To avoid pollution of another thread
http://forum.enjoysudoku.com/t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514.html
I open this one to summarize the work in progress
Curious to understand why the tridagon pattern came so late, I wanted to see what had been done.
Analyzing the pattern, I had the feeling that it could be a very frequent one, not seen mainly because it needed usually 26/27 clues, an area not searched for potential hardest.
Although this is not the preferred pattern for players, I tried to see if a non degenerated tridagon could be searched directly in solution grids.
And yes, with the constraints leading to such a pattern, it works.
I have no estimate of the number of such puzzles, just borings here and there in the catalog of min lexical solution grids, but we could see something as
Not far than one target per solution grid (I call here "target" a potential 3 digits tridagon pattern in the solution grid). Some have none, some have several of them
Likely thousands puzzles in average per target. My current test on a solution grid found in mith’s file delivers more than 10 000 sudokus in some seconds.
This is 5.7 billion x 10000 puzzles as possible order of magnitude for the count of such puzzles.
Most of them will be solved easily, but they can be used as seed for vicinity search of puzzles with gardians. This is a huge number of puzzles to analyze to select puzzles of interest.
Another constraint was to avoid redundancy with the already known puzzles.
I started with a 4 634 321 records file sent by mith. I think that all of them are in T&E(3) field.
I had no code to match files so it’s a long way to filter and select puzzles.
I had no T&E(1) filter (and no idea of the definition some days behind). I have now the code and I applied this filter on the primary output. This left billions of puzzles to rate. I have to see how to do that.
I have still another problem to solve. I have to select in mith’s file puzzles having a non degenerated tridagon to finish the debugging of my code and see if all expected puzzles are there. This will take me one or two more weeks.
At the end, I‘ll have a huge file of puzzles to share if anybody wants to work on it. I have samples of such results.
Ill report here slowly in the next days on what I did and what results I have.
Non degenerated tridagon puzzles direct search
54 posts
• Page 1 of 4 • 1, 2, 3, 4
Non degenerated tridagon puzzles direct search
by champagne » Mon Dec 23, 2024 3:35 pm
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Re: Non degenerated tridagon puzzles direct search
by coloin » Mon Dec 23, 2024 4:42 pm
A question as to what you are trying to do
Starting from a complete solution grid ....
are you removing clues from a reduced grid such as this ?
And if so... how ! ?
Starting from a complete solution grid ....
are you removing clues from a reduced grid such as this ?
And if so... how ! ?
- Code: Select all
+---+---+---+
|74.|.58|96.|
|9.8|6.7|5.4|
|.65|94.|7.8|
+---+---+---+
|.87|465|..9|
|6.9|87.|.45|
|45.|.9.|876|
+---+---+---+
|8.6|..9|457|
|594|7.6|283|
|.7.|584|691|
+---+---+---+
to give this
+---+---+---+
|74.|.58|9..|
|9.8|6.7|5..|
|.65|94.|7..|
+---+---+---+
|.87|..5|...|
|6.9|8..|...|
|45.|.9.|...|
+---+---+---+
|8.6|...|4..|
|...|...|..3|
|...|.8.|6.1|
+---+---+---+ 11.9
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Re: Non degenerated tridagon puzzles direct search
by champagne » Tue Dec 24, 2024 3:46 am
The puzzle generation is now in beta test, so I can easily answer to your question.
The process used is derived from the 17 clues search and is quite different of what you have in mind.
Basically, you collect a reasonable set of unavoidable sets (say around 2000), you expand it and you check each puzzle against the required properties.
As you noticed in another post, this is generally an endless work.
My first remark was that in the loki familyi, for the 3 digits of the tridagon, the given (2 minimum) could not be a given in another place that in one box.
This was not enough to reach a feasible process.
But giving as constraint to have a non degenerated tridagon at the start, as I wrote, the game changes.
Each of the 12 cells of the pattern must see the 6 other digits. In other terms, each of the other digits must be given in row or in column or in box.
This is a kind of unavoidable set of size 2 or 3, and we have 12x6 of them (less due to redundancy).
Mixing classical unavoidable sets and these one, expansion of the UAs table looks more like expanding a sequence of UAs of size 2, sometimes 3, and in the last steps possibly more.
