The New Sudoku Players' Forum

[mith]

and to puzzles in the ph database (going backward).

You can avoid this part of the work.
I've checked long ago that:
- there's no T&E(3) puzzle (and no puzzle with BxB > 7) in the old ph2010 database and in older databases like MLagictour, 17-clues..., my [cbg] collection of 6M puzzles....
- there's no (non-degenerate) tridagon in them either

More recently, I've checked that there are lots of degenerate-cyclic tridagons, almost everywhere, with a high frequency in the top of ph2010. They are the most likely precursors of the non-degenerate tridagon.

To clarify, I won't be looking for T&E(3) puzzles in the old ph2010 database; what I'm curious about is what seeds they may have developed from. It won't be a perfect representation of the path my scripts took to get there since I haven't saved the "parent" puzzle in any case, but what I can do is a vicinity search on the earliest T&E(3) puzzle to find the earliest (in my databases) neighbor puzzle (presumably a T&E(2) puzzle I generated with a non-degenerate tridagon) and work backwards from there to puzzles without non-degenerate tridagons and eventually to something in ph2010.

[denis_berthier]

To clarify, I won't be looking for T&E(3) puzzles in the old ph2010 database; what I'm curious about is what seeds they may have developed from. It won't be a perfect representation of the path my scripts took to get there since I haven't saved the "parent" puzzle in any case, but what I can do is a vicinity search on the earliest T&E(3) puzzle to find the earliest (in my databases) neighbor puzzle (presumably a T&E(2) puzzle I generated with a non-degenerate tridagon) and work backwards from there to puzzles without non-degenerate tridagons and eventually to something in ph2010.

OK, I had misunderstood.It would indeed be very interesting to have an idea of how many steps of vicinity search were involved.

[mith]

It looks like the answer is going to be "a lot". The first depth 3 puzzle in the 27c database is at position 2009985/4357595 (skfr 10.3, lowered due to uniqueness); for comparison, Loki is at position 4334584/4428910 of the 26c database - the switch to focusing on T&E depth was not long after Loki was found and you identified it as in T&E(3).

Running the script on 26c now. No depth 3 puzzles in the 19-22c and 31-37c ranges, not terribly surprising since these are minimals.

[mith]

Based on the 27c database, the first depth 3 puzzle was probably found in August 2021.

Code: Select all

1771897
~ August 13, 2021 (post 308061, first puzzle)

2009985
.............12.34..135.6.2....34.65...2....1.5.16..2...5.4....6.7.....38.9....4.  ED=10.5/1.2/1.2 (DCFC+FC), depth 3

2667557
~ September 29, 2021 (post 310474, first puzzle)

If the first depth 3 puzzles are in similar positions for other clue counts, I may not be able to identify definitively which came first. But we'll see.

[mith]

To clarify, I won't be looking for T&E(3) puzzles in the old ph2010 database; what I'm curious about is what seeds they may have developed from. It won't be a perfect representation of the path my scripts took to get there since I haven't saved the "parent" puzzle in any case, but what I can do is a vicinity search on the earliest T&E(3) puzzle to find the earliest (in my databases) neighbor puzzle (presumably a T&E(2) puzzle I generated with a non-degenerate tridagon) and work backwards from there to puzzles without non-degenerate tridagons and eventually to something in ph2010.

OK, I had misunderstood.It would indeed be very interesting to have an idea of how many steps of vicinity search were involved.

Actually, I'm finding some non-degenerate tridagons in puzzles which were in the ph2010 (and earlier) database, though they are lower rated; perhaps you only checked above some SER for this? The oldest appears to be this one from dobrichev, dating to 2012 (still running on <28c, it's slow because of the sorting I'm having to do, but the ones smaller than 32c so far are from Paquita in 2019 (28c-30c) or me (31c)):

Code: Select all

..............1..2..3.4..15.341.6..7.7.38..418.1.7...6.478.....16.4.3.7.3.8.67...;10.90;1.20;1.20;dob;12_12_03;545448;32;*

TO n259b4578 => 6r5c3 (still skfr 9.6 from here)

[denis_berthier]

Actually, I'm finding some non-degenerate tridagons in puzzles which were in the ph2010 (and earlier) database, though they are lower rated; perhaps you only checked above some SER for this?

