The New Sudoku Players' Forum

by **coloin** » Thu Jun 27, 2024 4:44 pm

Paquita wrote:I have been collecting new NOT tridagon puzzles - at least I think they are new ......-

Unfortunately almost all of these minimal puzzles are already in my collection of posted puzzles, posted by mith , hendrik and yourself...
These are the new ones - all from same max puzzle which is B6B

Code: Select all: 98.76.5..5.7..98...465......7..85.....94.6......97..5..6....43...4....2......4... 98.76.5..7.5.489...46..9....7.4.6.....895........87.9..6.....3...4...62.......... 98.76.5..5.7.4..9..4.......67..94....5.8.7.....4.5...9.68...9.......632.......... 98.76.5..5.7.4..9..4.......67..94....598.7.....4.5.....68...9.......632.......... .234.67..4.7..9.3.69.......26....3......6.85..........37.24.....46.93...9.26.7..3 expanded min lex solution grid puzzle

by **Paquita** » Fri Jun 28, 2024 3:10 pm

Yes, my mistake.
I thought I was dealing with non-tridagon puzzles and did not test them against tridagon puzzles.

by **Paquita** » Thu Jul 11, 2024 3:42 pm

This is one of my T&E(2) puzzles
98.76.5..7.5.48.....65.9...5.86...7.47.9...6..6......8.94....5.......4.3........2 ED=11.7/1.2/1.2
published Sept 16th, 2023.

This is the expanded version
98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2

These are the minimals
98.76.5..7.5.48.....65.9...5.86...7.47.9...6..6......8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
98.76.5..7.5.48.....65.9...5..6...7.47.98..6..6......8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
98.76....7.5.48.....65.9...5.86...7.47.98..65.6........94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
98.76....7.5.48.....65.9...5.86...7.47.9...65.6......8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
98.76....7.5.48.....65.9...5..6...7.47.98..65.6......8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
.8.76.5..7.5.48.....65.9...5.86...7.47.9...6..69.....8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
.8.76.5..7.5.48.....65.9...5..6...7.47.98..6..69.....8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
.8.76....7.5.48.....65.9...5.86...7.47.98..65.69.......94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
.8.76....7.5.48.....65.9...5.86...7.47.9...65.69.....8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2
.8.76....7.5.48.....65.9...5..6...7.47.98..65.69.....8.94....5.......4.3........2;98.76.5..7.5.48....465.9...5.86...7.47.98..65.69.....8.94....5.......4.3........2

in maxlex
98.76.5..7.5.48.....65.9...5.86...7.47.9...6..6......8.94....5.......4.3........2
98.76.5..7.5.48.....65.9...5..6...7.47.98..6..6......8.94....5.......4.3........2
98.76.54.7.5.8..6..6.......8.7...9.545....68...6....74.49.7.......3.9......2.....
98.76.5..7.4.8.6...6.4.....8.7....9454....86...6...7.5.59.7.......3.9......2.....
98.76.54.7..5...6.....8.7..6.9.....757....89..48....56...6..9.4....34.......2....
98.76.5..7.54......64..98..6.8.74......98.......5.6...4.6...7...9.....32.....7.5.
98.76.5..5.7....6..4.5..9..7.8...4.........38.......2.6..95...4.94.86.....54.7...
98.76.54.7.5.8..6..64......8.7...9.5.5....68...6....74.49.7.......3.9......2.....
98.76.5..7.54......64..98..6.8.74......98.......5.6...4.6...7...97....32.......5.
98.76.54.7.5.4.....6.9..7..5.86.........38.......2....4.....97..96....84..7...6.5