The results will be a puzzle with usually 26/27 clues. Most of the others will be discarded because some UAs are not hit.
If we take as limit 27 clues, we have an expansion process having to consider something in the range 2**27 - 3** 27 possible cases.
From my test, this is something covered in some seconds (less than 10) with one core.
I'll give later more details on this code still in dirty mode and waiting for a final check that nothing is missing.
The process used is derived from the 17 clues search and is quite different of what you have in mind.
Basically, you collect a reasonable set of unavoidable sets (say around 2000), you expand it and you check each puzzle against the required properties.
As you noticed in another post, this is generally an endless work.
My first remark was that in the loki familyi, for the 3 digits of the tridagon, the given (2 minimum) could not be a given in another place that in one box.
This was not enough to reach a feasible process.
But giving as constraint to have a non degenerated tridagon at the start, as I wrote, the game changes.
Each of the 12 cells of the pattern must see the 6 other digits. In other terms, each of the other digits must be given in row or in column or in box.
This is a kind of unavoidable set of size 2 or 3, and we have 12x6 of them (less due to redundancy).
Mixing classical unavoidable sets and these one, expansion of the UAs table looks more like expanding a sequence of UAs of size 2, sometimes 3, and in the last steps possibly more.
The results will be a puzzle with usually 26/27 clues. Most of the others will be discarded because some UAs are not hit.
If we take as limit 27 clues, we have an expansion process having to consider something in the range 2**27 - 3** 27 possible cases.
From my test, this is something covered in some seconds (less than 10) with one core.
I'll give later more details on this code still in dirty mode and waiting for a final check that nothing is missing.
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More on unavoidable set expansion
by champagne » Thu Dec 26, 2024 3:35 am
Hi coloin,
A little more to close temporarily comments on the non-degenerative tridagon finder
Here an example on the solution grid 963106, one band having records in mith’s file.
The tridagon is on digits 348. My finder works with the four boxes in bottom right position so my start is the solution grid
The primary UAs finder produces 2249 UAs. We could start with less UAS, then, we would have more checks of potential sudokus having multiple solutions.
Having added the 2 families constraints:
2 of the 3 digits in band 1
The 11 cells of the tridagon starting with the 3 digits
Most of the 2249 UAs have subsets and we end with 160 UAs to expand
This is 43 pairs and 56 UAS of size 2/3
Let’s see now 3 typical UAs
The first one is to clean ‘1’ in r4c6
The second one is to clean ‘9’ in r4c7
The third one is a classical UA defining one necessary given to avoid a multiple solution, here for digits 12 in r1c78 r6c78.
The code is a general engine based on UAs expansion, but with such constraints, one could start with a tailored made process.
In fact, with so many pairs and disjoints UAs, I changed the UA engine (compared to the 17/18 clues search) and I expand in recursive steps of three disjoint UAs as long as possible.
A little more to close temporarily comments on the non-degenerative tridagon finder
Here an example on the solution grid 963106, one band having records in mith’s file.
The tridagon is on digits 348. My finder works with the four boxes in bottom right position so my start is the solution grid
- Code: Select all
978 365 214
234 981 567
615 724 938
789 213 456
123 546 789
456 879 123
861 492 375
592 637 841
347 158 692
The primary UAs finder produces 2249 UAs. We could start with less UAS, then, we would have more checks of potential sudokus having multiple solutions.
Having added the 2 families constraints:
2 of the 3 digits in band 1
The 11 cells of the tridagon starting with the 3 digits
Most of the 2249 UAs have subsets and we end with 160 UAs to expand
Hidden Text: Show
This is 43 pairs and 56 UAS of size 2/3
Let’s see now 3 typical UAs
- Code: Select all
978365214234981567615724938789213456123546789456879123861492375592637841347158692
..............1................1................................................. 0 n=2
........................1....1..............1.................................... 43 n=3
......11...........................................11............................ 56 n=4
- Code: Select all
978 365 214
234 981 567
615 724 938
789 213 456
123 546 789
456 879 123
861 492 375
592 637 841
347 158 692
The first one is to clean ‘1’ in r4c6
The second one is to clean ‘9’ in r4c7
The third one is a classical UA defining one necessary given to avoid a multiple solution, here for digits 12 in r1c78 r6c78.
