The New Sudoku Players' Forum

[Paquita]

Indeed Denis, this procedure does not change the solution.
Maybe I did not understand your challenge. What kind of procedure do you have in mind that might generate high BxB from T&E(3) puzzles?
In the procedure that I described I assume that some kind of vicinity search must be used, other than this one. But preferably while preserving the tridagon. (Instead of generating a lot more puzzles of which only some just happen to have kept the tridagon)
What did you mean by "procedure (that needs to take one out of the given solution grid)" ?

[denis_berthier]

Hi Paquita

Indeed Denis, this procedure does not change the solution.
Maybe I did not understand your challenge. What kind of procedure do you have in mind that might generate high BxB from T&E(3) puzzles?

Actually, that's the whole point of the challenge: finding such a procedure - or perhaps just describing in detail the procedure you are using - because you do succeed in generating such puzzles and the starting point was the T&E(3) puzzles. By "you", I mean you, Hendrik and coloin.

What did you mean by "procedure (that needs to take one out of the given solution grid)" ?

Indeed, it's just a reminder that the T&E(3) and BxB≥7 sets of solution grids are almost disjoint; so it's better to concentrate on a procedure that produces different solution grids.

In the procedure that I described I assume that some kind of vicinity search must be used, other than this one. But preferably while preserving the tridagon. (Instead of generating a lot more puzzles of which only some just happen to have kept the tridagon)

Yes, this is indeed the heart of the question. I've been thinking about it but I don't see how to do it while still using gsf's program for minimisation. (That's why I asked if you used this program.)
If you add any clue from the solution grid, you get into the problem in the previous paragraph.
If you add a clue (say a non-tridagon one) not from the solution grid, you get an inconsistent puzzle and minimisation via gsf doesn't work. As a result, before applying minimisation, you also need to delete at least one other clue in order to get back to a consistent puzzle. Is there a smart way of doing it? I guess this is what you call "some kind of vicinity search" and this is probably the most interesting part of the procedure.

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[Paquita]

Further thoughts on the challenge

I went back to the start of this thread, as the question is how to generate BxB>6 puzzles. This is related to the length of inner braids. Calculating BxB was proposed as a way to measure hardest puzzles, alternative for SER.

Quote :
"one more geenral conclusion is, the SHC allows much better computation times than the SER (or even its PGXplainer variant) and it could replace it in the search of the hardest T&E(2) puzzles."

This was a conclusion while no BxB>7 was known. It is no longer true, the SER or its quicker alternative skfr is much faster than SHC. There are differences per system of course, but in my PC a typical B10B takes between 30 minutes and 2 hours. And B9B and B11B are almost equally timeconsuming. The funny thing is that the B14B costs much less time. This may be reflected by the observation that a typical B10B is skfr 11.6 or 11.7, and B14B is skfr 11.2. These are not incidents but overall results. If we choose not to compare the BxB to skfr anymore, the anomaly remains that B10B is the most calculation consuming, and not B14B.

Now it seems almost impossible to use the BxB rating on most T&E(2) puzzles. If they rate higher with skfr, they usually have a low BxB, <7. In other words, by using the BxB rating the number of puzzles that rate high is radically diminuished.

I can understand the desire for a clean criterium for rating. If the length of braids is the sole test, that is cleaner than the SER or skfr that test for several complex constellations in a puzzle.
Now that it has been used, and higher BxBs have been found, what is the evaluation? I it indeed a better rating instrument? Are the rare B14Bs indeed the hardest puzzles?

I looked at Champagnes tridagon puzzles, they are skfr rated. A lot of T&E(2) with tridagons, and almost no BxB>6. Or at miths T&E(3), also with tridagons, but as it now seems, to get higher BxBs from them with vicinity search is a rare occurence.

I was looking at the early posts of this thread, to see if I can find an answer to the question : what defines a high number of inner braids? Is this a certain constellation, like the tridagon is? Even, a constellation in addition to a tridagon, or a certain kind of tridagon?

[denis_berthier]

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Hi Paquita

Many topics in a single post.

The main point is about goals: do you want to mine for coal or for diamonds? Same atoms, different substance. Also different quantities to be expected and different worths. High BxB puzzles are very rare; one of these diamonds is worth tons of high SER coal.

For decades, puzzle diggers have mined for millions of high SER puzzles and the collector-in-chief has merely stuffed them into a large database. This has left thousands of puzzles in it with a tridagon undetected for more than 10 years. Now, this approach starts to apply mith's idea of expansion by Singles and re-minimisation, in combination with Methuselah's old idea of vicinity search. And high SER puzzles can easily be found by millions to fill up some google drive. Apart from the quantity, what's new?

The SER and its alternative implementations rely on no theoretical ground; the SER is a hotpot of rules of different kinds (not even popular ones) assigned arbitrary ratings. Find an anomaly in a collection, you can't use it to conclude anything, except that it may be due to an arbitrary threshold in the SER (see [PBCS] for an example) or to some new type of its rules starting to be used in the rating - or to uniqueness...
I haven't studied the anomaly you mention about the low SER of high BxB puzzles. But mith has done it for T&E(3) puzzles. It was almost always due to the uniqueness rules in the SER. A purely artificial cause. Did you try to eliminate uniqueness rules in your calculations?

On the other hand, after his use of expansion by Singles and of T&E-depth as the unique filter in vicinity search, mith could find millions of T&E(3) puzzles - and a non-circular conclusion could be drawn: they all have a tridagon. (Non-circular, because the tridagon was not part of the search criteria.)

T&E-depth, B, BxB, BxBB have intrinsic, purely structural meanings. They are defined in purely logical terms. (Not only the SER IS NOT, but IT CANNOT BE defined so.) It's anyone's choice to decide if they want to build on solid foundations or on quicksands.
Like the SER, these classifications rely on the notion of the hardest step and they exclude the number of times this step needs to be reached in the solution. It is therefore inherent both in them and in the SER that the computation times for a fixed value have a very large variance and a puzzle with a lower value may indeed take much more time than a "harder" one. It is also the case that the most extreme values often require shorter computation times than intermediate ones, because there are fewer possibilities for many non-visible useless partial chains of smaller lengths to be present.

There's a reason why I call T&E-depth, B, BxB, BxBB classificationS and not ratings.
When one talks of A rating, there is always the totalitarian view that it must hold the ultimate truth about the difficulty of a puzzle. See how SER worshippers behave about it! The best of it is when the words "rating" and/or "hard" are used twice in the same sentence with different meanings.

About the challenge, it didn't include any "smart" condition. This word came out in our discussion, but it may be ill advised to add it to the challenge - in particular if that leads to adding tridagon condition that would make the conclusion that all the B7B+ have a tridagon circular.

Some practical note: when you are looking for high BxB puzzles, this can be done in stages. Do all the search with the fast-to-compute condition BxB ≥ 7 *. You get rough diamonds. At the end, do a precise BxB computation to determine their worth.
(*) in SHC, this can be done by choosing max-length=6 and buffer-size large. Any puzzle with BxB≥7 will get the -3 value, which will mean BxB>6 (if you have previously filtered for T&E(2) puzzles).
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