The New Sudoku Players' Forum

[P.O.]

i read this thread and that you made that observation: "On the other hand one of the SER 11.9 puzzles can be solved with 4." and left it at that is appalling.

[champagne]

All this becomes ridiculous.

We surely can change the goal of the thread, usually this leads to a new thread.
I stick to the original goal of the opener : can we find the "hardest sudoku" for a manual player .

Rating the tiny area of hardest puzzles is somehow a nonsense. You rate against a given set of rules, but if this set of rules does not include "exotic patterns" . You have lost manual players.

The Thor Hammer is not in my list of "exotic patterns", it should be but I did not update my list for long. I have no statistic, but my bet is that it is a very low probability in a random generation.

The strategy till now to try to answer to the question has been to produce as may grids resisting to a given set or rules (more or less SER rating) and to study this set of grids

Recently with the Thor Hammer discovery, the thread has been used to discuss the properties of this very rich pattern. It would have been wise to open quickly a separate thread.

In line with eleven I would suggest to avoid to pollute more this thread and to discuss the rating of hardest grids" in another thread .

[P.O.]

i agree that this has become ridiculous, and if this thread is reserved for manual solvers, i certainly have nothing to do with it so i will leave it at that.

[mith]

I've been meaning to create a new thread for the te3 puzzles anyway. I'll plan to do that for the next update. I just cut off the {-2+1} script, and all the expanded form scripts had already stabilized, so just waiting on SER to finish (~2400 to rate right now, shouldn't take long). Hopefully I'll have the update ready this week.

I do think it's worth taking a look at the expanded ph db (which I need to update with hendrik's puzzles and make available) at some point and searching for exotic patterns - we already know that most puzzles above 26c (approximately) have trivalue oddagons, but I've never run anything on the minimals to determine if *all* the new ones do.

For SET (including MSLS and SK-loops) I can run the fractional dimension but that's pretty slow - I'll have to code up something faster at some point (and maybe I can handle Exocets at the same time - since JExocets and Seniors can also be viewed in a SET way).

[denis_berthier]

I've been meaning to create a new thread for the te3 puzzles anyway.

IMO, the new TE3 thread should start with the first known TE3 puzzle; but we have nobody to move all the posts to a new thread.
It was the starting point for 3 new search criteria:
- use membership in T&E(3) instead of high SER,
- give up any pre-filter for high number of candidates,
- use expansions by Singles to allow searching for more puzzles near the already found ones.

I do think it's worth taking a look at the expanded ph db (which I need to update with hendrik's puzzles and make available) at some point and searching for exotic patterns - we already know that most puzzles above 26c (approximately) have trivalue oddagons, but I've never run anything on the minimals to determine if *all* the new ones do.

This is extremely ambiguous. When are you talking of the ph db and when of Hendirik's puzzles?
I haven't studied the new Henrdrik puzzles (waiting for their integration in your new release).
I strongly doubt the number of clues has anything to do with the presence or not of a trivalue oddagon.

What I consider important is keeping TE2 and TE3 puzzles in separate databases. Retrospectively, the main characteristic of the ph database is, it is in TE2. Still retrospectively, we could say that it is the result of ill-guided search based on high SER and that a systematic search for TE2 puzzles still remains to be done. I think this would also justify a new thread of its own.

For SET (including MSLS and SK-loops) ...

I don't have the slightest idea of what you mean by SET and I don't think anybody here knows.
If it includes things as different as MSLS, sk-loops and J-Exocets, I strongly doubt it can be in any way related to pattern-based solving.

[coloin]

I suggest, that you move your posts to this thread from 2012.

Well that is quite an interesting thread - which deserves a modified title [Pattern Overlay Method / Templates] perhaps ?

In support of P.O. I would observe that at the beginning of this thread there is a list of so called top-rated puzzles by several rating methods... not just SE.

There are puzzles which are rated highly with -q2 or suexratt which arnt rated so highly with the SE rating ... but are still mentionable and a curiosity as to why they score highly with their respective rating....

Perhaps we could have a list of a few puzzles which are only solvable with ? 6 templates [I believe the infamously misspelt Tungsten Rod is in this catagory. I am not sure how it was thought sufficiently hard by me [ perhaps the suexratt rating at that time] that I thought to give it a special name !!!

For comepletness perhaps also we could have a list of the puzzles top rated by Denis's analytic rating.

[denis_berthier]

For comepletness perhaps also we could have a list of the puzzles top rated by Denis's analytic rating.