The code is a general engine based on UAs expansion, but with such constraints, one could start with a tailored made process.
In fact, with so many pairs and disjoints UAs, I changed the UA engine (compared to the 17/18 clues search) and I expand in recursive steps of three disjoint UAs as long as possible.
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Naming and storing puzzles
by champagne » Thu Dec 26, 2024 8:48 am
I have limited experience in databases for sudokus. In the database of potential hardest, I had at the end a little more than 3 million grids.
The file sent by “mith” contains 4.3 million grids and is a tiny part of the field already explored.
This pushes to think of another way to store the results.
Cleaning “similar puzzles” requires a canonical form of the puzzle. In my database of potential hardest, it was the max lexical morph of the puzzle. But this is 81 characters for the ED puzzle.
Recently I published with a low interest another proposal for canonical sudokus
http://forum.enjoysudoku.com/proposal-for-a-canonical-puzzle-t45209.html
I’ll use what seems to me good, a 2 steps naming process:
A “rank + bitfield” ED sudoku with 25 bytes per sudoku
My universal name of 6 x 19 = 114 bits, derived from the first one.
To check redundancy, the universal name is enough, and starting from the universal name, the sudoku morphed as a min lexical solution grid is easy to get back.
For sure, such a puzzle is of small interest for a player, the solution always starts with “12345678945” and r4c2=2. But after random morphing and relabeling, we get a puzzle to play.
However, puzzles of interest will surely be stored with the original puzzle. Here, to work on mith’s file, I use records as this one
3636310645 is the rank in the min lexical catalog
LWLJWaj13O0843 is the 81 bits field of the puzzle morphed to the min lexical solution
117 is for a rating 11.7 done using skfr.
Loading the file in Access gives room for many filters and/or statistics. I did the skfr rating of mith’s file and open the corresponding Access base.
Next post will give the first comments on it.
The file sent by “mith” contains 4.3 million grids and is a tiny part of the field already explored.
This pushes to think of another way to store the results.
Cleaning “similar puzzles” requires a canonical form of the puzzle. In my database of potential hardest, it was the max lexical morph of the puzzle. But this is 81 characters for the ED puzzle.
Recently I published with a low interest another proposal for canonical sudokus
http://forum.enjoysudoku.com/proposal-for-a-canonical-puzzle-t45209.html
I’ll use what seems to me good, a 2 steps naming process:
A “rank + bitfield” ED sudoku with 25 bytes per sudoku
My universal name of 6 x 19 = 114 bits, derived from the first one.
To check redundancy, the universal name is enough, and starting from the universal name, the sudoku morphed as a min lexical solution grid is easy to get back.
For sure, such a puzzle is of small interest for a player, the solution always starts with “12345678945” and r4c2=2. But after random morphing and relabeling, we get a puzzle to play.
However, puzzles of interest will surely be stored with the original puzzle. Here, to work on mith’s file, I use records as this one
- Code: Select all
3636310645;LWLJWaj13O0843;........1.....2.34..2.3156.....5......4...6...78..6.......651..1..2.43..4..3...25;117
3636310645 is the rank in the min lexical catalog
LWLJWaj13O0843 is the 81 bits field of the puzzle morphed to the min lexical solution
- Code: Select all
........1.....2.34..2.3156.....5......4...6...78..6.......651..1..2.43..4..3...25
117 is for a rating 11.7 done using skfr.
Loading the file in Access gives room for many filters and/or statistics. I did the skfr rating of mith’s file and open the corresponding Access base.
Next post will give the first comments on it.
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First comments on mith’sfile.
by champagne » Thu Dec 26, 2024 9:23 am
Basically, I don’t need here any existing file, except to understand what is of interest for others and to speed up the debugging of the code.
Mith kindly sent me a file of 4 633 043 records, each of them assumed having a tridagon pattern and being T&E(3).
The file contains many records not “pure tridagon pattern”. They have no role to play here, so I tried to get rid of them.
