The New Sudoku Players' Forum

by **Serg** » Wed Mar 08, 2017 9:34 am

Hi, Afmob!

Afmob wrote:I can confirm that F11 has no valid puzzles. I had to check 4.2e9 ED puzzles which took about 10 hours though I added some lines to my otherwise general code for this pattern to filter out invalid puzzles, otherwise it would have taken too long.

Glad to see your result, well done!

Afmob wrote:Serg, do you have an estimate on how many patterns you have to analyze for this study?

My estimations are in accordance with yours. Sadly, but I found an error in my algorithm. For some patterns not all possible puzzles were checked. So, the speed of search was too high. It is evident, that exhaustive search for F11 pattern couldn't be done in 7 minutes

.

So, my result (and timings) for patterns F7, F9, F10 and F11 are not correct (but the rest results, including the search through F12, should be correct). I will execute really exhaustive search for F7 and F11 patterns after bug fixing. (If F11 has no valid puzzles, it will be no sense to check F9 and F10, because they are subsets of F11.)

Serg

by **Afmob** » Wed Mar 08, 2017 9:40 am

I think you misunderstood me. I was asking for the number of (fully symmetrical invalid) patterns that are left to be analyzed. So how many F"xxx" are left to be checked? Also, you should check the superset pattern first to avoid unnecessary computations.

by **Serg** » Wed Mar 08, 2017 12:11 pm

Hi, Afmob!

Afmob wrote:I think you misunderstood me. I was asking for the number of (fully symmetrical invalid) patterns that are left to be analyzed. So how many F"xxx" are left to be checked?

Not more than 24 patterns are left to check. The answer depends on agreement - what patterns already checked can be reliably considered as invalid.

Afmob wrote:Also, you should check the superset pattern first to avoid unnecessary computations.

Yes, you are right. It's my mistake.

Serg

by **Serg** » Wed Mar 08, 2017 3:12 pm

Hi, Afmob!
If patterns F1-F11 are invalid (you checked their invalidity), then there are 16 fully symmetrical patterns only, whose status (valid/invalid) is still unknown. Here they are.

Code: Select all: F12 F13 F14 F15 x x . . x . . x x . x . . x . . x . . . . x . x . . . . x . . x . . x . x . . . . . . . x x x . . . . . x x . . . . x . . . . x x . . . . . x x . . . . . . . . . . . . . . . . . . . . x . . . x . . . . . . . . . . . . . . x . x . . . . . . x . x . . . x . . x . x . . x . . . x . x . . . x . . . x . . . x x . . . x . . . x . x . . x . . x . x . . . . . . . x . . . x . x . . . . . . x . x . . . x . . x . x . . x . . . x . x . . . . . . . . . . . . . . . . . . . . . . . x . . . x . . . . . . . . . . . x . . . . . . . x x x . . . . . x x . . . . x . . . . x x . . . . . x x x x . . x . . x x . x . . x . . x . . . . x . x . . . . x . . x . . x . F16 F17 F18 F19 x x . . x . . x x . x . x . x . x . x . . x . x . . x x x . x . x . x x x . . . . . . . x x . . . . . . . x . x . . . . . x . x . . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . x . . . x . . x . x . . x x . . x . x . . x x . . x . x . . x x . . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . x . . . x . . x . x . . x x . . x . x . . x x . . x . x . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . . x x . . . . . . . x . x . . . . . x . x . . . . . . . x x x . . x . . x x . x . x . x . x . x . . x . x . . x x x . x . x . x x F20 F21 F22 F23 . . . x . x . . . . . . x . x . . . . . . x . x . . . . . . x . x . . . . . . . x . . . . . x . . x . . x . . . . . x . . . . . x . . x . . x . . . x . . . x . . . . . . . . . . . . . x . . . x . . . . . . . . . . . x . . x . x . . x x . . x . x . . x x . . . . . . . x x . . . . . . . x . x . . . . . x . . x . . . . . x . . x . . x . . x . . x . . x . . x . x . . x . x . . x x . . x . x . . x x . . . . . . . x x . . . . . . . x . . x . . . x . . . . . . . . . . . . . x . . . x . . . . . . . . . . . . . . . x . . . . . x . . x . . x . . . . . x . . . . . x . . x . . x . . . . x . x . . . . . . x . x . . . . . . x . x . . . . . . x . x . . . F24 F25 F26 F27 . . . x . x . . . . . . x . x . . . . . . x . x . . . . . . x x x . . . . . . . x . . . . . x . . x . . x . . x . . x . . x . . x . . x . . x . . . x . . . x . . . . . . . . . . . . . . . x . . . . . . . . . . . . . x . . . . . . . x x . . . . . . . x x . . . . . . . x x . . . . . . . x . x . . . . . x . . x . . . . . x . . x x . . . x x . x x . . . . . x x x . . . . . . . x x . . . . . . . x x . . . . . . . x x . . . . . . . x . . x . . . x . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . . . x . . . . . x . . x . . x . . x . . x . . x . . x . . x . . x . . . . x . x . . . . . . x . x . . . . . . x . x . . . . . . x x x . . .

