The New Sudoku Players' Forum

by **Paquita** » Fri Sep 12, 2025 12:26 pm

Hidden Text: Show

Website · by **denis_berthier** » Fri Sep 12, 2025 1:41 pm

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Wow, Paquita
That's an impressive number of new high BxB puzzles, including new B13Bs and B14Bs
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by **Paquita** » Sat Sep 13, 2025 9:58 am

Of the last batch, these are 11.9 :

....56..9..71.9..6.9.37..........8..531...6.7.......2.31.7......75.9....9.6..1... ED=11.9/1.2/1.2
1...56..9..71.9..6.9.37..........8..531...6.7.......2.3..7......75.9....9.6..1... ED=11.9/1.2/1.2
....5.......1.9236...7.....2.1..469.39....4...64..1.23.4....96...2....149.....3.2 ED=11.9/1.2/1.2
....5.......1.9236...7.....2.4..1.9.39....4...61..4.23.4....96...2....149.....3.2 ED=11.9/1.2/1.2
....5.......1.9236...7.....2.4..169.39....4...61..4.23.4....96...2....149.....3.2 ED=11.9/1.2/1.2
....5.......1.9236...7.....2....169.39....4...61..4.23.4....96...2....149.....3.2 ED=11.9/1.2/1.2
....5.......1.9236...7.....2.4..196.39....4...61..4.23.4....69...2....149.....3.2 ED=11.9/1.2/1.2
.234.....45...9...6.9.2....235...46.........1.......7.....659..54.29.6...9.3.4... ED=11.9/1.2/1.2

All B10B. Somehow it seems that B10B is hardest. As you explained Denis, this may be due to more braids (not all with length 10) available in those puzzles. One might say that not just the length of braids but also the occurence of multiple braids makes a puzzle harder. Well, you said that you are not looking for the hardest. But an interesting fact anyhow.

by **hendrik_monard** » Sat Sep 13, 2025 10:24 am

Indeed an impressive list from paquita with 5222 new puzzles resulting in 114 new solutions. I'll add those to the database (same link as before) later today.

Website · by **denis_berthier** » Sun Sep 14, 2025 6:10 am

Hi Hendrik
It seems there are 16 duplicates in your new list of solutions - because you forgot to put them all in solution-minlex form.

Code: Select all: diff /Users/berthier/Desktop/B7Bp-solutions.txt /Users/berthier/Desktop/B7Bp-solutions-nodup.txt < 523469781417583296986172534874695123265317849391248657649821375758936412132754968 < 381256749752149836496738152238597461514362978967814325873621594645983217129475683 < 963287514457139286128456739249763158716548392835912647372895461584621973691374825 < 523467189947185632681392547274918356395674218168253794416739825752841963839526471 < 523467189947185632681392547274918356395674218168253794412739865756841923839526471 < 123467589457189236968253714249736158716548392835912647372895461584621973691374825 < 123476589457891236968235174249763851716548392835912647372159468584627913691384725 < 128456739457139286639278451294317568365894127781625943512783694876942315943561872 < 153426789427189536689573124548762913291834657736915842375648291862391475914257368 < 143856729257149836896732514324695187681274953975318462439521678562987341718463295 < 123956748457183269698742135264397581319825674785614923536471892841269357972538416 < 143652789957481236862379145386215974271948563594736812639127458725864391418593627 < 123456798457189236689723145264915387875632419931847652592364871316578924748291563 < 123456789457189236689273451264817593895364127731925648512738964978642315346591872 < 413256789857149236926378154241793865579681342638524917762835491184967523395412678 < 128456739357289164649713582284531976915867243736924851562398417873142695491675328

[Edit]:
I also find 2 solution grids that were in a previous list but are now missing. I noticed it when i tried to update my list of solutions common with those for T&E(3).