I have no code to detect the tridagon in a grid, but the I could easily search grids having at the start four boxes in square with 11 cells having the same triplet.
This left me with 1 691 652 records.
I rated the entire file using skfr, enough for me and much faster then “serate”. As (nearly?) all grids have singles at the start, I only keep the ER rating and, to enter them in Access, I change x.y in xy.
My first action has been to get the count of grids per ER and I got this table
Most of the grids have ER>=10.0, what was expected.
I see more grids with 9< ER < 10 than I thought.
8.0 is in serate/skfr the first point where a non T&E(1) can appear.
We see here ratings below 8.0.
The last record delivers the clue.
If the solving path contains a UR step, the rating without a uniqueness rule is unpredictable. We can bet that all records below 8.0 have one such step.
My next step will be to use the upper part of this table to finish the debugging of the tridagon finder.
EDIT this table shows also that The T&E(3) can appear with relatively low ratings (after cleaning of T&E(1)). This is not good new to define a cut off in the huge files produced by the tridagon finder.
Mith kindly sent me a file of 4 633 043 records, each of them assumed having a tridagon pattern and being T&E(3).
The file contains many records not “pure tridagon pattern”. They have no role to play here, so I tried to get rid of them.
I have no code to detect the tridagon in a grid, but the I could easily search grids having at the start four boxes in square with 11 cells having the same triplet.
This left me with 1 691 652 records.
I rated the entire file using skfr, enough for me and much faster then “serate”. As (nearly?) all grids have singles at the start, I only keep the ER rating and, to enter them in Access, I change x.y in xy.
My first action has been to get the count of grids per ER and I got this table
- Code: Select all
er Count
118 149
117 36064
116 205527
115 5638
114 2368
113 773
112 2859
111 71709
110 49403
109 164832
108 53441
107 507
106 8072
105 58503
104 194071
103 209719
102 443013
101 132845
100 20631
99 672
98 63
97 221
96 472
95 173
94 929
93 1830
92 15284
91 4529
90 2096
89 115
88 13
85 97
84 203
83 172
78 209
77 122
76 27
72 69
71 237
68 3
67 47
66 1013
45 2932
Most of the grids have ER>=10.0, what was expected.
I see more grids with 9< ER < 10 than I thought.
8.0 is in serate/skfr the first point where a non T&E(1) can appear.
We see here ratings below 8.0.
The last record delivers the clue.
If the solving path contains a UR step, the rating without a uniqueness rule is unpredictable. We can bet that all records below 8.0 have one such step.
My next step will be to use the upper part of this table to finish the debugging of the tridagon finder.
EDIT this table shows also that The T&E(3) can appear with relatively low ratings (after cleaning of T&E(1)). This is not good new to define a cut off in the huge files produced by the tridagon finder.
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Re: First comments on mith’sfile.
by coloin » Fri Dec 27, 2024 12:36 pm
Thanks for that ... thats some process even as I dont understand it !! 
.
SKFR with a switch off uniqueness function would have been useful as many 10.9s and lesser probably were lost as they were potentially upogradable to 11.5 when a clue was added !!
As a quick tridagon finder i used SKFR, basically anything over 11.0 and always 11.5 were potentially tridagon puzzles with BxB above 4.
.champagne wrote:If the solving path contains a UR step, the rating without a uniqueness rule is unpredictable.
.... This is not good news to define a cut off in the huge files produced by the tridagon finder.
SKFR with a switch off uniqueness function would have been useful as many 10.9s and lesser probably were lost as they were potentially upogradable to 11.5 when a clue was added !!
As a quick tridagon finder i used SKFR, basically anything over 11.0 and always 11.5 were potentially tridagon puzzles with BxB above 4.
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Re: First comments on mith’sfile.
by champagne » Fri Dec 27, 2024 3:07 pm
coloin wrote:Thanks for that ... thats some process even as I dont understand it !!champagne wrote:If the solving path contains a UR step, the rating without a uniqueness rule is unpredictable.
.... This is not good news to define a cut off in the huge files produced by the tridagon finder.
SKFR with a switch off uniqueness function would have been useful as many 10.9s and lesser probably were lost as they were potentially upogradable to 11.5 when a clue was added !!