Before puzzles in T&E(3) were discovered, the 3 top rated puzzles were the only known 3 in B7B:

Code: Select all

..3....8..5....2.17...........5.8..6.9.12....8....3....6.9....5..4....7.....1.6.2; eleven; 11.9
.2...67..4...8......9.......3.....7.5.8....4..1.3....2....9..5....6.1..3...2..6.7; eleven; 11.8
1.......6.5.7...8...3...4.....5.8.9.....3.....8.92....6.....3...7...5.2...4.....1; Metcalf; 11.7

If you want a longer list, we have to take those in B6B. You can find some of them in [PBCS].

After the discovery of puzzles in T&E(3), we now have thousands of much harder puzzles; the Wn+OR5CHn rating allows to find the hardest known puzzles in T&E(3).

Note: I don't agree with those who say the puzzles in T&E(3) are easy once we use Tridagons. The arguments I've seen amount to no more than saying one of the following: "every puzzle is easy after we know a pattern that can solve it" and "hardest means uninteresting for human solving".

Contrary to what has been said in some of the posts above:
- there are indeed (various) classification/rating systems;
- exotic patterns (which are, according to the definition I gave them when I introduced this expression, extremely rare and brittle) cannot be a significant part of any rational rating or classification system; what's interesting with them is to see how they modify a classification/rating;
- as shown by the first post, all this thread is and has always been about rating(s); "hardest" doesn't mean anything if not wrt some predefined rating system; "potentially" doesn't mean anything else than "hardest until solved";
- the 2 problems with this thread are, it concentrated on SER and it concentrated on looking for specific patterns (e.g. Exocets) and on trying to make them look more frequent than they are.

[mith]

I've been meaning to create a new thread for the te3 puzzles anyway.

IMO, the new TE3 thread should start with the first known TE3 puzzle; but we have nobody to move all the posts to a new thread.
It was the starting point for 3 new search criteria:
- use membership in T&E(3) instead of high SER,
- give up any pre-filter for high number of candidates,
- use expansions by Singles to allow searching for more puzzles near the already found ones.

Actually, it was only the starting point for the first of those. My own filters had never involved number of candidates and had been removed anyway before the first TE3 puzzle was known, and I had been using singles expansion for a while as well. (I agree that it would be the clear starting point for a new thread if we could move the posts, though.)

I do think it's worth taking a look at the expanded ph db (which I need to update with hendrik's puzzles and make available) at some point and searching for exotic patterns - we already know that most puzzles above 26c (approximately) have trivalue oddagons, but I've never run anything on the minimals to determine if *all* the new ones do.

This is extremely ambiguous. When are you talking of the ph db and when of Hendirik's puzzles?

When I say "expanded ph db" here I mean my local copy of the minimal database (really databases, since I have them separated by clue count for neighborhood search reasons) based on high SER, which has expanded from the ~3mil puzzles in ph2010 to ~32mil puzzles currently. I have not inserted all of hendrik's puzzles to those databases, whereas I have checked them for depth 3, added them to the minimal_te3 db, and run all the te3 scripts to generate any related puzzles.

I haven't studied the new Henrdrik puzzles (waiting for their integration in your new release).
I strongly doubt the number of clues has anything to do with the presence or not of a trivalue oddagon.

The wording here was ambiguous - I'm not saying that most puzzles with lots of clues in the space of all puzzles have trivalue oddagons, I'm saying most puzzles with lots of clues in my databases do. The number of clues doesn't necessarily have much to do with the presence of a trivalue oddagon, no, other than tending to need some minimum number of clues (potentially after singles) to make it viable for actual use. However, the high SER puzzles in the expanded ph databases tend to be dominated at higher clue counts by trivalue oddagon puzzles - high clue count high SER puzzles were previously hard to find with neighborhood searching, until my scripts started hitting trivalue oddagon neighborhoods and the puzzle generation exploded.

I would like to determine whether *all* puzzles in my local ph databases at high clue count have trivalue oddagons after a certain point, as well as determining when the first was added (the best I can do here is find the first by clue count, but I may be able to correlate this with postings here to narrow it down further). (Low on the priority list relative to other things, though.)

Aside: In the minimal_te3 database, the clue count ranges from 21c to 32c, with only a single puzzle at the lowest count (which happens to have 5 guardians in 4 boxes after basics): ........1.....2.3..45....6.....7.2......8.6.4..3..5....1.4......62......3..16...5
The expanded_te3 database ranges from 24c to 40c now.

What I consider important is keeping TE2 and TE3 puzzles in separate databases. Retrospectively, the main characteristic of the ph database is, it is in TE2. Still retrospectively, we could say that it is the result of ill-guided search based on high SER and that a systematic search for TE2 puzzles still remains to be done. I think this would also justify a new thread of its own.