Serg

[Edited. I corrected typos in F15 pattern - clues r5c1 and r5c9 were absent in original post.]

by **Afmob** » Wed Mar 08, 2017 4:33 pm

Thanks for all the patterns, Serg! F12 has no valid puzzles. I had to check 1.92e9 ED puzzles which took about 4.5 hours. Also F24 and F25 can have no valid puzzles since they only have 16 clues. Have you checked whether some patterns are subsets of magic pattern?

by **Serg** » Wed Mar 08, 2017 9:11 pm

Hi, Afmob!
Yes, patterns were preliminary filtered by "40 maximal patterns list", plus maximal "Cross Pattern":

Code: Select all: Cross Pattern x . . x . x . . x . . . x . x . . . . . . x . x . . . x x x x x x x x x . . . x x x . . . x x x x x x x x x . . . x . x . . . . . . x . x . . . x . . x . x . . x

coloin invented this pattern and blue proved that it has no valid puzzles and, moreover, it is maximal, i.e. cannot be extented by 1 clue provided that resulting pattern must not have valid puzzles. I confirmed blue's proof (by own exhaustive search), so this pattern can be safely used. I also used for filtering known fully symmetrical valid patterns.

Some words about 16 "unknown" patterns, published in my previous post. Pattern F12 was already checked by me (exhaustive search). The rest were tested by 100 millions random puzzles each. (No valid puzzles were found.)

You can see that some patterns in "16 unknown patterns" are subsets of others. It turns out, that 9 patterns in this list are "irreducible", i.e. they are not subsets of other patterns in the list. Here they are: F12, F13, F14, F18, F19, F21, F23, F26, F27. Pattern F12 was already checked. If remaining 8 patterns are invalid, all fully symmetrical patterns became "known" (valid or invalid).

Serg

[Edited. I corrected grammatic errors.]

by **JPF** » Wed Mar 08, 2017 10:33 pm

Hi Serg,

Interesting work!
What about the subsets of this fully symmetrical invalid pattern:

Code: Select all: x x x | x x x | x x x x x x | . . . | x x x x x x | . . . | x x x -------+-------+------- x . . | . . . | . . x x . . | . x . | . . x x . . | . . . | . . x -------+-------+------- x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x

After a fast check, none of your F1-F27 are ed-included in it.
Here are two examples of subsets:

Code: Select all: . . x | x x x | x . . . x . | . . . | . x . x . x | . . . | x . x -------+-------+------- x . . | . . . | . . x x . . | . x . | . . x x . . | . . . | . . x -------+-------+------- x . x | . . . | x . x . x . | . . . | . x . . . x | x x x | x . .

Code: Select all: x . . | . . . | . . x . x . | . . . | . x . . . . | x x x | . . . -------+-------+------- . . x | . . . | x . . . . x | . x . | x . . . . x | . . . | x . . -------+-------+------- . . . | x x x | . . . . x . | . . . | . x . x . . | . . . | . . x

JPF

by **Serg** » Wed Mar 08, 2017 11:34 pm

Hi, JPF!