What I checked about the old collections is precisely the following.

Before I found that Loki required TE(3), I was only interested in possible puzzles with BxB > 7; I checked BxB (and therefore T&E-depth 2) for all the puzzles with SER ≥ 11.6, as soon as they were published. This was largely enough as the only 3 known B7B had SER ≥ 11.8.
For (non-degenerate) tridagons, after the pattern was discovered, I checked the same sub-collection of ph2010: SER ≥ 11.6.

Not long after I found that Loki required TE(3), I checked the whole ph2010 and eleven gotchi collections for T&E-depth. No puzzle required depth 3. As for [cbg], it has always been known to be at depths 0 and 1.

More recently, I checked all the old collections for both non-degenerate and degenerate-cyclic tridagons at the same time; I published the global results in the tridagon thread. I didn't check them independently for the non-degenerate case, but I might be able to recover separate results; I must check what I have kept.
Also recently, I used the SHC to compute the BxB classifications of the whole ph2010 and eleven's gotchi collections (no B7B or more was found in them, other than the 3 old ones).
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[mith]

I see your comment here: post340760.html#p340760 but this does not mention ph2010 (only eleven's gotchi, top1465, and cbg). I would guess that you checked ph2010 for T&E(3) but not for non-degenerate tridagons. Regardless, the puzzle in my previous post is in ph2010 (and earlier) and does have a non-degenerate single guardian trivalue oddagon.

My script was pretty slow because I was sorting the database to find the oldest at each count, but I've just restarted it to ignore order and just print all potential NDTO puzzles (this is just a first pass filter to get a more manageable list, some of these may not actually have the pattern).

[denis_berthier]

I see your comment here: post340760.html#p340760 but this does not mention ph2010 (only eleven's gotchi, top1465, and cbg). I would guess that you checked ph2010 for T&E(3) but not for non-degenerate tridagons.

No T&E(3) in ph2010 or eleven gotchi are old results (not long after Loki).

For tridagons, I checked ph2010 after the mentioned post. I forgot to publish the results on the forum.
After reviewing what I've recorded about the full old lists, what I checked about tridagons is both the non-degenerate and degenerate-cyclic forms, undifferentiated. So that I can't say how many puzzles have a non-degenerate form, but I guess they are very rare.
I was looking for potential precursors of Loki and similar puzzles and I thought a precursor would be more likely if both forms were allowed.

[Edit: I think, I had done this before, but I can't find it; so I re-did the calculations: there's no non-degenerate tridagon in ph2010 for SER ≥ 11.6.]
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[denis_berthier]

.
I've tried a longer search in ph2010, down to SER 11.2 (included, i.e. for the highest 47795 puzzles):
There's indeed one and only one puzzle with a non-degenerate tridagon, with SER 11.3:
#18678
9876..5..4...8........7..4.3.2.9.....1..5...4.....67...59...4.......8..6.......8.;11.30;1.20;1.20;PAQ;2019_03_16;2318799;23;

Code: Select all

Trid-OR20-relation for digits 1, 2 and 3 in blocks:
        b2, with cells (marked #): r1c5, r2c4, r3c6
        b3, with cells (marked #): r1c8, r2c7, r3c9
        b8, with cells (marked #): r8c5, r7c4, r9c6
        b9, with cells (marked #): r8c7, r7c8, r9c9
with 20 guardians (in cells marked @): n4r1c5 n5r2c4 n9r2c4 n6r2c7 n9r2c7 n5r3c6 n9r3c6 n8r3c9 n9r3c9 n7r7c4 n7r7c8 n4r8c5 n9r8c7 n4r9c6 n5r9c6 n7r9c6 n9r9c6 n5r9c9 n7r9c9 n9r9c9

   +-------------------------------+-------------------------------+-------------------------------+
   ! 9         8         7         ! 6         1234#@    1234      ! 5         123#      123       !
   ! 4         236       1356      ! 12359#@   8         12359     ! 12369#@   123679    12379     !
   ! 126       236       1356      ! 12359     7         12359#@   ! 123689    4         12389#@   !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 3         467       2         ! 1478      9         147       ! 168       156       158       !
   ! 67        1         68        ! 2378      5         237       ! 23689     2369      4         !
   ! 5         9         48        ! 12348     1234      6         ! 7         123       1238      !
   +-------------------------------+-------------------------------+-------------------------------+
   ! 8         5         9         ! 1237#@    6         1237      ! 4         1237#@    1237      !
   ! 127       2347      134       ! 1234579   1234#@    8         ! 1239#@    123579    6         !
   ! 1267      23467     1346      ! 1234579   1234      1234579#@ ! 1239      8         123579#@  !
   +-------------------------------+-------------------------------+-------------------------------+

There are many more possibilities of having a tridagon here, but 20 is the smallest number of guardians. Pretty much useless.

