My fault. It was in the database in my google drive but I forgot to add the new puzzles of November 6th to my local database which I use in the novelty verification script.coloin wrote:hendrik_monard wrote: Has this puzzle been published before?
Hi.... its in mastermax 16 in the TE2 thread, thought i had deleted it for a second ... !!
T&E(3) Puzzles (split from "hardest sudokus" thread)
Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by hendrik_monard » Wed Nov 12, 2025 1:41 pm
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Thu Nov 13, 2025 7:18 am
coloin wrote:All the B7B+ and TE3 puzzles were found from minimization and re-expansion of all new expanded B6B puzzles ...TE3 puzzles were much more common, but rarely both were produced.
I guess your main purpose was about the high BxB puzzles and the T&E(3) ones were only by-products.
After further analysis of the T&E(3) ones and after generation of all their minimals (204390), I noticed the number of minimals per solution grid is much smaller than in mith's collection: 21.41 vs 68.61.
There may be two reasons:
- some intrinsic one: these puzzles were found later because they are less likely to be found,
- some reason due to the search process, maybe the non-closure under BRT-expansion and minimisation. Did you iterate the two operations until quiescence?
.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by coloin » Thu Nov 13, 2025 9:46 am
Maybe they dont max expand [ and keep TE3] as much... and therefore less minimals per grid ...
I doubt I have max expanded [ and then twinned] all of them ....
Maybe you would expect TE3 puzzles originating from a B6B [ these ones] to be more complex than those originating from a B5B.
I doubt I have max expanded [ and then twinned] all of them ....
Maybe you would expect TE3 puzzles originating from a B6B [ these ones] to be more complex than those originating from a B5B.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Thu Nov 13, 2025 12:04 pm
coloin wrote:Maybe they dont max expand [ and keep TE3] as much... and therefore less minimals per grid ...
I doubt I have max expanded [ and then twinned] all of them ....
I've done computations on about 1/3 of your solution grids. There are (in the mean) 1.078 T&E(3)-expands per solution (vs 1.079 in mith's collection). No difference here.
As far as I can remember, mith never said he had computed all the minimals for all the "max-expands" (i.e. T&E(3)-expands). This is something I never checked in his database. But that would probably be out of reach with reasonable bounds on time. But he may have done it for some of the "max-expands" - I don't know.
What I remember he said (and what I partly checked) is:
- for every minimal in the database, its BRT-expand is in the database,
- for every min-expand in the database, all its minimals are in the database.
That's what I call closure under BRT-expansion and minimisation.
In order to ensure it, both processes need to be iterated an a priori undefined number of times.
Considering the difference noted in my previous post, I wondered if you had done this (which could allow to multiply your number of T&E(3) minimals by 3+)
coloin wrote:Maybe you would expect TE3 puzzles originating from a B6B [ these ones] to be more complex than those originating from a B5B.
Maybe. But in what sense of "more complex"? They're all in T&E(W2, 2).
.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by blue » Fri Nov 14, 2025 2:40 am
denis_berthier wrote:As far as I can remember, mith never said he had computed all the minimals for all the "max-expands" (i.e. T&E(3)-expands). This is something I never checked in his database. But that would probably be out of reach with reasonable bounds on time. But he may have done it for some of the "max-expands" - I don't know.
His list is very close to being closed with respect to minimizing max-te3-expands and twins of max-te3-expands.
There are 142 missing "minimals from max-te3-expands":
Hidden Text: Show
There are 40 missing from "minimizing twins (2) of max-te3-expands" ... adding 2 to the grid count.
Hidden Text: Show
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Fri Nov 14, 2025 4:28 am
Hi Blue
Very interesting
By adding these 142 minimals, we can be sure that mith's collection becomes closed under minimisation and T&E(3) expansion.
The (obvious) reason is, none of these new minimals can have a new T&E(3)-expand (contrary to what may happen with BRT-expansion).
It doesn't imply one couldn't find new T&E(3) minimals for the solution grids, but they would be completely disconnected from the already known ones, allowing to deal with them separately. (Here, I'm thinking of how to expand previous results to extended collections without re-doing all the computations.)