Agreed - my own searching is now entirely focused on TE3 puzzles, and that will remain separate from the old database. That said, I have never done a complete search of the old database for depth 3 puzzles - the initial seed for the TE3 database was a search of SER 11.3(?)+ puzzles, and it's likely there were others in the ph databases that just had lower SER. Much like with the trivalue oddagon patterns generally, it would be nice to find the earliest TE3 puzzles in the old databases (by clue count) - Loki was the first identified as TE3, but may not have been the first generated.

For SET (including MSLS and SK-loops) ...

I don't have the slightest idea of what you mean by SET and I don't think anybody here knows.
If it includes things as different as MSLS, sk-loops and J-Exocets, I strongly doubt it can be in any way related to pattern-based solving.

I discussed an example of SET at the end of page 89, but a couple years ago I gave some concrete examples:

Place a Digit
Garam Masalas

I believe it is the case that all MSLS has a corresponding SET partition - though I haven't actually proven it (it's clear for the basic row/column based MSLS/SET, but adding in boxes makes it less obvious). SK loops are just a subset of MSLS (and I've previously shown a complimentary relationship between SK loops and the Phistomefel Ring, which is itself a specific SET partition - the development of SET came about from discussions about generalizing the Ring and alternative solves to puzzles like Tatooine Sunset).

As for Exocets, I wrote a document a while back about generalizing SET to cover Exocets here: Exocets as Generalized SET (It needs a rewrite in some places, and was written for a very different audience, but the ideas are there.)

At some point, I intend to write this stuff up more formally - but as always, it's hard to find the time!

[eleven]

@Mith I appreciate your work very much (e.g. showing me, how biased my hardest search was - and late thanks for your SET explanation last month), and in my eyes it's a good idea to make an own T&E hardest thread. I always had the feeling, that this topic just hijackes the hardest thread. T&E never has been interesting for the big manual solvers.
So i hope, that you keep enough time left for their interests like exotic patterns and really hardest.

[denis_berthier]

I've been meaning to create a new thread for the te3 puzzles anyway.

IMO, the new TE3 thread should start with the first known TE3 puzzle; but we have nobody to move all the posts to a new thread.
It was the starting point for 3 new search criteria:
- use membership in T&E(3) instead of high SER,
- give up any pre-filter for high number of candidates,
- use expansions by Singles to allow searching for more puzzles near the already found ones.

Actually, it was only the starting point for the first of those. My own filters had never involved number of candidates and had been removed anyway before the first TE3 puzzle was known, and I had been using singles expansion for a while as well. (I agree that it would be the clear starting point for a new thread if we could move the posts, though.)

OK, but my remark was more logical than temporal. The real boost in the search for "hardest" puzzles is the combination of these 3 factors. But I agree that the starting point for a TE3 thread should be with using membership in T&E(3) as the search criterion.


About your expanded ph database, I guess it contains (some of) the T&E(2) puzzles you have generated in the vicinity of T&E(3) ones and that didn't make it to your TE3 database. Now, the question about them having anti-tridagons is whether you allow degenerated forms of this pattern (i.e. at least one of the 123-candidates missing in at least one of the 12 cells):
- if yes, the problem is how to identify them, especially when there are lots of guardians; as you know, your additional criterion (essential in the efficient detection of anti-tridagons) doesn't work in the degenerated case;
- if no, examples would be very interesting: until now, based on the puzzles in your 63,137 db: "in T&E(3)" => "has a non-degenerated anti-tridagon" for all the known T&E(3) puzzles (I've checked this). And conversely, because of the proof that the trivalue oddagon pattern requires T&E(3) to be proven contradictory, "has a non-degenerated anti-tridagon" => "in T&E(3)", provided that no other rule can be applied that would short-circuit the whole anti-tridagoin thing.

What I consider important is keeping TE2 and TE3 puzzles in separate databases. Retrospectively, the main characteristic of the ph database is, it is in TE2. Still retrospectively, we could say that it is the result of ill-guided search based on high SER and that a systematic search for TE2 puzzles still remains to be done. I think this would also justify a new thread of its own.

Agreed - my own searching is now entirely focused on TE3 puzzles, and that will remain separate from the old database.
That said, I have never done a complete search of the old database for depth 3 puzzles - the initial seed for the TE3 database was a search of SER 11.3(?)+ puzzles, and it's likely there were others in the ph databases that just had lower SER. Much like with the trivalue oddagon patterns generally, it would be nice to find the earliest TE3 puzzles in the old databases (by clue count) - Loki was the first identified as TE3, but may not have been the first generated.

