## exotic patterns below the potential hardest

Advanced methods and approaches for solving Sudoku puzzles

### Re: exotic patterns below the potential hardest

I've spent quite a lot of time reworking my prototype Excel Multi-sector Locked Set worksheet into a respectable format.

Alongside a copy of the PM grid extra cells for each house allow me to select which ones should be covered either by set A or set B of a complementary pair of digit sets. In the language of Xsudo both sets will be considered to be weak or strong together, and their intersection cells will contain a set of the opposite type. The option that is used is determined by considering which one gives the better truth/link balance. For a naked set, the house covers will be weak, and for a hidden set they will be strong.

A high level control allows the set identities to be swapped over at any time. This then changes a reported hidden set into its complementary native set (and vice versa). Being unfamiliar with ranking matters, it came as a surprise to me that a rank 1 ANS is complemented by a rank –1 AHS.

If I had this 3 days ago I would have then found ronk's first solution! However I'm prepared to forgo identifying cover types for individual cells which would take much longer to input.

Blue, yes, before the eliminations are made I should call that loop a continuous AIC loop. It's only after the eliminations are made that it becomes a conjugate loop.

However, if we have two instances of a digit spaced apart in a conjugate loop that are conjugate to each other, any candidate that sees both of them must be false, and so provides an extra elimination. I therefore have trouble understanding:
Blue wrote:(Eliminations from a conjugate loop are rank 1 -- like eliminations from discontinuous loops).

The best sense I can make of it is to say that if I only notate the chain segment from one to the other it will be a rank 1 elimination but if I notate the full loop it will be rank 0.

I'm now going to play my 'dummy' card. In explaining how something works I'm interested in the effect an action has, not the whys and wherefores that lie behind it. (Consider what it takes to describe the workings of a limited-slip differential.) Would it make you happier if I added the word in red here?
I wrote:In following the chain strong links are expressed using the digits involved and weak links are (effectively) expressed as strong links for the complementary set of digits

David
David P Bird
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### Re: exotic patterns below the potential hardest

Hi Champagne,

As I was modifying my spreadsheet, I sampled your collection of puzzles that looked promising for a rank 0 pattern. Out of 6 tried, I only found 1 hit, and that only provided a single elimination (regrettably I discarded it as I hoped to find better later).

I therefore have to agree with ronk, that it would be more profitable to use chains to find the eliminations than multi-fish type logic. There are too many options to explore, and these puzzles have numerous chain exclusions that would be much faster to process.

David
David P Bird
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### Re: exotic patterns below the potential hardest

David P Bird wrote:Hi Champagne,

As I was modifying my spreadsheet, I sampled your collection of puzzles that looked promising for a rank 0 pattern. Out of 6 tried, I only found 1 hit, and that only provided a single elimination (regrettably I discarded it as I hoped to find better later).

I therefore have to agree with ronk, that it would be more profitable to use chains to find the eliminations than multi-fish type logic. There are too many options to explore, and these puzzles have numerous chain exclusions that would be much faster to process.

David

Hi David,

No objection to accept that more filtering will help.

The question is always the same, who define the filter, who does the coding .....

I have the impression that in some 's view, the answer is "champagne".

For the time being, my priority would be to follow leren and to replace my very low search for rank 0 logic by the 4x4 cells search. I follow your discussions on that topic with a great interest.

Regarding my current search of the rank 0 logic, I am running a test on a small part of the big file, waiting for the end of the rating, and the first results let me think that it would take one more month (at the minimum) to explore the entire file.

If lern's approach gives hope to go say 10 times faster, I'll code it in priority.
champagne
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### Re: exotic patterns below the potential hardest

Hi David,

David P Bird wrote:However, if we have two instances of a digit spaced apart in a conjugate loop that are conjugate to each other, any candidate that sees both of them must be false, and so provides an extra elimination. I therefore have trouble understanding:
Blue wrote:(Eliminations from a conjugate loop are rank 1 -- like eliminations from discontinuous loops).