I wonder how much processor time this took. Did you find a trick allowing not to regenerate all of mith's 4M+ minimals?
So, this small collection of 40 should also be closed under the two operations.
Considering coloin's new T&E(3) collection shares 116 solutions with mith's, I wonder if it includes any of the above puzzles. No time to check now.
.
Very interesting
blue wrote:There are 142 missing "minimals from max-te3-expands":...
By adding these 142 minimals, we can be sure that mith's collection becomes closed under minimisation and T&E(3) expansion.
The (obvious) reason is, none of these new minimals can have a new T&E(3)-expand (contrary to what may happen with BRT-expansion).
It doesn't imply one couldn't find new T&E(3) minimals for the solution grids, but they would be completely disconnected from the already known ones, allowing to deal with them separately. (Here, I'm thinking of how to expand previous results to extended collections without re-doing all the computations.)
I wonder how much processor time this took. Did you find a trick allowing not to regenerate all of mith's 4M+ minimals?
blue wrote: There are 40 missing from "minimizing twins (2) of max-te3-expands" ... adding 2 to the grid count.
So, this small collection of 40 should also be closed under the two operations.
Considering coloin's new T&E(3) collection shares 116 solutions with mith's, I wonder if it includes any of the above puzzles. No time to check now.
.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by blue » Fri Nov 14, 2025 6:47 am
denis_berthier wrote:I wonder how much processor time this took. Did you find a trick allowing not to regenerate all of mith's 4M+ minimals?
It took ~145 minutes (@4.3 GHz) -- no "tricks"
~75m to get (ED) T&E(2) expansions of initial minimals
~24m to make (ED) max-te3-expands from those (and check for new twins)
~45m to minimize results & check for anything new.
(plus a second or two to do the recursion for the new puzzles).
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by blue » Fri Nov 14, 2025 8:56 am
denis_berthier wrote:Considering coloin's new T&E(3) collection shares 116 solutions with mith's, I wonder if it includes any of the above puzzles. No time to check now.
Nothing in common.
Above, I listed puzzles with 32+2 (minlex) solution grids.
None of them is in the list of (minlex) solutions for Colin's puzzles.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Sat Nov 15, 2025 11:20 am
.
Hi Blue
I've been busy with going around a bug in CLIPS 6.4.
Thanks for your answers.
As your computation times are very low, could you compute all the T&E(3)-expands of coloin's T&E(3) collection and all the associated minimals? As I said before, considering the differences with mith's list, I think his list is far from being saturated.
BTW, which software do you use for these calculations?
.
Hi Blue
I've been busy with going around a bug in CLIPS 6.4.
Thanks for your answers.
As your computation times are very low, could you compute all the T&E(3)-expands of coloin's T&E(3) collection and all the associated minimals? As I said before, considering the differences with mith's list, I think his list is far from being saturated.
BTW, which software do you use for these calculations?
.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by hendrik_monard » Sat Nov 15, 2025 5:27 pm
Compared to my composite list of TE3 solutions, the second batch of Blue (40 puzzles) has two puzzles with 'new' TE3 solutions:
- Code: Select all
123456789457189236689372451246893517735641892918725643362514978571968324894237165
....6..94.7..9.....937.45.2.....5...3..4......8...64..6.5.497..7....3...9..37.6.
123456789457189236869237145241675398376948512985312467512893674638724951794561823
1.3.56.....7.....686..371........3.8.7....51..8.3...6751.8.3.......24.......6....
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by coloin » Sat Nov 15, 2025 8:52 pm
blue wrote:-- no "tricks"
~75m to get (ED) T&E(2) expansions of initial minimals
~24m to make (ED) max-te3-expands from those (and check for new twins)
~45m to minimize results & check for anything new.
(plus a second or two to do the recursion for the new puzzles).
blue is a wizard.
I think when I "cleaned" up miths big file, removing the non-minimals but I found only a few more by expanding and minimizing.
max expanding is tricky enough and sometimes its "branches out" and these are easily missed [by me]
Perhaps you can check whether I completely max expanded my file ..... pretty sure I twinned many of them .....