As a quick tridagon finder i used SKFR, basically anything over 11.0 and always 11.5 were potentially tridagon puzzles with BxB above 4.
I made this test to try to understand what is in the file and what is of interest for others, but it seems to me that a T&E(1) filter, what I implemented easily is fast and cleans most of the finder output.
A T&E(2) filter is not too hard to implement, but I think that some "solving steps" before are better if you want to have a reasonable runtime. This is not in the top part of my to do list.
and if I write
champagne wrote:If the solving path contains a UR step, the rating without a uniqueness rule is unpredictable.
I don't think that it cuts the very high ratings ( but in this field, you can always find exceptions)
Next post should be on the results for one solution grid in mith's file where I see one "miss" of the finder to explain or debug.
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Re: First comments on mith’sfile.
by champagne » Sat Dec 28, 2024 11:59 am
champagne wrote:Next post should be on the results for one solution grid in mith's file where I see one "miss" of the finder to explain or debug.
The "miss" showed a wrong test cutting a big part of the potential output.
I think to have also seen a tiny window for another wrong cut.
I'll report anyway on the solution grid 963106 when I have the ratings of the new output with the current code.
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some results on solution grid 963106
by champagne » Sat Dec 28, 2024 4:49 pm
As first test on solution grids of mith's file, I took the lowest min lexical solution.
It has the rank 963106, so it has the band 1 (index 0) as first band.
This solution grid has two possibilities to produce the tridagon, both with the digits 348.
Here are the morphs used in the tridagon finder
978365214234981567615724938789213456123546789456879123861492375592637841347158692;963106
861249753347815926592763418123654897456987231789321564615472389978536142234198675;963106
Mith's file has 12 records for this solution grid, all with very high ratings and attached to the first case.
2 records have 28 clues, out of the current limit for the finder;
I have still a small redundancy to study and a possible bug seen in the minimal analysis, but this will not change much the results.
With the current code, I got with a limit of 27 clues
49917 grids for the first case
11828 grids for the second case.
with the following distribution for each value M of a rating M.N
The second case did not deliver very high ratings, but the 2 first classes 10.x and 9.x have good chances to have some T&E(3).
And the first case has likely many of them if we compare this distribution to the mith's file distribution.
After the fix, we have about 4 times more grids, without a definition of what is of interest, the results can not be shared.
Here below, the highest ratings in both cases. For each record we have
rank of the solution,81 bits field , grid found, skfr ER
for the case 1 ratings >=11.1
rating 10.2 for the second case
It has the rank 963106, so it has the band 1 (index 0) as first band.
This solution grid has two possibilities to produce the tridagon, both with the digits 348.
Here are the morphs used in the tridagon finder
978365214234981567615724938789213456123546789456879123861492375592637841347158692;963106
861249753347815926592763418123654897456987231789321564615472389978536142234198675;963106
Mith's file has 12 records for this solution grid, all with very high ratings and attached to the first case.
2 records have 28 clues, out of the current limit for the finder;
I have still a small redundancy to study and a possible bug seen in the minimal analysis, but this will not change much the results.
With the current code, I got with a limit of 27 clues
49917 grids for the first case
11828 grids for the second case.
with the following distribution for each value M of a rating M.N
- Code: Select all
Expr1 Count
11 31
10 1321
9 13563
8 10974
7 12621
6 1338
5 3997
4 2137
3 135
2 1066
1 2734
49917
- Code: Select all
Expr1 Count
10 80
9 1514
8 4230
7 2554
6 3450
11828
The second case did not deliver very high ratings, but the 2 first classes 10.x and 9.x have good chances to have some T&E(3).
And the first case has likely many of them if we compare this distribution to the mith's file distribution.
After the fix, we have about 4 times more grids, without a definition of what is of interest, the results can not be shared.
Here below, the highest ratings in both cases. For each record we have
rank of the solution,81 bits field , grid found, skfr ER
for the case 1 ratings >=11.1
Hidden Text: Show
rating 10.2 for the second case
Hidden Text: Show
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Re: First comments on mith’sfile.
by eleven » Sun Dec 29, 2024 12:55 am
For me neither SE nor BxB ratings for tridagon puzzles are of interest. The 3 i looked at from your list are easy to solve.champagne wrote:... what is of interest for others ...