The best sense I can make of it is to say that if I only notate the chain segment from one to the other it will be a rank 1 elimination but if I notate the full loop it will be rank 0.

By "spaced apart", I'm assuming you mean that an AIC chain for the loop, would look like ((A = ? - ? ... = B) - ? ... = ? - loop), and that A and B can't see each other. To get an elimination for a candidate 'Z', you need to add two links into the situation... (Z - A) and (B - Z). That would make it rank 2, and Z still wouldn't be eliminated using Obi-Wahn arithmetic, since it's only in two weak links (cover sets). If you throw out the part of the chain from B, to the loop point, though, then you lose one more weak than strong links, and it becomes a rank 1 situation, where Z is eliminated. There's another situation, that I'll admit I didn't consider ... and maybe this is what you were thinking of ... where A,B and Z all see each other through a "digit in a house" link. In that case, if you threw out the same part of the chain as before, and closed the loop with that link, you'ld have a rank 0 elimination for Z, just as you suggested.

David P Bird wrote:I'm now going to play my 'dummy' card. In explaining how something works I'm interested in the effect an action has, not the whys and wherefores that lie behind it. (Consider what it takes to describe the workings of a limited-slip differential.) Would it make you happier if I added the word in red here?
I wrote:In following the chain strong links are expressed using the digits involved and weak links are (effectively) expressed as strong links for the complementary set of digits

David P Bird wrote:Alongside a copy of the PM grid extra cells for each house allow me to select which ones should be covered either by set A or set B of a complementary pair of digit sets. In the language of Xsudo both sets will be considered to be weak or strong together, and their intersection cells will contain a set of the opposite type. The option that is used is determined by considering which one gives the better truth/link balance. For a naked set, the house covers will be weak, and for a hidden set they will be strong.

OK, you've got me totally dazed and confused, but from your results I know you must be doing something right.
Actually I think I can understand all of what you're saying, but I have to read a lot into it, including that when you say "cover", you don't mean "cover" like in "base/cover", and that when you're talking about naked-vs-hidden sets, you're leaving out that the naked sets involve strong cell links, and the hidden sets, weak cell links.

Regards,
Blue.
blue

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### Re: exotic patterns below the potential hardest

blue wrote:
David P Bird wrote:There is a straightforward conjugate loop covering these eliminations:

(5)r4c7 = (5)r6c7 - (5)r6c4 = (5-4)r1c4 = (4)r9c4 - (4)r9c7 = (4)r4c7 – Loop

As conjugate loops are rank 0, (...)

This is a not a conjugate loop, but a continuous loop.
(Eliminations from a conjugate loop are rank 1 -- like eliminations from discontinuous loops).

I cut David P Bird some slack on this terminology, at least relative to my post where the size of the truth set is/was more important. David is from the Eureka! forum where "loop" was synonymous with "continuous." From that perspective, "conjugate loop" is a continuous loop where all the links are conjugate.

David's mistake is assigning the "conjugate" label to the loop as if the continuous loop exclusions were already made, another hangover from the Eureka! forum, I think.

All these labeling (naming) discussions, usually with David P Bird's labeling being involved, is unfair to the thread owners. Maybe we need a separate thread for these discussions.
ronk
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### Re: exotic patterns below the potential hardest

ronk wrote:All these labelling (naming) discussions, usually with David P Bird's labelling being involved, is unfair to the thread owners. Maybe we need a separate thread for these discussions.

I wanted to have a separate thread to summarize the findings (to come) of the big lot coming out of the +-3 generation starting from the potential hardest, but I am not at all disturbed when the discussion turns to some "out of thread" issue.

I sent on another topic a pm to blue to tell that I was thinking the discussion had reached a point where a separate thread could have a sense, but for "on the spot discussions", I feel they can take place everywhere.
champagne
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### Re: exotic patterns below the potential hardest

champagne wrote:
ronk wrote:All these labelling (naming) discussions, usually with David P Bird's labelling being involved, is unfair to the thread owners. Maybe we need a separate thread for these discussions.