Code: Select all: 123456789457189236689273451216895374395724168748361592572618943831947625964532817 123456789457189236689732415295361847346978521718245693531827964864593172972614358

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Website · by **denis_berthier** » Sun Sep 14, 2025 6:15 am

Paquita wrote:Of the last batch, these are 11.9 :
[...]
All B10B. Somehow it seems that B10B is hardest. As you explained Denis, this may be due to more braids (not all with length 10) available in those puzzles. One might say that not just the length of braids but also the occurence of multiple braids makes a puzzle harder. Well, you said that you are not looking for the hardest. But an interesting fact anyhow.

Any rating/classification based on the "hardest" step will face the same facts. I didn't check specifically for this short list, but SER times may not the longest for the highest SER values. (But SER mixes so many unrelated things that it's hard to make any predictions while my crystal ball is again on strike.)

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by **Paquita** » Mon Sep 15, 2025 8:46 am

Too good to be true!

The last batch had a lot of non-minimals. Skip it for now. I will give an update for the puzzles that are minimals later!

by **Paquita** » Mon Sep 15, 2025 11:11 am

Denis,

Is it correct that an expanded puzzle has the same BxB as its minimals? If not, what is the relation?

Website · by **denis_berthier** » Mon Sep 15, 2025 12:07 pm

Paquita wrote:Is it correct that an expanded puzzle has the same BxB as its minimals? If not, what is the relation?

No.
For any puzzle P in T&E(2), BRT-expand(P) has the same BxB as P (indeed has all the same classifs as P).

But for BRT-expand(P), its minimals P2 can only be (non-strictly) harder than P, i.e.:
- either in T&E(3)
- or in T&E(2) with BxB(P2) ≥ BxB(P)

That's all the point of expanding the minimals and re-minimalising the expansions. You can sometimes get harder ones.

There's a special case when you can say that the minimals of BRT-expand(P) have the same classif as P; it's when P is an isolated puzzle in the BRTinc topology. But this property is stronger than what you mention and harder to prove.
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Website · by **denis_berthier** » Wed Sep 17, 2025 3:14 pm

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After Hendrik asked if a solution grid could have both T&E(3) and T&E(2) puzzles, some time ago, I compared the files of solution grids and Ifound a only a few cases where this happens.

As of today there are only 17 solution grids (not counting possible ones posterior to the Mastermins 1 to 15).
So, it's very rare.

This morning, I wondered whether they could have high BxB. For the 17 solution grids, there are 259 minimal puzzles in the Mastermins 1 to 15.
Their BxB distribution is as follows:
7 : 68
8 : 191

No (known) high BxB.
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by **hendrik_monard** » Wed Sep 17, 2025 7:02 pm

denis_berthier wrote:Hi Hendrik
It seems there are 16 duplicates in your new list of solutions - because you forgot to put them all in solution-minlex form.

Hi Denis,
Indeed 16 solutions not in solminlex format. I adapted my script to exclude it for the future. I'll replace these solutions by their solminlex isomorph and deal with possible new duplicates with these solutions.

I also find 2 solution grids that were in a previous list but are now missing. I noticed it when i tried to update my list of solutions common with those for T&E(3).
Code: Select all
123456789457189236689273451216895374395724168748361592572618943831947625964532817 123456789457189236689732415295361847346978521718245693531827964864593172972614358

Without the associated puzzles it is not possible to examine this issue. Do you still have a copy of the previous list that you refer to?

Website · by **denis_berthier** » Thu Sep 18, 2025 5:47 am

hendrik_monard wrote:
denis_berthier wrote:I also find 2 solution grids that were in a previous list but are now missing. I noticed it when i tried to update my list of solutions common with those for T&E(3).
Code: Select all
123456789457189236689273451216895374395724168748361592572618943831947625964532817 123456789457189236689732415295361847346978521718245693531827964864593172972614358

Without the associated puzzles it is not possible to examine this issue. Do you still have a copy of the previous list that you refer to?