To avoid any confusion: there is no T&E(3) puzzle in the ph database. There may be some in your extended version of it, i.e. in, the vicinity of the old ones, but that's another question.

For SET (including MSLS and SK-loops) ...

I don't have the slightest idea of what you mean by SET and I don't think anybody here knows.
If it includes things as different as MSLS, sk-loops and J-Exocets, I strongly doubt it can be in any way related to pattern-based solving.

I discussed an example of SET at the end of page 89, but a couple years ago I gave some concrete examples...

OK, thanks for the references. I have to look at it more closely. At first sight, it seems quite far from pattern-based.

[mith]

- if no, examples would be very interesting: until now, based on the puzzles in your 63,137 db: "in T&E(3)" => "has a non-degenerated anti-tridagon" for all the known T&E(3) puzzles (I've checked this). And conversely, because of the proof that the trivalue oddagon pattern requires T&E(3) to be proven contradictory, "has a non-degenerated anti-tridagon" => "in T&E(3)", provided that no other rule can be applied that would short-circuit the whole anti-tridagoin thing.

It's not the case "has non-degenerate trivalue oddagon => in T&E(3)"; T&E(2) is often sufficient to bypass the pattern (perhaps even T&E(1), I'll have to try to construct an example sometime). As an example from the databases, this is the highest SER puzzle in the (local ph) 36c database:

Code: Select all

...........1..2.34..2.1356..17.86..3.6.2.1.8.2.873.6...7..28...12.36..7.8.61.73..  ER=10.6/1.2/1.2

T&E depth is 2, non-degenerate TO+2 (the guardian candidates imply each other) on 459 in b4578.

As I said, I think most (almost all) of the puzzles in my high clue databases have a (non-degenerate) TO pattern, though admittedly that is based on biased sampling (looking mostly at new "record" SER puzzles) - that's why I'll be checking them at some point (and taking a closer look at some of the ones that don't have a non-degenerate TO).

Anyway, I think the likely progression was:

Moderate clue count (~25c) minimal with high SER
=> Moderate clue count (~25-26c) minimal with high SER and non-degenerate TO in T&E(2) (they were first noticed when I started posting 28c+ puzzles, IIRC, but if the singles expansion script wasn't running yet they were likely present at lower counts first)
=> Lots of non-degenerate TO puzzles in the 25-36c minimal range and in T&E(2)
=> Somewhere along the way, the first T&E(3) puzzle - possibly Loki, possibly not

[denis_berthier]

- if no, examples would be very interesting: until now, based on the puzzles in your 63,137 db: "in T&E(3)" => "has a non-degenerated anti-tridagon" for all the known T&E(3) puzzles (I've checked this). And conversely, because of the proof that the trivalue oddagon pattern requires T&E(3) to be proven contradictory, "has a non-degenerated anti-tridagon" => "in T&E(3)", provided that no other rule can be applied that would short-circuit the whole anti-tridagoin thing.

It's not the case "has non-degenerate trivalue oddagon => in T&E(3)"; T&E(2) is often sufficient to bypass the pattern (perhaps even T&E(1), I'll have to try to construct an example sometime). As an example from the databases, this is the highest SER puzzle in the (local ph) 36c database:

Code: Select all

...........1..2.34..2.1356..17.86..3.6.2.1.8.2.873.6...7..28...12.36..7.8.61.73..  ER=10.6/1.2/1.2

T&E depth is 2, non-degenerate TO+2 (the guardian candidates imply each other) on 459 in b4578.

Good. There was no real reason (other than the lack of examples) why the tridagon pattern couldn't be short-circuited. Indeed, the hard part of finding hard instances of patterns is avoiding to have them destroyed or made irrelevant by their context in the puzzle.

The puzzle is in B2B - the low part of T&E(2); which is consistent with SER = 10.6.
The only direct OR2-chain elimination I could find is:

Code: Select all

Trid-OR2-whip[1]: OR2{{n3r7c1 n3r5c3 | .}} ==> r7c3≠3

which has no impact on the B2B classification.
In order not to overload this thread with resolution paths, I'll propose it in the "Puzzles" thread. I'm curious to see if other tridagon-related eliminations can be found.

[mith]

Finished updating IDs. There are 847778 expanded forms in total currently. I discovered that in the first update there were actually some IDs which were skipped (due to a duplicated puzzle that I didn't catch before assigning IDs), so the IDs in the latest will go up to 847781. (155299-155301 are the missing IDs; 155302 appears 4 times in the original update)

Will assign solution tree IDs next and then get the min-expands and max-expands.

[mith]

New thread created here: t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514.html

[amiami]

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