... I am not at all disturbed when the discussion turns to some "out of thread" issue.

... for "on the spot discussions", I feel they can take place everywhere.

You must have noticed that it was David P Bird, blue and lastly myself involved in this "on the spot discussion" about labeling or naming. Courteous people would allow David P Bird and/or blue time to respond before interjecting.
ronk
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### Re: exotic patterns below the potential hardest

Blue, I'm sorry but I don't rate your critique very highly.

On the first item after some rambling about the continuous loop you finally reached the points I made – so why not edit it?.

On the second item you didn’t recognise that I was pointing out that the AIC I gave to make the elimination could be translated into cover sets using one set of digits for the strong links and the other set of digits for the weak links in the corresponding houses (the sets involved were shown alongside the grid). In fact later tests show that this only seems to work when all the links inside cells are the same type, so we can now both forget that idea.

On the third item
Blue wrote:
David P Bird wrote:Alongside a copy of the PM grid extra cells for each house allow me to select which ones should be covered either by set A or set B of a complementary pair of digit sets. In the language of Xsudo both sets will be considered to be weak or strong together, and their intersection cells will contain a set of the opposite type. The option that is used is determined by considering which one gives the better truth/link balance. For a naked set, the house covers will be weak, and for a hidden set they will be strong.

OK, you've got me totally dazed and confused, but from your results I know you must be doing something right.
Actually I think I can understand all of what you're saying, but I have to read a lot into it, including that when you say "cover", you don't mean "cover" like in "base/cover", and that when you're talking about naked-vs-hidden sets, you're leaving out that the naked sets involve strong cell links, and the hidden sets, weak cell links.

I've explained to you before that traditionally cover sets can be described as weak or strong – you're only recognising the Xsudo terminology which came later. And what part of my section in red didn't you understand to make you write your section in blue?

I suggest that you aren't prepared to pay the same amount of attention to other peoples posts as you expect others to pay to yours. Either that or you had some lubricant at your elbow.

Regards

David
David P Bird
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### Re: exotic patterns below the potential hardest

Hi David,

David P Bird wrote:Blue, I'm sorry but I don't rate your critique very highly.

A pity for you. Did you try to understand it ?

David P Bird wrote:On the first item after some rambling about the continuous loop you finally reached the points I made – so why not edit it?.

Taking ronk's post into account, I don't know whether it's worth replying to this or not.
Here's what happened: I was assuming that when you said "conjugate loops", you meant "conjugate loop". You said that eliminations from conjugate loops were rank 0. I said they were rank 1. It turns out that they can be either -- we were both wrong. I began by explaining why the ones that are rank 1, are rank 1, when I realized that some of them are rank zero. Not knowing what you were originally thinking, I finished that, and went on to cover the rank 0 cases as well, which I consider to be "special cases". Maybe they aren't so "special". Anyway ... I wasn't going to remove anything about why the ones that are rank 1, are rank 1, and it would have been dishonest to ignore the ones that really are rank 0 -- WYSIWYGot.

David P Bird wrote:On the second item you didn’t recognise that I was pointing out that the AIC I gave to make the elimination could be translated into cover sets using one set of digits for the strong links and the other set of digits for the weak links in the corresponding houses (the sets involved were shown alongside the grid). In fact later tests show that this only seems to work when all the links inside cells are the same type, so we can now both forget that idea.

There is nothing wrong with the idea that the weak house link, is equivalalent to a set of weak cell links (cell covers), covering candidates in a set of strong links for the same house, or that several weak links in the house, can be treated similarly. The only issue is that you can end up with duplicate cell links, if there were (totally unrelated) cell links present in the initial situation. It's an issue for presentation only ... not for the logic. If you can use similar tricks to make one of the duplicates go away, then presentation issue goes away with it. This was Obi-Wahn's point.