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by coloin » Sat Nov 15, 2025 9:01 pm
denis_berthier wrote:Maybe. But in what sense of "more complex"? They're all in T&E(W2, 2).
puzzle 1 TE3 from miths file plus a few clues -> goes to B5B most of the time
puzzle 2 TE3 from the selected puzzles plus a few clues -> goes to B12B
The two puzzles are TE3 - but the 2nd puzzle logically should be superior in some sense of the analysis
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Sun Nov 16, 2025 4:58 am
coloin wrote:max expanding is tricky enough and sometimes its "branches out" and these are easily missed [by me]
Perhaps you can check whether I completely max expanded my file ..... pretty sure I twinned many of them .....
At the end of my systematic process of (1+BRT)-expansion, I find all the T&E(3)-expands. My process isn't very fast, partly because I compute intermediate results that I need for other purposes. A trick about expansion is, one shouldn't re-apply solution-minlexing at each phase (only at the start, for the minimals and solutions). But one should apply elimination of duplicates (note: not of isomorphs). If you look at the Tables in [HCCS3], you'll see how I reduce the branching factor at each phase.
For your collection, I find 10,120 T&E(3)-expands - 1.06 per solution grid. Not far from the 1.079 in mith's collection, but considering the large sizes of the two samples, the 2% difference may nevertheless suggest that your collection is not completely closed under T&E(3) expansion and minimisation. Blue will tell us the answer if he can do the calculations.
My main problem about computation times is for minimisation (which is fortunately not needed in the expansion process itself). I use gsf's software and it already takes much time to get all the minimals of the min-expands. I thought it was almost impossible for the T&E(3)-expands, until Blue said he could do it so fast.
.
Last edited by denis_berthier on Sun Nov 16, 2025 12:20 pm, edited 1 time in total.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Sun Nov 16, 2025 5:06 am
coloin wrote:denis_berthier wrote:Maybe. But in what sense of "more complex"? They're all in T&E(W2, 2).
puzzle 1 TE3 from miths file plus a few clues -> goes to B5B most of the time
puzzle 2 TE3 from the selected puzzles plus a few clues -> goes to B12B
The two puzzles are TE3 - but the 2nd puzzle logically should be superior in some sense of the analysis
OK, but the question is, how hard is it to add these clues by some resolution rules?
The only idea I have now is to apply the tridagon pattern.
The 2 puzzles have an ordinary tridagon.
The first is in Trid+BC4, the second in Trid+Z6 (harder).
.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)
by denis_berthier » Sun Nov 16, 2025 9:45 am
.
I've finally done a few calculations with coloin's T&E(3) collection, starting from the T&E(3)-epxands I had previously computed.
Using only the sample made of the 1st 1000 solution grids in the collection (and the corresponding 1061 T&E(3)-expands), I searched for their minimals with gsf's solver.
First thing to notice: computation times are reasonable: 1h22mins on a MacBookPro M1Max (no longer the fastest available beast). Sure not as fast as Blue, but dealing with the whole collection would take only 13 hrs.
Contrary to what I expected, the number of minimals thus obtained is very different from what one gets with mith's collection.
Indeed, only one new minimal is obtained:
Main conclusion (supposing the results for the first 1000 grids can be extended to the whole collection - which I now don't doubt):
there's a clear difference between the mith and coloin T&E(3) collections: there are many more puzzles per T&E(3)-expand in mith's collection (more than 3 times more).
And this difference is due:
- neither to a different number of T&E(3)-expands per solution grid,
- nor to a lack of saturation of the minimals wrt T&E(3)-expansion.
As of now, the reasons for such a difference remain a mystery. I have nothing more convincing than my first suggestion (mith's puzzles were found first because they were easier to find - there are more of them per grid). But this is not very satisfactory, it doesn't really explain why there is such a gap. Complementary explanations may come from the way the puzzles came out during the search for high BxB puzzles.