of these 10, 8 are T&E(2)
98.76.5..7.5.48.....65.9...5.86...7.47.9...6..6......8.94....5.......4.3........2
98.76.5..7.5.48.....65.9...5..6...7.47.98..6..6......8.94....5.......4.3........2
98.76.5..7.4.8.6...6.4.....8.7....9454....86...6...7.5.59.7.......3.9......2.....
98.76.54.7..5...6.....8.7..6.9.....757....89..48....56...6..9.4....34.......2....
98.76.5..7.54......64..98..6.8.74......98.......5.6...4.6...7...9.....32.....7.5.
98.76.5..5.7....6..4.5..9..7.8...4.........38.......2.6..95...4.94.86.....54.7...
98.76.5..7.54......64..98..6.8.74......98.......5.6...4.6...7...97....32.......5.
98.76.54.7.5.4.....6.9..7..5.86.........38.......2....4.....97..96....84..7...6.5

and two are T&E(3)
98.76.54.7.5.8..6..6.......8.7...9.545....68...6....74.49.7.......3.9......2.....
98.76.54.7.5.8..6..64......8.7...9.5.5....68...6....74.49.7.......3.9......2.....

I seem to have more puzzles where this happens, I can dig them up in case anyone is interested in such genealogy

Website · by **denis_berthier** » Thu Jul 11, 2024 4:12 pm

.
Hi Paquita,
Yes, genealogy would be very interesting here.

I'm surprised that you get T&E(3) puzzles just by taking minimals after expanding a T&E(2) one.
Now, the question is, where did your original T&E(2) puzzle come from? From a T&E(3) one?

In [HCCS2], I've tried such procedures (expansion by Singles + minimals) starting from various puzzles at various depths and I didn't find puzzles at larger T&E-depth.
And this even after triple expansion: Singles, +1-expand, Singles.
An obvious reason why it doesn't work in general is, T&E(n+1) puzzles are very rare wrt T&E(n) ones.

.

by **Paquita** » Thu Jul 11, 2024 5:40 pm

Hi Denis

I can't find the origin of this puzzle from Sept 2023. Not exactly, anyways. It is from an expanded 11.70 rated puzzle, that had been published at that time, but I can't say which one. I think that by then I already was looking for T&E(2) puzzles and that I selected my seeds to be such. It is very well possible that one of the 10 minimals that came out of the expansion was the original seed : so it could have been a T&E(3) but the chance that it was T&E(2) is much higher.

(At that time I did not find all minimals with my algorithms. Not so strange because I built the module myself and I built in some shortcuts : for example, a puzzle with 26 expanded clues can lead to 5000 minimal puzzles and my software could not handle that. I found that gridchecker does it well and quite fast - I have been able to test it on an old laptop.) Currently I am revising my old puzzles for minimals from expands that I previously overlooked.

by **Paquita** » Thu Jul 11, 2024 6:02 pm

At that time these puzzles were known

98.76.54.7..5...6.....8.7..6.9.....757....89..48....56...6..9.4....34.......2....
98.76.5..7.54......64..98..6.8.74......98.......5.6...4.6...7...97....32.......5.
98.76.54.7.5.4.....6.9..7..5.86.........38.......2....4.....97..96....84..7...6.5 (T&E2)

98.76.54.7.5.8..6..6.......8.7...9.545....68...6....74.49.7.......3.9......2..... (T&E3)

so it is one of these

by **Paquita** » Thu Jul 11, 2024 8:52 pm

It is not the T&E(3), that is an 11.8 rated puzzle, not 11.7

Website · by **denis_berthier** » Sat Jul 13, 2024 5:29 am

.
Hi Paquita,
As you know, mith has found many puzzles with a (non-degenerate) tridagon in the ph2010 database, puzzles in which this pattern remained unnoticed for 12 years (for the oldest 2). Most of the other puzzles are yours, dating back to 2019 and with SER 11.0 - before mith started to find huge numbers of T&E(3) puzzles.