My issue with you:
In the quote above, and in statements in your recent posts, you seem to use the term "cover", with no regard for its meaning. In base/cover problems ... and to my knowledge, this is the origin of the word "cover" ... "cover" refers to weak links only ... weak links between candidates for the same digit in a house, or weak links for multiple digits in one cell. "Cover sector" is the term to use when you don't care to distinguish the type ... "digit in a house" -vs- "cell". When the topic is a strong link for a digit in a house, or for all digits in a call, the term to use is "base sector". The phrase "strong cover", is nonsensical. Paying heed to ronk's advice, I'll grant that I never read more than a page or two at a time, in the Eureka forum -- too much bickering and a long time between new ideas, was my impression. If "strong cover" is a phrase from the Eureka forum, then please define what it means in excruciating detail, in base/cover terms. Leave XSudo, and it's "exactly one of" links ("truths"), out of the picture (unless for some reason it's absolutely necessary).

David P Bird wrote:
Blue wrote:
David P Bird wrote:Alongside a copy of the PM grid extra cells for each house allow me to select which ones should be covered either by set A or set B of a complementary pair of digit sets. In the language of Xsudo both sets will be considered to be weak or strong together, and their intersection cells will contain a set of the opposite type. The option that is used is determined by considering which one gives the better truth/link balance. For a naked set, the house covers will be weak, and for a hidden set they will be strong.

OK, you've got me totally dazed and confused, but from your results I know you must be doing something right.
Actually I think I can understand all of what you're saying, but I have to read a lot into it, including that when you say "cover", you don't mean "cover" like in "base/cover", and that when you're talking about naked-vs-hidden sets, you're leaving out that the naked sets involve strong cell links, and the hidden sets, weak cell links.

I've explained to you before that traditionally cover sets can be described as weak or strong – you're only recognising the Xsudo terminology which came later. And what part of my section in red didn't you understand to make you write your section in blue?

To answer the last question first: you only mention digits, and never cells. Do I need to say more than that ?

To address another point: you've gotten me to a point where when you use the term "cover set", I have no idea what the indended meaning is. Whatever "traditionally" means in your sentence above ... it's totally beyond me. Maybe you really only mean "sector", as in "base sector" or "cover sector". In that case, sure ... you can talk about (weak) cover sectors, or (strong) base sectors. To use the term "cover sector" to refer to either, is IMO, totally inappropriate.

Finally: When you say that I only recognize XSudo terminology, I don't know what you mean. If there is anything that I'm paying close attention to, it's the base/cover aspect of things. I can be faulted for using the terms "truth" and "link", when I mean "base sector" and "cover sector". Given the audience (only a few members from the UFG days), I've been using XSudo language, on the assumption that it would make things too confusing to try to use the base/cover language. The truth is that I'm sadly disappointed by XSudo's use of "exactly one of" links ("truths", in the strict XSudo sense), and its total inability to deal with "strong only"/"at least one of" links .. even with its limited (ans misnamed) "SIS" feature. The good thing is that it does show the right eliminations from a base/cover perspective, at least some of the time, if you enter base sectors as "truths", and cover sectors as "links". Actually it always shows the base/cover eliminations, but sometimes it shows more.

David P Bird wrote:I suggest that you aren't prepared to pay the same amount of attention to other peoples posts as you expect others to pay to yours. Either that or you had some lubricant at your elbow.

Evidently I've been paying too much attention.
I spent a long time trying to digest your paragraph that I said left me "dazed and confused".
To my total amazement, I actually succeeded in (finally) making sense of every line.
I'm tempted to say that if this is what you really think of my efforts, then that's it ... I'm out.
I'll let it slide for now, given ronk's post and the possibility that obscure language (IMO)
from the Eureka forum, has been the source of our mutual consternations.

Regards,
Blue.
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### Re: exotic patterns below the potential hardest

Hi Blue,

Well we've managed to well and truly upset one another – Pax!