JPF wrote:Hi Serg,
Interesting work!

Thanks!

JPF wrote:What about the subsets of this fully symmetrical invalid pattern:
Code: Select all
x x x | x x x | x x x x x x | . . . | x x x x x x | . . . | x x x -------+-------+------- x . . | . . . | . . x x . . | . x . | . . x x . . | . . . | . . x -------+-------+------- x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x

After a fast check, none of your F1-F27 are ed-included in it.

Well, well, well ...
This pattern is my favorite maximal pattern (i.e. having no valid puzzles and unextendable by clue cells). I call it "Magic Pattern". I used it in almost all my sudoku studies. Maybe I can write a book about this pattern ...

This pattern is part of the "40 maximal patterns list", published in the thread Investigation of one-crossing-free patterns. (See my post, dated by May 26, 2013 or blue's post, dated by May 30, 2013.) Magic Pattern has number P134 in my list and number 20 in blue's list. (Both lists are identical, but use different representations of the patterns.)

It is not surprising that you didn't found subsets of Magic Pattern among F1-F27 patterns. Those subsets were filtered out (by "40 maximal patterns list") at earlier stages of my work. I started from 6016 ed fully symmetrical patterns and came to 16 "unknown" patterns list. The work is going to the end.

Serg

by **blue** » Thu Mar 09, 2017 2:47 am

Hi Serg & Afmob,

Serg wrote:Yes, patterns were preliminary filtered by "40 maximal patterns list", plus maximal "Cross Pattern":
Code: Select all
Cross Pattern x . . x . x . . x . . . x . x . . . . . . x . x . . . x x x x x x x x x . . . x x x . . . x x x x x x x x x . . . x . x . . . . . . x . x . . . x . . x . x . . x

coloin invented this pattern and blue proved that it has no valid puzzles and, moreover, it is maximal, i.e. cannot be extented by 1 clue provided that resulting pattern must not have valid puzzles. I confirmed blue's proof (by own exhaustive search), so this pattern can be safe used.

That was news to me :!:

I don't doubt your claim. I have 100% confidence that you're reporting acccurately.
"Well done", for using it !

Trivia (FWIW):

---

Serg wrote:Some words about 16 "unknown" patterns, published in my previous post. Pattern F12 was checked by me too (exhaustive search). The rest was tested by 100 millions random puzzles each. (No valid puzzles were found.)

You can see that some patterns in "16 unknown patterns" are subsets of each other. It turns out, that 9 patterns in this list are "irreducible", i.e. they are not subsets of other patterns in the list. Here they are: F12, F13, F14, F18, F19, F21, F23, F26, F27.

Two items to report:

Pattern F18 has a valid puzzle: Edit: This was not F18. My bad.

Code: Select all
7 . . | 3 . 9 | . . 4 . 8 . | . 6 . | . 5 . . . . | . . . | . . . ------+-------+------ 4 . . | . . . | . . 5 . 5 . | . . . | . 1 . 9 . . | . . . | . . 3 ------+-------+------ . . . | . . . | . . . . 2 . | . 8 . | . 6 . 3 . . | 5 . 4 | . . 9 F18: 20 clues
One of my first "exhaustive search" projects -- 2006/2007 (?) -- was a search for "fully symmetric", 17-clue puzzles.

Cheers,
Blue.

by **Serg** » Thu Mar 09, 2017 9:33 am

Hi, blue!

blue wrote:
Serg wrote:Yes, patterns were preliminary filtered by "40 maximal patterns list", plus maximal "Cross Pattern":
Code: Select all
Cross Pattern x . . x . x . . x . . . x . x . . . . . . x . x . . . x x x x x x x x x . . . x x x . . . x x x x x x x x x . . . x . x . . . . . . x . x . . . x . . x . x . . x

coloin invented this pattern and blue proved that it has no valid puzzles and, moreover, it is maximal, i.e. cannot be extented by 1 clue provided that resulting pattern must not have valid puzzles. I confirmed blue's proof (by own exhaustive search), so this pattern can be safe used.

