....65...12...95....1...8.....2.... MM2831 98.76.5..5.7...6...........85...4......32.8.....1...9.6....598.4....7.6..95...7.4 MM2937 98.76.5..5.7...6...........85..74......32.8.....1...9.6....598.4......6..95...7.4 MM2773 98.76.5..5.7...6...........85...4......32.8.....1...9.6....598.4.8..7.6..9....7.4 MM2952 98.76.5..5.7...6...........85..74......32.8.....1...9.6....598.4.8....6..9....7.4 MM2964 98.76.5..7.49......6..4....85.....32.9.....1....58.4..6....7...5..89..76.......5. MM785 98.76.5..7.49......6..4....85.....32.9.....1....58.4..6...57...5..89..76......... MM2962 98.76.5..7.54......64.8....8......3.59.....21...9..4.66.........7.5........89..67 MM2817 98.76.5..7.54..6....4.8....8......3.59.....21...9..4.66.........7.5........89..67 MM2814 98.76.5..7..4.96....4.8....8......3..9.....21...95.4..6.........7.5......5.89..67 MM2950 98.76.5..7.49......6..48...8......32.9.....1....58.4..6....7...5..89..76.......5. MM783 98.76.5..7.49......6..48...8......32.9.....1....58.4..6...5....5..89..76.7....... MM693 98.76.5..7.49......6..48...8......32.9.....1....58.4..6...57...5..89..76......... MM782 98.76.5..7.5..4....4..8.9..67.5...98...8.........9..5.56....4.....6...32....7..1. MM588 98.76.5..7.5..4....4..8.9..67.5...98.5.8.........9....56....4.....6...32....7..1. MM2935 98.76.5..7.54..6....4.85...8......3..9.....21...95.4..6......5..7..........89..67 MM682 98.76.5..7.59.4....4..8....67.5...98...8.........9..5.56....4.....6...32....7..1. MM616 98.76.5..7.59.4....4..8....67.5...98..98............5.56....4.....6...32....7..1. MM610 98.76.5..7.59.4....4..8....67.5...98.5.8.........9....56....4.....6...32....7..1. MM615 98.76.5..7.59.4....4..8....67.5...98.598..............56....4.....6...32....7..1. MM2974 98.76.5..7.59.4....4..85...67.....98...8.........9..5.56....4.....6...32....7..1. MM695 98.76.5..7.54..6....4.8....84.....3..9.....21...9..4.66.........7.5........89..67 MM2813 98.76.5..7.54......64.8....84.....3..9.....21...9..4.66.........7.5........89..67 MM2816 98.76....75..4......3...6..2.....41..1...4.26......7.3..7.1...2..1.2.34......6..7 MM605 98.76....75.4.......3...6..21....46..7...........2...1..12.73.....64.2......13.47 MM603 98.76....75..4......3...6..2..6..41..1...4.2.......7.3..7.1..62..1.2.34.........7 MM696 98.76.5..5......9.......8..45.....7.32....6....165......91...8....89.76.....75..1 MM2943 98.76....75..4......3......2.....41..1...4.26......7.3..7.1..62..1.2.34......6..7 MM608 98.76....75..4......3......2..6..41..1...4.26......7.3..7.1..62..1.2.34.........7 MM618 98.76....75.4.......3...6..21....46..7...........2...1...64.21....2.73......13.47 MM607 98.76.5..7.49......6..4....85.....32.9.....51....8.4..6...57...5..89..67......... MM2963 98.76.5..7.54......64.8....8......5359.....21...9..4...7.5.6......89..76......... 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MM2826 98.76.5..7.54......64.8....84.....53.9.....21...9..4..6.........7.5........89..76 MM2821 9876.....54..9......3...7..2.....61..1...6.27......9.3..91....2..12..36......7..9 MM606 9876.....54..9......3...7..2.....61..1.9.6.27........3..91....2..12..36......7..9 MM2941 9876.....54..9......3...7..29....61..1...6.27......9.3..12..36....1....2.....7..9 MM604 9876.....54..9......3...7..29....61..1.9.6.27........3..12..36....1....2.....7..9 MM2938 9876.....54.79......3......2.....61..1...6.27......9.3..91....2..12..36......7..9 MM404 9876.....54.79......3......29....61..1...6.27......9.3..12..36....1....2.....7..9 MM403 98.76.5..5.7...6...........6....598.4.8....6..9....7.4.5..74......32.8.....1.8.9. MM2775 98.76.5..5.7...6...........6....598.4.8..7.6..9....7.4.5...4......32.8.....1.8.9. MM591 98.76....7.5...4...32....7.8..9..1.6...1..74.....46..9.1.47......6...8.......8.1. 