Mauling one another is counter-productive, so it's best if we simply agree to differ.

David
David P Bird
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### Re: exotic patterns below the potential hardest

Hi David,

I wish I knew what it was that we might agree to disagree about.
I'm open to that suggestion.

BTW: at this moment, I do have something something at my elbow.

Cheers,
Blue.
blue

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### exotic patterns below the potential hardest first split

Code: Select all
`split base    Count      V count   JEcount      Exo-band    r0                              gr_103_      1 213 477   54 928   908 060      1 002 818      4.53%   74.83%   82.64%                     gr_100      949 376      39 617   642 438      777 291         4.17%   67.67%   81.87%                     gr_95_99   4 343 616   274 815   2 305 518   2 820 868      6.33%   53.08%   64.94%                     gr_93_94   7 964 268   412 636   2 683 494   3 484 816      5.18%   33.69%   43.76%                     gr_92      16 179 828   582 640   3 484 711   4 969 262      3.60%   21.54%   30.71%                     gr_91      8 237 713   121 491   1 328 716   2 076 658      1.47%   16.13%   25.21%                     gr_90      41 892 662   407 397   5 083 822   9 306 575      0.97%   12.14%   22.22%                     gr_89      20 687 148   111 010   2 319 237   4 802 305      0.54%   11.21%   23.21%                     gr_88      4 728 355   14 590   547 656       209 907      0.31%   11.58%   25.59%                     gr_87      274 551      691   27 794      63 400         0.25%   10.12%   23.09%                     gr_86      1 176 412   6 238   83 287      201 866         0.53%   7.08%   17.16%                     gr_85      11 144 131   77 694   745 021      1 909 658      0.70%   6.69%   17.14%                     gr_84      15 218 746   42 903   945 559      2 696 026      0.28%   6.21%   17.72%                     gr_83      15 617 235   24 129   1 024 230   3 232 090      0.15%   6.56%   20.70%                     gr_82      8 423 970   5 719   822 895      2 802 711      0.07%   9.77%   33.27%                                                                        158 051 488                                          `

I have covered several steps for the study of that collection of puzzles below the potential hardest.
The main task has been to make a split of the entire file based on the rating.
Compiling the results of all work done meantime, I decided to cut all puzzles rating below SER 8.2

This is more or less the limit for XY chains and fishes. Puzzles with lower rating should not show properties of big interest.

The rating has been done using skmpp, my fastest tool. The general rating policy is in line with serate and skfr, but with slightly different options in the limitation of the search for the shortest path. Usually, the rating will be in line with skfr, sometimes slightly higher.

SER ratings are not a "linear" basis. Ratings are done by steps of 0.5 based on the process used with a correction on length. The distribution of ratings shows peaks in some places.
For highest ratings, I grouped several ratings

I wanted to deliver the entire files, but faced a volume problem.
I loaded files without the rating sorted on the puzzle form to have the best compression ratio. I made another check for redundancy and cleared some puzzles, but I am not 100% sure that all morphs were filtered.
In case somebody would have a specific file with the ratings, We can arrange to exchange it trough a specific channel later.

the link to that storage place is here

The first task and original target has been to see the distribution of the exotic patterns in these lots.

This is done for 3 properties

. V loop
. Jexocets
. Exocets in a band

The count is the number of puzzle where at least on occurrence of the corresponding property has been found.
The task has been partially done for the rank 0 logic, but I intend to restart all that very long process after I have made the coding of new patterns seen in the recent work

We see here some tendencies in the expected direction :

The chance to find a "V" or SK loop are close to nil with lower ratings

The JE frequency goes down sharply, but remains far over the expected average frequency for the lowest ratings. This is undoubtedly an effect of the seed.

The "exocet in band" frequency" offers a better resistance, what blue noticed in another sample.

Next step will be to study and published in the appropriate way the files of puzzles having specific properties
champagne
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