That was news to me
...
I usually have a pretty good memory for "patterns", and (for some reason), I don't remember this one.

I somewhat confused ...
Here is link to your post, dated by March 22, 2013, in the thread Investigation of one-crossing-free patterns, where you reported that Cross Pattern has no valid puzzles and is maximal. My confirmation of your result published in the same thread - Investigation of one-crossing-free patterns (post was dated by January 17, 2017).

blue wrote:Pattern F18 has a valid puzzle:

Code: Select all
7 . . | 3 . 9 | . . 4 . 8 . | . 6 . | . 5 . . . . | . . . | . . . ------+-------+------ 4 . . | . . . | . . 5 . 5 . | . . . | . 1 . 9 . . | . . . | . . 3 ------+-------+------ . . . | . . . | . . . . 2 . | . 8 . | . 6 . 3 . . | 5 . 4 | . . 9 F18: 20 clues

I am confused again, but this is not F18 pattern... F18 pattern contains 4 clues in the central box.

blue wrote:With full cofidence at this point: you can take this post as "would be" confirmation, that no fully symmetric pattern with <= 17 clue positions, has a valid puzzle.

Thank you for useful information!

Serg

by **coloin** » Thu Mar 09, 2017 12:42 pm

Just to refer back to this thread Fully symmetrical puzzles
You may have seen this ..
it tried initially to do what you are doing , the numenclature is good i think
JPFpublished this

Code: Select all: Number Number Number of clues of patterns of S-different (n) N(n) patterns N'(n) 0 1 1 1 1 1 4 8 4 5 8 4 8 34 10 9 34 10 12 104 24 13 104 24 16 253 52 17 253 52 20 512 98 21 512 98 24 888 165 25 888 165 28 1344 246 29 1344 246 32 1794 323 33 1794 323 36 2128 380 37 2128 380 40 2252 402 41 2252 402

and Ocean explained the nomenclature

Code: Select all: This puzzles is a [0-9-6-0-0][ binary] 0 0 0 | 0 0 . | . . . . 1 0 | 0 1 . | . . . . . 1 | 1 0 . | . . . -------+-------+------- . . . | 0 0 . | . . . . . . | . 0 . | . . . . . . | . . . | . . . -------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . 1 . | . 2 . | . 3 . . . 4 | 5 . 6 | 7 . . -------+-------+------- . . 6 | . . . | 5 . . . 2 . | . . . | . 8 . . . 8 | . . . | 9 . . -------+-------+------- . . 5 | 4 . 7 | 6 . . . 8 . | . 9 . | . 1 . . . . | . . . | . . . 0-9-6-0-0, 0-10-5-0-0, 17-0-6-0-0, 17-10-0-0, 18-0-5-0-0, 18-9-0-0-0