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MM778 98.76.5..7.54......64.8....8......3..9.....21...95.4..6.........7.5........89..67 MM694 98.76.5..7.54..6....4.8....8......3..9.....21...95.4..6.........7.5........89..67 MM716 98.7..6..7.65..4....5.8....8......3..9.....21...96.5..4......6..7...4......89...7 MM392 98.76.5..7.54..6....4......64.89..7.5.8..7.96............9....3...58..21......4.. M2404 987.........96.8......5....74...32..2.8.......39.4278.3......97..24..3.8......42. M2506 98.76.5..7.5.4.86...4......65.9.4...4.8.5.....7.68.....9...........7.3........21. M2494 98.76.54.7..8..6.......5...32.......1..5.8.....4...96....6.985....4..7.......7.94 M2403 98.76.5..75...98.....8.....43.......2.....1.....1.6......95..86...6.17.5....7891. M2550 98.76.5..75...98.....8.....43.......2.....1.....1.6.....795..86...6.17.5.....891. M2552 98.76.5..5..4.9........8...7.....43.4.8....21....4.6.5.7.9...56..457...9....86... MM2843 98.76.5..7.58.4....64.9....6....7...4.8....75...5....6...4.98.3.....8.21......95. MM2842 98.76.5..5..4.9........8...87.9...65..457..9......6...7.....4.34.8....21....4.65. MM2793 98.76.5..7.5.9..8..64......89......75.6..74.9.4..........32..48...1.8..5....76... MM2840 98.76.5..7.5.9..8..64......89......75.6...4.9.47.........32..48...1.8..5....76... MM2782 98.76.54.7.5.9...8.6.......89.....7.5.6...49..47......4...76......32..8....1.8.5. MM2784 98.76.54.7.5.9...8.6.......89.....7.5.6..749..4.......4....6......32..8....1.8.5. MM2820 98.76.5..5..4.9........8...7......834.8....21....4.6...7.9...65..457..9.....86... MM2830 98.76.5..5..4.9........8...87.9...65..457..9......6...7......834.8....21....4.6.. MM411 98.76.5..7.5.9.....64......5.6..749..9.....7..4....8....8..6......34..5....21..84 MM2833 98.76.5..7.5.9.....64......89.....7.5.6..749..4....8.....34..5....21..84.....6... MM2834 98.76.5..7.5.9..8..64......89......75.6..74.9.4..........34...5...21..48.....6... MM2827 98.76.54.7.5.9.....6.......5.6..749..9.....7..4....8....8..6......34..5....21..84 MM406 98.76.54.7.5.9.....6.......5.6..749..9.....7..4....8..4.8..6......34..5....21..8. MM2847 98.76.54.7.5.9.....6.......89.....7.5.6..749..4....8..4....6......34..5....21..8. MM405 98.76.54.7.5.9...8.6.......89.....7.5.6..749..4.......4....6......34..5....21..8. MM410 98.76.5..5.7...69..4.......7.4.9.....9..5.....658.....6......54....8632.....7.1.8 MM2981 98.76....7.5.9.8...64......84...9.7...7..6.9...6...5...5.9.4......32..56....1..8. MM3283 98.76.5..7.5..4....648..9...96....32.4....61.......7.5..895.......4.6..8.......9. MM3248 98.76.5..7.5.94....648......96....32.4....61......97....8.5.......4.6.58.......9. MM3281 98.76.5..5.7....9..4.......89..5...67.4.9...5.6.8.........8632.....7.1.8.......54 MM2790 98.76.5..5.7....9..46......89..5...67.4.9...5.6.8.........8632.....7.1.........54 MM2999 98.76.5..5.7..8.9..4.......89..5...67.4.9...5.6...........8632.....7.1.8.......54 MM2792 98.76.5..5.7..8.9..46......89..5...67.4.9...5.6...........8632.....7.1.........54 MM3002 98.76.5..5.7...69..4.......89..5....7.4.9...5.6.8.........8632.....7.1.8.......54 MM2789 98.76.5..7..8...96.....4...32....95.1.5....6..74.5......764..8....5.8.7......9... MM2972 98.76.5..7.4.......6.8...9.5...84......32.7.5...1....949...8..6.56..7..8..7...... MM3512 98.76.5..7.4.......6.8...9.5...84......32.7.5...1.5..949...8..6.56.....8..7...... 