The New Sudoku Players' Forum

by **hendrik_monard** » Tue Aug 26, 2025 6:06 am

Hi Denis,
Sorry for this late reaction. I found your new question only now.
As I have not been following the T&E(3) thread closely, I have no idea where to look for the link you asked.
BTW, I am now preparing an answer to your other question of yesterday morning.

by **hendrik_monard** » Tue Aug 26, 2025 3:27 pm

denis_berthier wrote:
hendrik_monard wrote:The list contains now 1747 solutions.
Statistics:
7 306
8 232
9 524
10 526
11 44
12 77
13 33
14 5

What do you count in these stats? The total is the number of solution grids, but most grids have several B7B+. Do you count the highest (known) BxB value for each solution?
.

In this post, x (in BxB) is always considered to be at least 7 and puzzles have a rating of B7B or higher.
In the solution list, the x (second column) comes from the first published puzzle with that solution.
As far as I remember, there were only a small number of cases with different x values sharing the same T&E(2) solution grid.
There have been some cases where new puzzles had a larger x than the first published puzzles with the same solution. However, after verification, the higher x was due to a typo.
In most, and perhaps all known cases, the original x was decreased with one point (f.i. 10 -> 9)
When a list of new puzzles is published, I check whether the solutions of these puzzles are not already in the solution list. A log file keeps the (rejected) matches .
I have now examined those files and recomposed some of the earlier log files.
Sometimes a lower x occurs in clusters. See this extract of a log file where 11 puzzles were derived from a single original:

Hidden Text: Show

Code: Select all: 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1......8.7.3..1......9..378....65.......2...583.6..81...537...6..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1......8.7.3..1......9..378....65.......2...58..6..81...537..36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1....6.8.7.3..1......9..378....65.......2...583....81...537...6..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1....6.8.7.3..1......9..378....65.......2...58.....81...537..36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1......8.7.3..1......9..378....65.......2.7.58..6..81...53...36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1....6.8.7.3..1......9..378....65.......2.7.58.....81...53...36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....5.....5.1....668.7.3..1......9..378....65.......2...583....81.6..37...6..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....5.....5.1....668.7.3..1......9..378....65.......2...58.....81.6..37..36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....5.....5.1....668.7.3..1......9..378....65.......2.7.58.....81.6.53...36..7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....5.....5.1....668.7.3..1......9..378....65.......2...58..6..81.6..37..3...7... new 250617 9 123456789457189236689723541264578913378912465591364827745831692812695374936247158 1.3.56....571....668.7.3..1......9..378....65.......2.7.583.6..81...5....36..7... orig 250423 10 ....56....5.1.....68.7.3..1......9..378....65.......2...58..6..81.6..37..3...7... new 250617 9

There has been a case in the masters and other batches published by coloin on last June 18th where two puzzles in different batches had different ratings (7 and 8). The one with the lower rate was first processed by my novelty checking script. It contained one clue more than a puzzle processed later which by my script was signaled as a case of increased x. I discovered this situation in the 'old' logs while preparing this post. I have now changed the rating for this solution from 7 to 8 as both puzzles were published by the same author and on the same day.
Also an error in transmitting ratings for a group of 13 B8B puzzles has been corrected (changed from 7 to 8) and a couple of other corrections done.
NEW STATISTICS:
7 293
8 244
9 525
10 526
11 44
12 77
13 33
14 5
Conclusions:
The number of solutions where different x values occur is estimated as considerably less than 1 percent of the total number of solutions. The effect on the statistics is thus negligible.
From my point of vue, the main purpose of the list is to serve as a reference for checking whether a new puzzle belongs to a known group of puzzles (with the same solution grid) or not.
If it is considered useful, I am ready to update the list in my google drive after each post containing puzzles with a new solution grid.
The link to the modified solutions list (remains the same):
https://drive.google.com/file/d/1gLUBdAcdF9ntMiS_bc7Z_AEAu7XfhOnQ/view?usp=drive_link

Website · by **denis_berthier** » Thu Aug 28, 2025 5:54 am

.
Hi Hendrik
Thanks for your detailed analysis.
For the mastermins 1 to 4 + 5 to 10 + 11 to 15, I count 1532 solution grids. I think I had checked they were all different but I've checked again (see below).
I hadn't checked the differences in BxB within each solution grid. Your results about it are interesting.