Your case (..............1..2..3.4..15.341.6..7.7.38..418.1.7...6.478.....16.4.3.7.3.8.67...;10.90;1.20;1.20;dob;12_12_03;545448;32;*) has lower SER but only one guardian.

I can't say which is better as a precursor. SER 10.9 didn't tend to be used in the sets of seeds. BTW, which part of ph2010 did you use as seeds?

[Edit: BTW, does anyone know what 12_12_03 mean: is it 2012 or 2003?]
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[mith]

It's 2012

To clarify: my databases include the entirety of ph2010. There is no cutoff for SER. When selecting puzzles to use as seeds, I did use SER as one of the factors, however because my database is split by clue count (for size reasons, and for avoiding having to deal with database concurrency issues as much as possible) for less populated clue counts I have used much lower SER as seeds (32c in particular only has 8 puzzles in ph2010, all by dobrichev; I can see from the database that I have done searches on all of these at +2-1, +1-2, and singles expansion)

Script has been running overnight, I have 714 potential TO puzzles (all 11.1 or lower) so far. It's currently working on 26c, descending in clue count. So far 5 are from dobrichev (one 33c, two 32c, two 30c - all from late 2012 or early 2013) and the rest are from Paquita (all 29c or lower - all from 2019). I've done at least +1-2 neighborhood searches on all of these, +2-1 on the 33c and 32c puzzles, and singles expansion on about half.

[edit]When this is done running and I've checked the potential puzzles for actual TO patterns, I'll post an update in the tridagon thread. Getting off topic for the current thread.[/edit]
[edit2]Small correction: the script is actually running only on the ph1910 puzzles; apparently I never added the ID to the database for the new puzzles in ph2010 and the current script is using the ph ID to skip my newer puzzles. Shouldn't take long to run it on the new ph2010 puzzles (up to ID 3315007), including (but not limited to) the ones I contributed.[/edit2]

[mith]

Ok, I had an error in my script which was resulting in severely undercounting the number of TO puzzles. Only realized it because the dobrichev puzzle I posted above was not included in the latest results. (It was only printing puzzles with a xxxxxx111 pattern of digits, skipping xxxxxx110 which is way more common.)

I now have a total of 838844 puzzles which are potentially non-degenerate trivalue oddagon puzzles. I'm running a check for which of these actually have the pattern (the first pass does not check the arrangement of cells), but this is a huge portion of the ph2010 database regardless (>27%). I'm expecting at least a quarter of all puzzles in ph2010 to have a non-degenerate trivalue oddagon in them, which is surprising.

I'll also note as an example that the 11.3 Denis posted earlier does *not* have a valid non-degenerate trivalue oddagon (at least by my definition); because r1c9 is limited to 123, the three marked cells in box 3 already cannot all contain 123, so the OR branching can be reduced to considering that r2c7 and r3c9 cannot both contain 123. So far all of the puzzles I've looked at which fail the second pass have a similar structure. In fact, all of these so far instead have a Junior Exocet available to reduce the difficulty, involving the singleton digits. So perhaps there is some relationship here that I haven't appreciated before.

[denis_berthier]

I now have a total of 838844 puzzles which are potentially non-degenerate trivalue oddagon puzzles. I'm running a check for which of these actually have the pattern (the first pass does not check the arrangement of cells), but this is a huge portion of the ph2010 database regardless (>27%). I'm expecting at least a quarter of all puzzles in ph2010 to have a non-degenerate trivalue oddagon in them, which is surprising.

The 25% would not only be "surprising", they would require a full fledged miracle, with orchestra, fireworks and all the rest, because there's only one in the first 47,795 puzzles, the 11.3 I posted previously.