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MM2968 98.76.5..7.5.9..86..4......84......75.7.....9.96.........9.4......32.6.5....15..8 MM2781 98.76.5..5.7....9..46......89..5...67.4.9.....658.........8632.....7.1.........54 MM2986 98.76.5..5.7..8.9..46......89..5...67.4.9.....65..........8632.....7.1.........54 MM2990 98.76.5..7.5.9..8..64......84......75.7.....9.96.........9.4......32.6.5....15..8 MM2988 98.76.5..7.5.9..8..64......84......75.7..6..9.96.........9.4......32.6.5....1...8 MM3282 98.76.5..7.58.4....64.9....4.8....75...5....6.....7......6.8.32...4..8.1......95. MM3249 98.76.5..7.58.4....64.9....4.8....75...5....6.....7.....6...9.....6.8.32...4..8.1 MM862 98.76.5..7.58.4....64.9....4.8....75...5....6.....7.....6...95....4..8.3.....8.21 MM3250 98.76.5..7..8...96.....4...32.....5.1.5....6..7495.......64..89...5.8.7.....7.... MM2973 98.76.5..7.5.9..86..4......84.....675.7.....9.9.......6..9.4......32...5....15..8 MM2976 98.76.5..7.58.46....4.9....6....7...4.8....75...5........6.8.32...4..8.1......95. MM3247 98.76.5..7.58.46...64.9....4.8....75...5....6.....7.....6...9.....4..8.3.....8.21 MM871 98.76.5..5....9....4...8...7.....43...8....21....4.6.5.7.9...56..457...9....86... MM2770 98.76.5..7.48......6..94...57...6....49....6.....5...7....489.3.....9.21......85. MM397 98.76.5..7.58.4....64.9....4.8....75...5....6.....7.....6...9.....4.98.3.....8.21 MM723 98.76.5..7.58.46....4.9....6....7...4.8....75...5........4.98.3.....8.21......95. MM2832 98.76.5..7.5.9.....64......5.6..7.9..9...4.7..4....8....8.76......32..84...1...5. MM2998 98.76.5..7.5.9.....64......5.6..749..9.....7..4....8....8.76......32...4...1.8.5. MM2836 98.76.5..7.5.9.....64......5.6...49..9.....7...7...8..4.8.76......32...4...1.8.5. MM2835 98.76.5..7.5.94....648......47...63...6....21......7.5..895.......4.6..8.......9. MM2778 98.76.5..7.5.94....648......47...63...6....21.....97....8.5.......4.6.58.......9. MM2985 98.76.5..7.5.9.....64......89...4.7.5.6..7.9..4....8.....32..84...1...5.....76... MM2996 98.76.5..7.5.9..8..64......89...4..75.6..7..9.4..........32..48...1....5....76... MM3003 98.76.5..7.5.9.....64......89...4.7.5.6....9..47...8.....32..84...1...5.....76... MM2982 98.76.5..7.5.9..8..64......89...4..75.6.....9.47.........32..48...1....5....76... MM2991 98.76.54.7.5.9.....6.......5.6...49..9.....7..47...8....8.76......32...4...1.8.5. MM396 98.76.54.7.5.9.....6.......5.6...49..9.....7..47...8..4.8.76......32.......1.8.5. MM2786 98.76.54.7.5.9.....6.......5.6..749..9.....7..4....8....8.76......32...4...1.8.5. MM2769 98.76.54.7.5.9.....64......5.6...49..9.....7...7...8..4.8.76......32.......1.8.5. MM2846 98.76.5..5.7....9..4.......7.4.9...5.9..5...6..58.....6.......4....8632.....7.1.8 MM856 98.76.5..5.7....9..4.......7.4.9...5.9..5...6..58.....6.8.....4....7.3.8.....621. MM2953 98.76.5..5.7....9..4.......7.4.9...5.9..5...6..58.....6.8.....4....8632.....7.1.. 