from > 10 years ago !!!
C

by **coloin** » Thu Mar 09, 2017 12:50 pm

Here is the 98 at the 20 clue level

Code: Select all: 20: 16-13-0-0-0 16-4-5-0-0 25-0-4-0-0 21-8-0-0-0 8-9-4-0-0 4-8-5-0-0 20: 16-12-4-0-0 24-8-4-0-0 20-8-4-0-0 20: 16-12-1-0-0 16-5-4-0-0 24-1-4-0-0 20-8-1-0-0 9-8-4-0-0 5-8-4-0-0 20: 16-12-0-2-0 16-4-4-2-0 24-0-4-2-0 20-8-0-2-0 8-8-4-2-0 4-8-4-2-0 20: 16-12-0-1-0 16-4-4-1-0 24-0-4-1-0 20-8-0-1-0 8-8-4-1-0 4-8-4-1-0 20: 16-11-0-0-0 16-0-7-0-0 19-8-0-0-0 19-0-4-0-0 0-11-4-0-0 0-8-7-0-0 20: 16-10-4-0-0 16-8-6-0-0 18-8-4-0-0 18-4-0-0-0 8-0-6-0-0 4-10-0-0-0 20: 16-10-1-0-0 16-1-6-0-0 18-8-1-0-0 18-1-4-0-0 1-10-4-0-0 1-8-6-0-0 20: 16-10-0-2-0 16-0-6-2-0 18-8-0-2-0 18-0-4-2-0 0-10-4-2-0 0-8-6-2-0 20: 16-10-0-1-0 16-0-6-1-0 18-8-0-1-0 18-0-4-1-0 0-10-4-1-0 0-8-6-1-0 20: 16-9-5-0-0 16-5-1-0-0 17-9-4-0-0 17-8-5-0-0 9-1-4-0-0 5-8-1-0-0 20: 16-9-4-2-0 16-8-5-2-0 17-8-4-2-0 17-4-0-2-0 8-0-5-2-0 4-9-0-2-0 20: 16-9-4-1-0 16-8-5-1-0 17-8-4-1-0 17-4-0-1-0 8-0-5-1-0 4-9-0-1-0 20: 16-9-2-0-0 16-2-5-0-0 17-8-2-0-0 17-2-4-0-0 2-9-4-0-0 2-8-5-0-0 20: 16-9-1-2-0 16-1-5-2-0 17-8-1-2-0 17-1-4-2-0 1-9-4-2-0 1-8-5-2-0 20: 16-9-1-1-0 16-1-5-1-0 17-8-1-1-0 17-1-4-1-0 1-9-4-1-0 1-8-5-1-0 20: 16-9-0-3-0 16-0-5-3-0 17-8-0-3-0 17-0-4-3-0 0-9-4-3-0 0-8-5-3-0 20: 16-8-4-3-0 16-4-0-3-0 8-0-4-3-0 4-8-0-3-0 20: 16-8-3-0-0 16-3-4-0-0 8-0-3-0-0 4-3-0-0-0 3-8-4-0-0 3-4-0-0-0 20: 16-8-2-2-0 16-2-4-2-0 8-0-2-2-0 4-2-0-2-0 2-8-4-2-0 2-4-0-2-0 20: 16-8-2-1-0 16-2-4-1-0 8-0-2-1-0 4-2-0-1-0 2-8-4-1-0 2-4-0-1-0 20: 16-8-1-3-0 16-1-4-3-0 8-0-1-3-0 4-1-0-3-0 1-8-4-3-0 1-4-0-3-0 20: 16-6-0-0-0 16-4-2-0-0 8-2-4-0-0 10-0-4-0-0 4-8-2-0-0 6-8-0-0-0 20: 16-5-0-2-0 16-4-1-2-0 8-1-4-2-0 9-0-4-2-0 4-8-1-2-0 5-8-0-2-0 20: 16-5-0-1-0 16-4-1-1-0 8-1-4-1-0 9-0-4-1-0 4-8-1-1-0 5-8-0-1-0 20: 24-9-0-0-0 25-8-0-0-0 20-0-5-0-0 21-0-4-0-0 0-13-4-0-0 0-12-5-0-0 20: 24-8-1-0-0 20-1-4-0-0 1-12-4-0-0 20: 24-8-0-2-0 20-0-4-2-0 0-12-4-2-0 20: 24-8-0-1-0 20-0-4-1-0 0-12-4-1-0 20: 