Solutions in mastermins-5to10 already in mastermins-1to4
123456789457189236689327541264538917591764823738912465345871692812695374976243158

Solutions in mastermins-11to15 already in mastermins-1to4
none

Solutions in mastermins-11to15 already in mastermins-5to10
123456789457189263689372514245967138738514926961823475392748651574631892816295347
123456789457189236896237514275341968634895172981672453319764825562918347748523691"
123456789457189236869237514275341698681972453934865172316794825592618347748523961
123456789457189236689273514241697358576328941938514627314765892792831465865942173

Total: 5 cases. Can't have much statistical impact.
.

Website · by **denis_berthier** » Fri Aug 29, 2025 8:31 am

.
I've just posted the results of a systematic procedure for producing high B T&E(1) puzzles from T&E(3) or T&E(2) ones: http://forum.enjoysudoku.com/1-brt-expansion-paths-within-t-e-n-and-beyond-t45647-98.html
Because the procedure remains with fixed solution grids, there cannot be any similar procedure for producing high BxB puzzles in T&E(2) from T&E(3) ones, with reasonably high throughput [remember that there are only 19 common solution grids between the T&E(3) and T&E(2) puzzles with BxB≥7.

On the other hand, coloin, Hendrik and Paquita have been very successful in finding thousands of B7B+ puzzles. So, here is my question/challenge:

Can anyone define a systematic procedure T&E(3) --> B7B+ (that needs to take one out of the given solution grid) and can one estimate its statistical throughput?
.

by **hendrik_monard** » Wed Sep 03, 2025 7:27 am

Yesterday (September 2nd) Champagne published in the thread "Non degenerated tridagon puzzles direct search" 4 puzzles (in two posts) with x > 6 and with 4 new solutions:

Code: Select all: .2..5.7..4...8..237.8.3...52.5....4.3......78.87...5.....9.......4.21.......7...4 B9B 1...5.7....678.1..78...35........69..3....8......6...43....5...5.16.8....78.1.... B10B .2......94.6.8...2.891....62...4.....9.86....8.19.2........4..8.......71.1....3.. B10B ...4...8945.....3...82..5...9..61..........9..3..7....3.2...84.58...2..3..9....52 B9B

I'll add tem to the solutions database.
They all have a relative low cc, so I guess there must be room for further exploring with expand/twin cycles.

Website · by **denis_berthier** » Wed Sep 03, 2025 10:34 am

.
Hi Hendrik
I've stopped following champagne's thread; but any new solution grid is good to take.
Just a question: the goal was to scan all the solution grids, filter them with some both overly restrictive and overly general "tridagon-solution" criterion and to conclude in a somewhat circular way that some puzzles for these grids had a tridagon.
To make it short: in terms of throughput, the whole process starts from gsf's list of 5 472 730 538 solution grids and finally gets 4 puzzles with BxB ≥ 7 (and none in T&E(3)) - correct me if these figures are incorrect.
.

by **Paquita** » Wed Sep 03, 2025 2:23 pm

Some new puzzles

Hidden Text: Show

by **Paquita** » Wed Sep 03, 2025 2:45 pm

As for the challenge, This is what I did

Select higher rated T&E(3) puzzles(skfr rates above 11.0)
Establish per puzzle which digits are in the tridagon (present only once in the puzzle); that has to remain so
Create new puzzles with each with one (non-tridagon)digit added
Get the minimals
Select high rated (skfr rated) results

If I do this on a random collection of T&E(3) I get no results from this selection at all. (I used Mith's collection)

I tried the same with the T&E(3) puzzles that I got while searching for BxB > 6 (starting from known BxB > 6 puzzles)
This does produce some puzzles and a few of them have higher BxB. But they are puzzles I already knew.
It suggests that T&E(2) puzzles with a tridagon and a high rate are likely to have a higher BxB. It does not tell how to obtain those from just any random T&E(3) puzzle; not even from a higher skfr rated T&E(3) puzzle.