I'm curious to see examples of your 27% in the first 47,795 puzzles of ph2010.
You say you're "not checking the arrangement of cells". I don't really understand what you mean. This is an essential condition of the pattern (3 cells in each of 4 blocks..). This may be the reason of your large number of potentaily...

the 11.3 Denis posted earlier does *not* have a valid non-degenerate trivalue oddagon (at least by my definition); because r1c9 is limited to 123, the three marked cells in box 3 already cannot all contain 123, so the OR branching can be reduced to considering that r2c7 and r3c9 cannot both contain 123.

"My" 11.3 (indeed Paquita's) has a non-degenerate trivalue oddagon (it has indeed many different ones), unless one is willing to add to the definition conditions (such as those you're mentioning) that have never been defined and that are potentially in unlimited numbers. I think you're confusing the presence of the pattern (defined in the precise, simple way I gave in the tridagon thread) with its usefulness in specific circumstances.
In the present case, there are two independent circumstances that make it useless: the one you're mentioning and the very high number of guardians.
.

[mith]

I now have a total of 838844 puzzles which are potentially non-degenerate trivalue oddagon puzzles. I'm running a check for which of these actually have the pattern (the first pass does not check the arrangement of cells), but this is a huge portion of the ph2010 database regardless (>27%). I'm expecting at least a quarter of all puzzles in ph2010 to have a non-degenerate trivalue oddagon in them, which is surprising.

The 25% would not only be "surprising", they would require a full fledged miracle, with orchestra, fireworks and all the rest, because there's only one in the first 47,795 puzzles, the 11.3 I posted previously.

I'm curious to see examples of your 27% in the first 47,795 puzzles of ph2010.

It's no miracle. It's just that the ones found prior to 2021 do not have the highest SER, and I suspect part of the reason why is that the pattern is much more likely to be found at higher clue counts, which weren't as thoroughly searched. The pattern was only discovered what I started posting SER 11.6+ puzzles with it.

You can check this for yourself, though. Here's the first and last 11.1 in ph2010 which have the pattern. The total in the first pass file is 72910 11.1 puzzles out of 184734 in ph2010 (nearly 40%).

Code: Select all

98.76.5..7.45.........84...59.6..8...48........7..89...6..9..5....4..........6.32;11.10;1.50;1.50;PAQ;2019_08_01;2455669;26;*
98.76.5..7.58.4....4.......6...9....4.....32...8..5....9.57.68..6..4.........6.5.;11.10;1.20;1.20;PAQ;2019_10_1110_220;3121253;26;*

Moved remaining comment to the T&E(3) thread: p346251

[denis_berthier]

I suspect part of the reason why is that the pattern is much more likely to be found at higher clue counts,

It's true that the puzzles in T&E(3) have a very high clue count in general.

Here's the first and last 11.1 in ph2010 which have the pattern. The total in the first pass file is 72910 11.1 puzzles out of 184734 in ph2010 (nearly 40%).

Code: Select all

98.76.5..7.45.........84...59.6..8...48........7..89...6..9..5....4..........6.32;11.10;1.50;1.50;PAQ;2019_08_01;2455669;26;*
98.76.5..7.58.4....4.......6...9....4.....32...8..5....9.57.68..6..4.........6.5.;11.10;1.20;1.20;PAQ;2019_10_1110_220;3121253;26;*

OK for these two. I'll have a closer look at the 11.1 puzzles tomorrow.
If there are many more (in %) than above 11.2, it means I stopped my checks at exactly the wrong point. But there must also be a deeper explanation for such a difference between 11.2 and 11.1.
.

[denis_berthier]

.
After your findings, I launched SudoRules on the puzzles in ph2010 down to #100,000 and I get some really funny results:

- as I said before, down to #47,795 (i.e. among all SER ≥ 11.2), there's one and only one non-degenerate tridagon,
- but, for SER = 11.1 (until now limited to the first 100,000 puzzles in the database), I find 12,282 ones. (I'm launching more computations to go lower.)

And guess what. All these puzzles are due to the same creator: Paquita. This requires further analysis, but a quick visual scan seems to show they go by large families of puzzles that are variants of one another.

I'm impatient to wake up tomorrow morning I see results down to #200,000.
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