24-4-0-0-0 20-4-0-0-0 8-4-4-0-0 12-8-0-0-0 12-0-4-0-0 4-12-0-0-0 20: 24-2-0-0-0 20-0-2-0-0 0-12-2-0-0 0-6-4-0-0 10-8-0-0-0 6-0-4-0-0 20: 24-1-1-0-0 20-1-1-0-0 9-8-1-0-0 5-1-4-0-0 1-12-1-0-0 1-5-4-0-0 20: 24-1-0-2-0 20-0-1-2-0 0-12-1-2-0 0-5-4-2-0 9-8-0-2-0 5-0-4-2-0 20: 24-1-0-1-0 20-0-1-1-0 0-12-1-1-0 0-5-4-1-0 9-8-0-1-0 5-0-4-1-0 20: 24-0-5-0-0 20-9-0-0-0 17-12-0-0-0 17-4-4-0-0 8-8-5-0-0 4-9-4-0-0 20: 24-0-2-0-0 20-2-0-0-0 8-8-2-0-0 4-2-4-0-0 2-12-0-0-0 2-4-4-0-0 20: 24-0-1-2-0 20-1-0-2-0 8-8-1-2-0 4-1-4-2-0 1-12-0-2-0 1-4-4-2-0 20: 24-0-1-1-0 20-1-0-1-0 8-8-1-1-0 4-1-4-1-0 1-12-0-1-0 1-4-4-1-0 20: 28-0-0-0-0 8-12-0-0-0 4-4-4-0-0 20: 24-0-0-3-0 20-0-0-3-0 0-12-0-3-0 0-4-4-3-0 8-8-0-3-0 4-0-4-3-0 20: 26-0-0-0-0 22-0-0-0-0 0-14-0-0-0 0-4-6-0-0 8-10-0-0-0 4-0-6-0-0 20: 25-1-0-0-0 21-0-1-0-0 0-13-1-0-0 0-5-5-0-0 9-9-0-0-0 5-0-5-0-0 20: 25-0-1-0-0 21-1-0-0-0 8-9-1-0-0 4-1-5-0-0 1-13-0-0-0 1-4-5-0-0 20: 25-0-0-2-0 21-0-0-2-0 0-13-0-2-0 0-4-5-2-0 8-9-0-2-0 4-0-5-2-0 20: 25-0-0-1-0 21-0-0-1-0 0-13-0-1-0 0-4-5-1-0 8-9-0-1-0 4-0-5-1-0 20: 16-3-1-0-0 16-1-3-0-0 3-8-1-0-0 3-1-4-0-0 1-8-3-0-0 1-3-4-0-0 20: 16-3-0-2-0 16-0-3-2-0 0-8-3-2-0 0-3-4-2-0 3-8-0-2-0 3-0-4-2-0 20: 16-3-0-1-0 16-0-3-1-0 0-8-3-1-0 0-3-4-1-0 3-8-0-1-0 3-0-4-1-0 20: 16-2-2-0-0 2-8-2-0-0 2-2-4-0-0 20: 16-2-1-2-0 16-1-2-2-0 2-8-1-2-0 2-1-4-2-0 1-8-2-2-0 1-2-4-2-0 20: 16-2-1-1-0 16-1-2-1-0 2-8-1-1-0 2-1-4-1-0 1-8-2-1-0 1-2-4-1-0 20: 16-2-0-3-0 16-0-2-3-0 0-8-2-3-0 0-2-4-3-0 2-8-0-3-0 2-0-4-3-0 20: 16-1-1-3-0 1-8-1-3-0 1-1-4-3-0 20: 18-9-0-0-0 18-0-5-0-0 17-10-0-0-0 17-0-6-0-0 0-10-5-0-0 0-9-6-0-0 20: 18-2-0-0-0 18-0-2-0-0 0-10-2-0-0 0-2-6-0-0 2-10-0-0-0 2-0-6-0-0 20: 18-1-1-0-0 1-10-1-0-0 1-1-6-0-0 20: 18-1-0-2-0 18-0-1-2-0 0-10-1-2-0 0-1-6-2-0 1-10-0-2-0 1-0-6-2-0 20: 18-1-0-1-0 18-0-1-1-0 0-10-1-1-0 0-1-6-1-0 1-10-0-1-0 1-0-6-1-0 20: 18-0-0-3-0 0-10-0-3-0 0-0-6-3-0 20: 19-1-0-0-0 19-0-1-0-0 0-11-1-0-0 0-1-7-0-0 1-11-0-0-0 1-0-7-0-0 20: 19-0-0-2-0 0-11-0-2-0 0-0-7-2-0 