Considering the large number of puzzles you proposed at that time, my question is, did you already use expansion by Singles or only the usual {-p+q} technique?
.

by **Paquita** » Sat Jul 13, 2024 6:37 pm

Hi Denis

I did not use expansion by singles at that time, indeed I used +n-n, but also other techniques like swapping rows from the same or other puzzles, and combining possible clue patterns with possible solutions.

by **Paquita** » Sun Jul 14, 2024 5:41 pm

As I said, it happens to me often that a min-expand has both T&E(2) and T&E(3) minimals.
This is the result of just one file of about 2.5K puzzles, posted Sept 16th 2023.
Does this mean that different minimal files of the same min-expand are different indeed, and not all the same puzzle?
Because untill now I still treat all unique minimals as different. It would be a huge save to work with min-expands instead, but what about the T&E rating then?
On the left are the minimals, on the right the expands as given bij SHC's expand.jar

Hidden Text: Show

Website · by **denis_berthier** » Sun Jul 14, 2024 6:52 pm

Paquita wrote:As I said, it happens to me often that a min-expand has both T&E(2) and T&E(3) minimals.

Of course.

Paquita wrote:Does this mean that different minimal puzzles of the same min-expand are different indeed, and not all the same puzzle?

Of course, they are different.

Paquita wrote:Because untill now I still treat all unique minimals as different. It would be a huge save to work with min-expands instead, but what about the T&E rating then?

Working on the min-expands only depends on what you are doing.
If you want to prove that all the minimals have a tridagon, it's enough to prove it for the min-expands: deleting clues can't destroy a tridagon (it can only increase the number of guardians).
But deleting clues to find minimals can increase any of the classifications, including T&E-depth.You can use the fact that it can't decrease it.
.

Website · by **denis_berthier** » Mon Jul 15, 2024 5:28 am

.
I realise my answer was incomplete.
The best way to save work is to use the equivalence relation defined in [HCCS2]:
P1 equivalent to P2 iff they have the same expansion by Singles.

All my classifications (T&E-depth, B, BxB, BxBB, ....) are invariant under this equivalence relation.
In mith T&E(3) collection, the gain factor is 7.
.

by **Paquita** » Mon Jul 15, 2024 11:27 am

Ah yes I see. Thank you, that clarifies it. In my examples, the T&E(3) puzzles share a min-expand that is a subset of the min-expand for the T&E(2) puzzles. That is why they both come out of the same min-expand (the larger set).

This is in my experience quite common, that I start with a T&E(2) seed, expand it, get the minimals and I have a few T&E(3) as well.
This may be the origin of how T&E(3) puzzles came to be found. It can happen if the T&E(2) puzzle has a tridagon.

Website · by **denis_berthier** » Mon Jul 15, 2024 11:36 am

Paquita wrote:Ah yes I see. Thank you, that clarifies it. In my examples, the T&E(3) puzzles share a min-expand that is a subset of the min-expand for the T&E(2) puzzles. That is why they both come out of the same min-expand (the larger set).

This is in my experience quite common, that I start with a T&E(2) seed, expand it, get the minimals and I have a few T&E(3) as well.
This may be the origin of how T&E(3) puzzles came to be found. It can happen if the T&E(2) puzzle has a tridagon.

Yes, but the question is, where did your T&E(2) puzzles come from? If they already come from digging for minimals of expanded forms of T&E(3) puzzles, this is not really surprising.
But if they come from "normal" T&E(2) puzzles with no tridagon, I think you very rarely get a T&E(3).
.

by **Paquita** » Mon Jul 15, 2024 3:00 pm

The seed came from puzzles by mith and hendrik that were published at the end of August 2023.
I did select the seed to be T&E(2) but by then already a new non-tridagon T&E(2)puzzle was rare.
There were non tridagon puzzles in the earlier puzzles of ph2010, but I did not select those as seed because they are long known and used as seed before by me and others.
So yes, most seed puzzles were T&E(2) tridagons.

You spotted T&E(2)tridagons to exist before there were T&E(3) puzzzles. This just illustrates how tridagon seed leads to T&E(3). It does not show how the first tridagon came up.

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