I haven't kept the original file, but I have the following two puzzles in a separate file. I'm not sure they correspond to what you need.

Code: Select all: 98.76.5..7.5..4....46..89..6.759.....5.8.7.6...8.46.....4....93...4............21 987......6..8...........5...4.32..51...1.42.8....5834...32.581.....134.........2.

[Edit]
Here are the 17 common solutions grids I now have (not updated after the mastermins 1 to 15)

Code: Select all: 123456789457189236689273415275368941391524867846791352568937124734612598912845673 123456789457189236698372514285761943316924857749538162561247398832695471974813625 123456789457189236896327154239671845574893612681542973315268497742915368968734521 123456789457189236968372514249738651571624398836591472314965827685217943792843165 123456789457189236698732514265893147834671952971245863319524678582367491746918325 123456789457189236689273451216895374395724168748361592572618943831947625964532817 123456789457189236689732415295361847346978521718245693531827964864593172972614358 123456789457189263689372514245967138738514926961823475392748651574631892816295347 123456789457189236896237514275341968634895172981672453319764825562918347748523691 123456789457189263896237145235648971681975324974312658368521497519764832742893516 123456789457189263689732451291375648538264917764891532375948126816527394942613875 123456789456789123798132564261574938349618275875293416514367892682941357937825641 123456789457189263869237415234715896576928134918364572392841657641573928785692341 123456789457189263698237415219368547385724196746915328574691832862543971931872654 123456789457189236689237541238915674546872913971364825365721498714598362892643157 123456789457189236698732415245693178316875924789214563564321897831947652972568341 123456789457189236698237415289714563316825974745693128564371892831942657972568341

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by **hendrik_monard** » Thu Sep 18, 2025 9:25 am

Hi Denis,

I tested the two puzzles and this was the result:

Code: Select all: 123456789457189236689237541245791863396824175871563492562348917738912654914675328 98.76.5..7.5..4....46..89..6.759.....5.8.7.6...8.46.....4....93...4............21 test 250918 B6B 123456789457189236698732514276894351389571462514263978731928645862345197945617823 987......6..8...........5...4.32..51...1.42.8....5834...32.581.....134.........2. monh 230514 B13B 987......6..8...........5...4.32..51...1.42.8....5834...32.581.....134.........2. test 250918

The first one is B6B and the second one is an identical duplicate of a B13B puzzle that I published in 2023 (14th May)

BTW,are you sure that the following two solutions (consecutive in your list of 17 'common solutions') once appeared in my solutions lists?
Until now I didn't find a trace of them in my old lists.
123456789457189236689273451216895374395724168748361592572618943831947625964532817
123456789457189236689732415295361847346978521718245693531827964864593172972614358

Website · by **denis_berthier** » Thu Sep 18, 2025 9:40 am

hendrik_monard wrote:BTW,are you sure that the following two solutions (consecutive in your list of 17 'common solutions') once appeared in my solutions lists?
Until now I didn't find a trace of them in my old lists.
123456789457189236689273451216895374395724168748361592572618943831947625964532817
123456789457189236689732415295361847346978521718245693531827964864593172972614358

Hi Hendrik
Good question. On second thoughts, I'm not so sure.
After constructing my own lists of solution grids starting from the mastermins 1 to 15, the only thing I can say is: the above 17 grids and only them are common with mith's last T&E(3) collection (also constructed directly from their minimals, given by Coloin's revised list).
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by **Paquita** » Wed Oct 01, 2025 1:33 pm

Denis,
I am looking into braids. I have some questions

-the braids for BxB, do they include bivalue chains and whips?
-there is some order as you indicated in PBC, what goes first, a longer bivalue or a shorter braid? So what is the BxB number based on then?
-braids as oppposed to whips seem to have more than one assumption. I wonder if that is a relation between the T&E level and the number of assumptions in a braid? It seems right that T&E(2) corresponds to 2 assumptions.

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