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Re: Non degenerated tridagon puzzles direct search
by coloin » Sun Dec 29, 2024 2:35 am
All your 11.6 puzzles are reductions of this maximally expanded puzzle
There are 12 minimal puzzles ..all 11.6..presumably these are the 12 in miths file
Some of these puzzles may well be T&E 2 ... but with a BxB > 6 which have been found here
Maybe if you find a few more 11.6 [ from random solution grids] you will generate some of these puzzles... those that dont expand so readily tend to be more tricky for the solvers ...as in
here
- Code: Select all
..8......234...5.7.1.72.......21..561..5.67.9....7912..61.92.75.9.6.7..1...15.... ED=11.6/11.6/3.4
There are 12 minimal puzzles ..all 11.6..presumably these are the 12 in miths file
Some of these puzzles may well be T&E 2 ... but with a BxB > 6 which have been found here
Maybe if you find a few more 11.6 [ from random solution grids] you will generate some of these puzzles... those that dont expand so readily tend to be more tricky for the solvers ...as in
here
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Re: First comments on mith’sfile.
by champagne » Sun Dec 29, 2024 8:28 am
eleven wrote:For me neither SE nor BxB ratings for tridagon puzzles are of interest. The 3 i looked at from your list are easy to solve.champagne wrote:... what is of interest for others ...
Hi eleven
The "player view" is not the hardest to understand. For sure, with 25 or more clues and a non degenerated tridagon, all skfr ratings below 10.5 can be discarded.
But finding what is interesting for the player is another story. From my experience, a player dislikes boring grids as the old "snail" where you clear step by step a candidate.
Many puzzles having a tridagon with guardians have been played. I flied over some of the corresponding threads and I have seen many new solving tools.
What is for sure is that low ratings don't give good opportunities except to play a "do it in once".
Once the "loki rule" known, none of the non degenerated is of interest , except may-be puzzles with a residual high rating after use of it.
In my view, highest ratings in new solution grids can be used to produce puzzles of higher interest (with guardians) in the way they have been found starting from loki.
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Re: Non degenerated tridagon puzzles direct search
by champagne » Sun Dec 29, 2024 8:40 am
coloin wrote:All your 11.6 puzzles are reductions of this maximally expanded puzzle ...
There are 12 minimal puzzles ..all 11.6..presumably these are the 12 in miths file
yes they are; the 2 missing have 28 clues and I currently limit the expansion to 27 clues.
coloin wrote:Some of these puzzles may well be T&E 2 ... but with a BxB > 6 which have been found here
I published statistics on the entire output of the finder, but I can now easily clear all T&E(1) (and below) puzzles.
I'll do it because it's faster than applying skfr, but I confess that I am not fun of this property.
coloin wrote:Maybe if you find a few more 11.6 [ from random solution grids] you will generate some of these puzzles... those that dont expand so readily tend to be more tricky for the solvers ...as in
here
I have to work more on the finder to clean redundancy and likely a bad use of fresh UAs in some cases, but I'll restart in parallel the scan of tiny areas of the solution grids field.
I should see new high cases. I have a small number of such ratings, likely for solution grids not in mith's file to check. I'll post new cases if any
EDIT: your example is nor a pure non degenerated tridagon, It would not come in the output of the finder.
Last edited by champagne on Sun Dec 29, 2024 9:15 am, edited 1 time in total.
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one new solution grid
by champagne » Sun Dec 29, 2024 9:02 am
As far as I can see, this solution grid is not in mith's file
4835028933;504On0rC63jO24;...31......9......32.....5..1856...3...4.1....64.8........34.61.....8..5...65.48.;115
4835028933;504On0rCM3jO20;...31......9......32.....5..1856...3...4.1....64.8.5......34.61.....8......65.48.;115
4835028933;504On0rC63jO24;...31......9......32.....5..1856...3...4.1....64.8........34.61.....8..5...65.48.;115
4835028933;504On0rCM3jO20;...31......9......32.....5..1856...3...4.1....64.8.5......34.61.....8......65.48.;115
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