The New Sudoku Players' Forum

[Serg]

Hi, colleagues!
I found an arithmetic error in my calculations (manual calculations are error-prone). eleven, you are right - total numbers of 18-clue symmetric patterns is still 2,402,330,656.

About filtering out patterns not complying to composition rules. I have proper C code, but embedded in another program. I'll try to code autonomous utility (reading eleven's file) ASAP.

Serg

[ronk]

With 2 automorphisms each puzzle has 3 equivalents with the same pattern.

Understanding automorphism eluded me for a long time, so I could still be wrong, but ... shouldn't that be "1 equivalent?"

[coloin]

I think its achieved by swapping c46 = 2
swapping stacks 1 and 3 and swapping c123 and c789 = 2

so at least 4 equivalents for each pattern
C

[ronk]

I think its achieved by swapping c46 = 2
swapping stacks 1 and 3 and swapping c123 and c789 = 2

so at least 4 equivalents for each pattern

OK, I should have been thinking about vertical symmetry, then automorphisms >= 4, not 2.

[edit: add the following]

my solver has code to canonicalize fish exemplars
a fallout of that process is the number of automorphisms

Use gsf's program on a file containing all known symmetric 18s to verify automorphisms >= 4.

[Afmob]

I currently have analyzed about 3000 patterns and I can confirm that the first 2147 patterns have no uniquely solvable 18 clue Sudoku.

eleven, I look into your question.

Edit: This one has the most essentially different puzzles of all patterns with a total of 4,693,836,890 essentially different puzzles and 4 automorphisms.

Code: Select all

....X......X...X...X.....X....X.X.....X...X..X.......X...XXX....X.....X.X.......X


It should take about a day to solve all those puzzles. An honourable mention goes to

Code: Select all

....X......X...X....X...X.....X.X....X.....X..X.....X....XXX...X.......XX.......X


with 1,146,653,411 essentially different puzzles and 32 automorphisms.

[Pat]

With 2 automorphisms,
each puzzle has 3 equivalents with the same pattern

• swapping c46
• swapping stacks 1 and 3 and swapping c123 and c789

so at least 4 equivalents

OK, I should have been thinking about vertical symmetry, then automorphisms >= 4, not 2.

eleven + coloin are right

at least 2 automorphisms

==> each puzzle is part of a class of at least 4 automorphs
i.e. has at least 3 automorphs

[eleven]

This one has the most essentially different puzzles of all patterns with a total of 4,693,836,890 essentially different puzzles and 4 automorphisms.

Code: Select all

....X......X...X...X.....X....X.X.....X...X..X.......X...XXX....X.....X.X.......X


It should take about a day to solve all those puzzles. An honourable mention goes to

Code: Select all

....X......X...X....X...X.....X.X....X.....X..X.....X....XXX...X.......XX.......X


with 1,146,653,411 essentially different puzzles and 32 automorphisms.

Thanks Afmob,
the first pattern is not very encouraging for this project. To solve all puzzles would probably take me 1 1/2 days on my PC on a single core.

I came across this one with 48 automorphs (dont know yet, if this is the maximum in the list).

Code: Select all

.............1.......1.1.....1...1....1...1....1...1....11111...1.....1.1.......1


[Afmob]

Do you mean maximum number of automorphisms? While searching for the one with the most essentially different puzzles I found one with 576 automorphisms if I remember correctly but there might be patterns in your file with more automorphisms.

By the way, I mentioned the other pattern with 32 automorphisms because if you disregard the automorphisms it would have the highest number of puzzles (over 32 billion).

[Serg]

Hi, colleagues!
I filtered eleven's list of patterns by applying composition rules. Here is my program report.

Code: Select all

Composition rules filter (8 rules), version 1.0

Total number of processed patterns: 294742

Filtering statistics

Empty rows (columns): filtered out      0 patterns
Composition rule 1:   filtered out  22670 patterns
Composition rule 2:   filtered out  40853 patterns
Composition rule 3:   filtered out    379 patterns
Composition rule 4:   filtered out      0 patterns
Composition rule 5:   filtered out      0 patterns
Composition rule 6:   filtered out    420 patterns
Composition rule 7:   filtered out      0 patterns
Composition rule 8:   filtered out   5567 patterns

Totally filtered out patterns:  69889
               Valid patterns: 224853

Total program execution time: 6 seconds


Number of "rectified" patterns - 224853. So, eleven was right when he predicted not less than 200000 patterns after filtering out invalid patterns. I hoped for the better ... . On the other hand we can imagine that we have already done exhaustive search for 70000 patterns. Not so bad .

Zipped file with filtered patterns has size almost 1 MB. You know this forum limits alone attached file size to 256 Kb. So, I had to split entire file onto 4 parts - the first part is attached to this post, other 3 parts are attached to my 3 next (dummy) posts.

Sorry for spoiling this thread.

Serg

[Serg]

Part 2 of 4
You must rename this file after downloading to "sym18pat_filtered.z01" and move to the directory, containing 1st part of archive.

[Serg]

Part 3 of 4
You must rename this file after downloading to "sym18pat_filtered.z02" and move to the directory, containing 1st part of archive.

[Serg]

Part 4 of 4
You must rename this file after downloading to "sym18pat_filtered.z03" and move to the directory, containing 1st part of archive.
Now you can unzip entire archive.

Serg

[eleven]

Fine, Serg,

I removed the remaining 304 equivalents and uploaded the file there.

[Serg]

Hi, eleven!
I loaded your file (without isomorphic duplicates). I have some ideas concerning additional filtering out patterns (but I don't expect significant search space reduction). I need several days to implement these ideas.

Serg

[Afmob]

I've analyzed the first 658 patterns of the new list and none of them have a uniquely solvable 18 clues Sudoku. As you can see the filtered list takes much longer than the original list. So every pattern before

Code: Select all

.............1.......111................1......11111............1.1.1.1..11...11.


can be omitted.