Website · by **denis_berthier** » Wed Sep 03, 2025 4:08 pm

.
Hi Paquita
Congrats for this new batch of high BxB.

Paquita wrote:As for the challenge, This is what I did.
Select higher rated T&E(3) puzzles(skfr rates above 11.0)
Establish per puzzle which digits are in the tridagon (present only once in the puzzle); that has to remain so
Create new puzzles with each with one (non-tridagon)digit added
Get the minimals
Select high rated (skfr rated) results

Just to make sure: when you add a non-tridagon digit, you choose it among the digits in the solution? Otherwise, you'd get an inconsistent puzzle and then gsf's software wouldn't be able to find minimals. Or are you using another software to compute the minimals?

Paquita wrote:If I do this on a random collection of T&E(3) I get no results from this selection at all. (I used Mith's collection)

If the added digit is selected in the solution grid as I suppose, that's not a surprise (retrospectively), regardless of any SER filtering, as the number of solution grids common to T&E(3) and B7B+ is only 19 as of now.
.

by **hendrik_monard** » Wed Sep 03, 2025 4:36 pm

denis_berthier wrote:.
Hi Hendrik
......
To make it short: in terms of throughput, the whole process starts from gsf's list of 5 472 730 538 solution grids and finally gets 4 puzzles with BxB ≥ 7 (and none in T&E(3)) - correct me if these figures are incorrect.
.

Hi Denis,
The puzzles with x>6 that I found were directly visible in Champagne's posts in the Thread "Non degenerated tridagon puzzles direct search". I did not examine all the (supposedly large) files on his google drive referred to in that Thread.
I suppose that the puzzles he listed in his posts were the most 'promising' ones (with SER or skfr 11.6 to 11.8). Only Champagne can confirm or complete your figures. I also suppose that finding 'high BxB' puzzles was not his objective. The name of the new thread, started by him, is perhaps an important clue.

by **Paquita** » Wed Sep 03, 2025 5:03 pm

Hi Denis

No I did not choose the solution digits per se in this case. But I include a check for valid puzzles after adding the digit. So the minimals are constructed from valid puzzles. I have not yet checked if the remaining results have the same solution. My guess is that they need not be. But I did not register what seed puzzle is used for every result. I will get back on that matter later.

Website · by **denis_berthier** » Wed Sep 03, 2025 5:07 pm

Paquita wrote:Hi Denis
No I did not choose the solution digits per se in this case. But I include a check for valid puzzles after adding the digit.

It amounts to the same. If the added digit is not in the solution, then your validity check will eliminate this case.
.

by **Paquita** » Wed Sep 03, 2025 5:22 pm

If the number of solutions for both T&E(3) and BxB>7 is so low, the search has to include to change the solution grid. The SE/skfr rate is just a selection criterium. All the BxB>7 that I know are above SER 11.0. Of course one can search without using SER or skfr rating. That means that more puzzles will have to be tested for T&E and BxB.

Website · by **denis_berthier** » Wed Sep 03, 2025 5:32 pm

Paquita wrote:If the number of solutions for both T&E(3) and BxB>7 is so low, the search has to include to change the solution grid.

OK, but that's my question. Apart from adding some (-p +q} search, the procedure you describe can't change the solution.
.

by **hendrik_monard** » Wed Sep 03, 2025 7:25 pm

Paquita wrote:Some new puzzles

Hi Paquita,
Indeed two impressive lists of high ranking puzzles. I found 77 new solutions and added them to the solution list that contains now 1828 solutions.

https://drive.google.com/file/d/1gLUBdAcdF9ntMiS_bc7Z_AEAu7XfhOnQ/view?usp=drive_link
.

The New Sudoku Players' Forum

The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles

Re: The BxB classification of T&E(2) puzzles