20: 19-0-0-1-0 0-11-0-1-0 0-0-7-1-0 20: 17-9-1-0-0 17-1-5-0-0 9-1-1-0-0 5-1-1-0-0 1-9-5-0-0 1-5-1-0-0 20: 17-9-0-2-0 17-0-5-2-0 0-9-5-2-0 0-5-1-2-0 9-1-0-2-0 5-0-1-2-0 20: 17-9-0-1-0 17-0-5-1-0 0-9-5-1-0 0-5-1-1-0 9-1-0-1-0 5-0-1-1-0 20: 17-5-0-0-0 17-4-1-0-0 8-1-5-0-0 9-0-5-0-0 4-9-1-0-0 5-9-0-0-0 20: 17-3-0-0-0 17-0-3-0-0 0-9-3-0-0 0-3-5-0-0 3-9-0-0-0 3-0-5-0-0 20: 17-2-1-0-0 17-1-2-0-0 2-9-1-0-0 2-1-5-0-0 1-9-2-0-0 1-2-5-0-0 20: 17-2-0-2-0 17-0-2-2-0 0-9-2-2-0 0-2-5-2-0 2-9-0-2-0 2-0-5-2-0 20: 17-2-0-1-0 17-0-2-1-0 0-9-2-1-0 0-2-5-1-0 2-9-0-1-0 2-0-5-1-0 20: 17-1-1-2-0 1-9-1-2-0 1-1-5-2-0 20: 17-1-1-1-0 1-9-1-1-0 1-1-5-1-0 20: 17-1-0-3-0 17-0-1-3-0 0-9-1-3-0 0-1-5-3-0 1-9-0-3-0 1-0-5-3-0 20: 0-7-0-0-0 0-4-3-0-0 8-3-0-0-0 11-0-0-0-0 4-0-3-0-0 7-0-0-0-0 20: 0-6-1-0-0 0-5-2-0-0 10-1-0-0-0 9-2-0-0-0 6-0-1-0-0 5-0-2-0-0 20: 0-6-0-2-0 0-4-2-2-0 8-2-0-2-0 10-0-0-2-0 4-0-2-2-0 6-0-0-2-0 20: 0-6-0-1-0 0-4-2-1-0 8-2-0-1-0 10-0-0-1-0 4-0-2-1-0 6-0-0-1-0 20: 0-5-0-3-0 0-4-1-3-0 8-1-0-3-0 9-0-0-3-0 4-0-1-3-0 5-0-0-3-0 20: 8-5-0-0-0 13-0-0-0-0 4-4-1-0-0 20: 8-4-1-0-0 12-1-0-0-0 12-0-1-0-0 9-4-0-0-0 4-5-0-0-0 5-4-0-0-0 20: 8-4-0-2-0 12-0-0-2-0 4-4-0-2-0 20: 8-4-0-1-0 12-0-0-1-0 4-4-0-1-0 20: 8-2-1-0-0 10-0-1-0-0 4-1-2-0-0 6-1-0-0-0 1-6-0-0-0 1-4-2-0-0 20: 8-1-2-0-0 9-0-2-0-0 4-2-1-0-0 5-2-0-0-0 2-5-0-0-0 2-4-1-0-0 20: 8-1-1-2-0 9-0-1-2-0 4-1-1-2-0 5-1-0-2-0 1-5-0-2-0 1-4-1-2-0 20: 8-1-1-1-0 9-0-1-1-0 4-1-1-1-0 5-1-0-1-0 1-5-0-1-0 1-4-1-1-0 20: 0-3-2-0-0 0-2-3-0-0 2-3-0-0-0 2-0-3-0-0 3-2-0-0-0 3-0-2-0-0 20: 0-3-1-2-0 0-1-3-2-0 3-1-0-2-0 3-0-1-2-0 1-3-0-2-0 1-0-3-2-0 20: 0-3-1-1-0 0-1-3-1-0 3-1-0-1-0 3-0-1-1-0 1-3-0-1-0 1-0-3-1-0 20: 0-3-0-3-0 0-0-3-3-0 3-0-0-3-0 20: 0-2-2-2-0 2-2-0-2-0 2-0-2-2-0 20: 0-2-2-1-0 2-2-0-1-0 2-0-2-1-0 20: 0-2-1-3-0 0-1-2-3-0 2-1-0-3-0 2-0-1-3-0 1-2-0-3-0 1-0-2-3-0 20: 2-2-1-0-0 2-1-2-0-0 1-2-2-0-0 20: 2-1-1-2-0 1-2-1-2-0 1-1-2-2-0 20: 2-1-1-1-0 1-2-1-1-0 1-1-2-1-0 20: 3-1-1-0-0 1-3-1-0-0 1-1-3-0-0 20: 1-1-1-3-0