[Edit]: computations extended to the first 3000 solutions grids: 16 new minimals (in addition to the previous one) for only two solutions. This doesn't change the previous conclusions:
.
I've finally done a few calculations with coloin's T&E(3) collection, starting from the T&E(3)-epxands I had previously computed.
Using only the sample made of the 1st 1000 solution grids in the collection (and the corresponding 1061 T&E(3)-expands), I searched for their minimals with gsf's solver.
First thing to notice: computation times are reasonable: 1h22mins on a MacBookPro M1Max (no longer the fastest available beast). Sure not as fast as Blue, but dealing with the whole collection would take only 13 hrs.
Contrary to what I expected, the number of minimals thus obtained is very different from what one gets with mith's collection.
Indeed, only one new minimal is obtained:
- Code: Select all
solution grid #680:
123456789457189236869327154298765413645913827731842695312574968584691372976238541
unique T&E(3)-expand in it:
1...5678........368..3.71...9..65...645..3...7.1...6...1.5...68...6.137......85.1
unique minimal in it:
1...5.78........368..3.71...9..65....45..3...7.1.............68...6.137......85.1
with its BRT-expand:
1...5678........368..3.71...9..65....45..3...7.1.......1.5...68...6.137......85.1
New minimal added after T&E(3)-expansion and minimisation:
1...5.78........368..3.71...9...5...645..3...7.1...6.........68...6.137......85.1
and its BRT-expand:
1...5678........368..3.71...9..65...645..3...7.1...6...1.5...68...6.137......85.1
(different from the previous one)
Main conclusion (supposing the results for the first 1000 grids can be extended to the whole collection - which I now don't doubt):
there's a clear difference between the mith and coloin T&E(3) collections: there are many more puzzles per T&E(3)-expand in mith's collection (more than 3 times more).
And this difference is due:
- neither to a different number of T&E(3)-expands per solution grid,
- nor to a lack of saturation of the minimals wrt T&E(3)-expansion.
As of now, the reasons for such a difference remain a mystery. I have nothing more convincing than my first suggestion (mith's puzzles were found first because they were easier to find - there are more of them per grid). But this is not very satisfactory, it doesn't really explain why there is such a gap. Complementary explanations may come from the way the puzzles came out during the search for high BxB puzzles.
[Edit]: computations extended to the first 3000 solutions grids: 16 new minimals (in addition to the previous one) for only two solutions. This doesn't change the previous conclusions:
- Code: Select all
1....678..........8..3.71.5..57.136....5...78.....8..1..2..3....49..5...7.....65.
1...5678..........8..3.71.5..57.136........78.....85.1..2..3....49..5...7.....65.
1...5678..........8..3.71.5..57.136....5...78.....8..1..2..3....49......7.....65.
1...5678.........68..3.71....57.136........78.....85.1..2..3....49..5...7.....65.
1...5678.........68..3.71....57.136....5...78.....8..1..2..3....49......7.....65.
12..5........89..........4.2.....3..31.6...27.743..61.......47.7......63.6...31.2
12..5........89..........4.2.....3..31.6...27.743..61.....6.47.7.......3.6...31.2
12..5........89..........4.2.....3..31.6...27.743..61..3....47.7......6..6...31.2
12..5........89.......3..4.2.....3..31.6...27.74...61.......47.7......63.6...31.2
12..5........89.......3..4.2.....3..31.6...27.74...61.....6.47.7.......3.6...31.2
12..5........89.......3..4.2.....3..31.6...27.74...61..3....47.7......6..6...31.2
12.45........89..........4.2.6...3..31.....27.743..61.....6.47.7.......3.6...31.2
12.45........89..........4.2.6...3..31.....27.743..61..3..6.47.7......6..6...31.2
12.45........89.......3..4.2.6...3..31.....27.74...61.....6.47.7.......3.6...31.2
12.45........89.......3..4.2.6...3..31.....27.74...61..3..6.47.7......6..6...31.2
12.45........89.......3..4.2.6...3..31.....27.743..61..3..6.47.7.......3.6....1.2
.
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