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MM2955 98.76.5..7..8...96.....4...32....9..1.5....6...495......764..8......9..5.....8.7. MM2768 98.76.5..5.7....9..46......7.469...5.9..5...6...8.....6.8.....4....7.3.8......21. MM3244 98.76....7.5.9.8...64......84...9.7...7....9...6...5..6....4......32..56....15.8. MM601 98.76....7.5.9.8...64......84...9.7...7....9...6...5..65...4......32...6....15.8. MM3227 98.76.5..7..8...96.....4...32.....5.1......6...495......95.8.7...764..89......... MM2956 98.76.5..7..8...96.....4...32.....5.1.5....6...495......764..89...5.8.7.......... MM2815 98.76.5..7.5.9..86..4......84...9.675.7.....9.........6....4......32...5....15..8 MM2818 98.76.5..7.5.9..86..4......84...9.675.7..6..9.........6....4......32...5....1...8 MM3229 98.76.5..7.5.9.....64......5.6..749..9.....7.......8..4.8..6......32...4...1.8.5. MM2823 98.76.54.7.5.9.....6.......5.6..749..9.....7..4....8..4.8..6......32.......1.8.5. MM2811 98.76.54.7.5.9.....64......5.6..749..9.....7.......8..4.8..6......32.......1.8.5. MM2812 98.76.5..5.7....9..4.......7.4.9...5.9..5...6.6.8.......8.....4....8632.....7.16. MM2942 98.76.5..5.7...69..4.......7.4.9...5.9..5.....6.8.......8.....4....8632.....7.16. MM2939 98.76.5..5.7...69..4.......7.469...5.9..5.......8.....6.8.....4....8.32.....7.16. MM2959 98.76.5..5....9....4.......7......834......21...84.6...7.9.4..5...57..98....86... MM3245 98.76.5..7..8...96.....4...39.....6.21....95...4.5......764..8....5.8.7......9... MM2940 98.76.5..7.4.......6.8...9.5....4......37...9...21.7.549...8..6.56.....8..7...... MM3230 98.76.5..7.5.9..8..64......84...9..75.7.....9..6.........63...8...21.6.5.....4... MM617 98.76.5..7..8...96.....4...39.....6.21.....5...495......764..89...5.8.7.......... MM2960 98.76.5..7.5.9..86..4......84...9.675.7.....9.........6....4......63...8...21...5 MM612 98.76.5..5....9....4...8...7......83..8....21....4.6...7.9...65..457..9.....86... MM2761 98.76.5..5....9....4...8...87.9...65..457..9......6...7......83...84.6.........21 MM2762 98.76.5..7.5.9.....64......5.6..749..9.....7.......8..4.8..6......34..5....21..8. MM2825 98.76.5..5.7....9..4.......7.4.9.....9..5...6..58.....6......54....8632.....7.1.8 MM2980 98.76.5..5.7....9..4.......7.4.9.....9..5...6..58.....6.8....54....7.3.8.....621. MM595 98.76.5..5.7....9..4.......7.4.9.....9..5...6..58.....6.8....54....8632.....7.1.. MM594 98.76.5..5.7....9..4.......7.4.9.....9..5...6.658.......8....54....7.3.8.....621. MM2934 98.76.5..5.7....9..4.......7.4.9.....9..5...6.658.......8....54....8632.....7.1.. MM2933 98.76.5..5.7....9..4.......7.4.9...5.9..5...6.6.8.......8....54....7.3.8.....621. MM2946 98.76.5..5.7....9..4.......7.4.9...5.9..5...6.6.8.......8....54....8632.....7.1.. MM2945 98.76.5..5.7....9..4.......7.469.....9..5...6..58.....6.8....54....7.3.8......21. MM593 98.76.5..5.7...69..4.......7.4.9.....9..5.....658.......8....54....7.3.8.....621. MM2764 98.76.5..5.7...69..4.......7.4.9...5.9..5.....6.8.......8....54....7.3.8.....621. MM2766 98.76.5..5.7...69..4.......7.469.....9..5......58.....6.8....54....7.3.8......21. MM2771 98.76....7.5..9....64..5....5.8.........4685.......7...4....32...6...1.4....74.89 MM2788 98.76....7.5..98...64..5....5.8.........46.5.........7.4.....32..6...4.1....7498. MM2997 98.76....7.5.9.8...64......84...9.7...7....9...6...5.....9.4......32..56....15.8. MM2787 98.76....7.5.9.8...64......84...9.7...7....9...6...5...5.9.4......32...6....15.8. MM2969 98.76.5..7.4.......6.8...9.5...84......32.7.....1....949...8..6..7....5...6..7..8 MM2944 98.76.5..7.4.......6.8...9.5...84......32.7.....1.5..949...8..6..7....5...6.....8 MM2767 