by **blue** » Thu Mar 09, 2017 1:09 pm

Hi Serg,

Serg wrote:
blue wrote:...
That was news to me
...
I usually have a pretty good memory for "patterns", and (for some reason), I don't remember this one.

I somewhat confused ...
Here is link to your post, dated by March 22, 2013, in the thread Investigation of one-crossing-free patterns, where you reported that Cross Pattern has no valid puzzles and is maximal. My confirmation of your result published in the same thread - Investigation of one-crossing-free patterns (post was dated by January 17, 2017).

Wow. Thank you. (It's near the bottom of the page).
I missed the post announcing your confirmation, too.

Serg wrote:
blue wrote:Pattern F18 has a valid puzzle:
(...)

I am confused again, but this is not F18 pattern... F18 pattern contains 4 clues in the central box.

Sorry. My mistake, obviously. It looks like a cross between F18 and F25.

by **Serg** » Thu Mar 09, 2017 2:46 pm

Hi, coloin!
Thank you for links! Of course, I saw the thread "Fully symmetrical puzzles". Moreover, I actively used information from this thread in my project.

Well, it's time to declare my project's goal. I want to prepare full catalog of fully symmetrical patterns, having valid puzzles, including full list of 20-clue fully symmetrical patterns. It is well known (see the thread "Fully symmetrical puzzles"), there are 6016 essentially different fully symmetrical patterns. I want to determine, what patterns have valid puzzles and what patterns have no valid puzzles.

The first thing what I've done - I collected valid patterns from the thread "Fully symmetrical puzzles" and other 3 threads, published fully symmetrical valid puzzles. Then I filtered 6016 ed patterns by this valid patterns list - about 5000 patterns were filtered out. About 800 patterns were filtered out by "40 maximal patterns list". Remaining 150 patterns were processed individually, and finally I came to F1-F27 "unknown" patterns list.

I hope all fully symmetrical patterns will be "known" (valid/invalid) in a month (or even earlier).

Serg

by **Afmob** » Fri Mar 10, 2017 6:31 am

I almost got all the "fast" patterns done. During the weekend I should be able to analyse F13, F14 and F27. Since F19 has the most clues and I haven't estimated the number of ED puzzles so far, I cannot say how long F19 will take.

Code: Select all: Pattern | ED puzzles | Valid puzzles | Time --------+----------------+---------------+-------- F13 | 7.256.543.758 | 0 | 13h 52m F14 | 12.726.561.951 | 2 | 22h 08m F15 | 2.365.232.472 | 0 | 04h 58m F16 | 627.069.631 | 0 | 01h 58m F17 | 645.580.730 | 0 | 02h 14m F18 | 662.332.640 | 0 | 02h 25m F19 | 16.155.120.596 | 2 | 37h 46m F20 | 4.001.897.601 | 0 | 10h 09m F21 | 1.490.830.830 | 0 | 04h 30m F22 | 52.338.965 | 0 | 00h 11m F23 | 20.336.312 | 0 | 00h 05m F24 | 8.843.584 | 0 | 00h 02m F25 | 3.490.587 | 0 | 00h 01m F26 | 2.348.126.021 | 0 | 07h 18m F27 | 2.348.126.021 | 0 | 05h 14m blue | 1.286.386.340 | 303 | 03h 12m

Edit: Done. Each of F14 and F19 has two valid puzzles! See coloin's post and my post for the actual puzzles.

The New Sudoku Players' Forum

Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns

Re: Fully symmetrical invalid patterns