98.76....7.5.9.8...64..5...5.....73...7....21.....86.4..94.........57.49.......8. MM2983 98.76....7.58.4....6..95...4....6....59...64........7...7...4.8....5..39.....921. MM2777 98.76....7.5.9.8...64..5...5.....73...7....21.....86.4..948........57.49......... MM2977 98.76....7.58.4....6..95...4....6....59...64........7.....7932.....5..19......4.8 MM2776 98.76....7.5.9.8...64..5...8.7....325.....71.......6.4..948........57.49......... MM2774 98.76.5..7.4.9.8...6...4...8.7....324.....71.......6.55..........958........47..9 MM2772 98.76.5..7.48......6..94...5....6....49....6.....5...7....79.32....4.9.1......85. MM2765 98.76.5..7.48......6..94...5....6....49....6.....5...7..7...8......79.32....4.9.1 MM2931 98.76.5..7.48......6..94...5....6....49....6.....5...7..7...85.....4.9.3.....9.21 MM2928 98.76.5..7.5..4....648..9...4....63...6....21.....97....8.5.......4.6.58.......9. MM3225 98.76.5..7.5..4....648..9...4....63...6....21.....97....895.......4.6.58......... MM683 98.76.5..7.5..4....648..9...4....63...6....21.....97.5..8.5.......4.6..8.......9. MM3226 98.76.5..7.5.94....648......4....63...6....21.....97.5..8.5.......4.6..8.......9. MM2984 98.76.5..7.5.94....648......96....32.4....61.......7.5..8.5.......4.6..8.......9. MM2967 98.76.5..7.58.46....4.9....6....7...4.8....75...5.......6...9.....4..8.3.....8.21 MM684 98.76.5..7.48......6..94...5....6....49....6.....5...7..7...8......489.3.....9.21 MM2929 98.76.5..7.5.9.....64......5.6...49..9.....7...7...8..4...76......32..8....1.8.5. MM2824 98.76.5..5.7...69..4.......7.469...5.9..5.......8.....6.8.....4....7.3.8......21. MM2808 98.76.5..5....98...4.......7......3.4......21...84.6...7.9.4.5....57...9....86... MM3246 98.76.5..5....98...4.......7.....43.4......21...8..6...7.9.4.5....57...9....86... MM2961 98.76.5..5....9....4.......7.....43.4......21...8..6...7.9.4.5....57..89....86... MM2810 98.76.5..7.4.......6.8...9.57...4......32.......1.5..949...8.76..6.....8.......5. MM2807 98.76.5..7.5.9.....64......5.6..749..9.....7.......8..4....6......32..8....1.8.5. MM2809 98.7..6..7...95....458......6.....9...8.6.......5.4..8.5.....39..4....21...4.97.. 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by **Paquita** » Sun Aug 13, 2023 5:29 pm

Thank you Denis for the link. That is 600 pages! I do'nt think I can finish that any time soon, interesting as it seems.

Do I understand correctly that T&E is Trial and Error, or brute force applied to the solution of a puzzle, and that T&E(3) means three recursive steps of brute force are needed to solve it?
That does sound like a possible rating for hard puzzles. But if I am correct, only two puzzles of T&E(3) are now available? (Found by Mith).

I would assume we do the T&E rating in addition to SER: we need to discern in the heaps of T&E(2)). And we would need more T&E(3) puzzles. Is there yet any perspective on how we can generate them? Or wat is specific about them? About these two, their rating as 11.8 and 11.9 shows that they are among the hardest as rated by SER. So both rating techniques support each other, although they do not completely overlap.

As for the other approach, the expansion of puzzles by Singles, I do not quite grasp the concept yet. Can anyone explain what it is and how it can be used to rate puzzles?

Thank you Hendrik for the update. I will add your puzzles from these dates to my own list of known puzzles.

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