Fully symmetrical puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Postby JPF » Sun Aug 26, 2007 1:08 pm

Nice work, Mauricio !

The first minimal puzzle with 32 clues has been posted by dukuso in september 2005. See here.

AFAIK, your puzzle is the first minimal fully symmetric 32 clues.

What about 33 clues ?:)

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Postby Mauricio » Sun Aug 26, 2007 9:24 pm

Two more. Unfortunately I can't find one with 33 clues. Perhaps Havard can help:D .
Code: Select all
#32 clues, FS abs. minimal
+-------+-------+-------+
| . . 1 | . 2 . | 3 . . |
| . 2 . | . . . | . 4 . |
| 5 . 3 | 1 . 6 | 2 . 7 |
+-------+-------+-------+
| . . 4 | 6 . 2 | 8 . . |
| 8 . . | . . . | . . 3 |
| . . 7 | 8 . 3 | 4 . . |
+-------+-------+-------+
| 1 . 2 | 7 . 8 | 5 . 4 |
| . 7 . | . . . | . 1 . |
| . . 5 | . 6 . | 7 . . |
+-------+-------+-------+

Code: Select all
#32 clues, FS abs. minimal
+-------+-------+-------+
| . . . | . . . | . . . |
| . 1 2 | . 3 . | 4 5 . |
| . 3 6 | 1 . 5 | 7 2 . |
+-------+-------+-------+
| . . 4 | . 8 . | 3 . . |
| . 6 . | 4 . 2 | . 1 . |
| . . 8 | . 1 . | 6 . . |
+-------+-------+-------+
| . 8 5 | 3 . 4 | 1 6 . |
| . 4 1 | . 5 . | 2 8 . |
| . . . | . . . | . . . |
+-------+-------+-------+
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Re: A question

Postby wintder » Mon Aug 27, 2007 10:21 pm

Eioru wrote:Are there puzzles with fully symmetric satisfing the article I list below?
(1) empty box ( more than 1 )
(2) empty rows or lines ( more than 6 )
(3) empty two diagonals, verticle axis, and horizontal axis (24 or 32 clues)
(4) the least clue ( less than 24 )


Six is the maximum possible empty rows and columns.

If you add a seventh one band or stack (floor or tower) will have
two empty rows or columns, which forces multiple solutions.
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Postby Mauricio » Mon Aug 27, 2007 10:26 pm

Note the difficulty.
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 2 3 4 | 5 . . |
| . 2 4 | . 6 . | 3 1 . |
+-------+-------+-------+
| . 1 . | . 5 . | . 6 . |
| . 6 3 | 1 . 7 | 8 5 . |
| . 5 . | . 2 . | . 3 . |
+-------+-------+-------+
| . 8 5 | . 7 . | 6 2 . |
| . . 2 | 3 8 6 | 1 . . |
| . . . | . . . | . . . |
+-------+-------+-------+   ER 9.0
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Postby Mauricio » Tue Aug 28, 2007 2:09 am

28 clues, minimal, 7 empty units, fully symmetric, ER 7.8, what else do you need? (32 clues maybe:D )
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 2 . 3 | 4 . . |
| . 2 3 | 4 . 5 | 1 6 . |
+-------+-------+-------+
| . 3 2 | . . . | 5 7 . |
| . . . | . . . | . . . |
| . 5 6 | . . . | 8 4 . |
+-------+-------+-------+
| . 1 5 | 3 . 4 | 6 8 . |
| . . 4 | 1 . 7 | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+

32 clues, minimal, 4 empty boxes, ER 9.0.
Code: Select all
+-------+-------+-------+
| . 1 2 | . . . | 3 4 . |
| 3 . 5 | . . . | 2 . 6 |
| 4 6 . | . . . | . 5 1 |
+-------+-------+-------+
| . . . | 2 4 7 | . . . |
| . . . | 8 . 1 | . . . |
| . . . | 5 6 9 | . . . |
+-------+-------+-------+
| 6 2 . | . . . | . 8 5 |
| 5 . 3 | . . . | 4 . 7 |
| . 4 1 | . . . | 6 3 . |
+-------+-------+-------+
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Postby Mauricio » Tue Aug 28, 2007 10:10 am

RW wrote:Are there any known minimal fully symmetrical puzzles with >32 clues yet? Guess there could be some lurking in the vast amount of 36s generated lately...

JPF wrote:What about 33 clues ?:)

Finally! The hard part was to choose the right pattern.
Code: Select all
#33 clues, abs. minimal, fully symmetrical, ER 9.0
+-------+-------+-------+
| . . . | . 1 . | . . . |
| . . 1 | 2 . 3 | 4 . . |
| . 2 5 | 6 . 4 | 1 3 . |
+-------+-------+-------+
| . 5 7 | . . . | 3 1 . |
| 1 . . | . 5 . | . . 4 |
| . 6 4 | . . . | 7 5 . |
+-------+-------+-------+
| . 7 6 | 1 . 5 | 8 4 . |
| . . 2 | 8 . 6 | 5 . . |
| . . . | . 4 . | . . . |
+-------+-------+-------+

Now a 36! That will be harder if not impossible.
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Postby RW » Tue Aug 28, 2007 11:38 am

Congratulations Mauricio!

I don't think the 36 is impossible, but indeed it must be very hard to find. Hope you can find it anyway!:)

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Postby coloin » Tue Aug 28, 2007 3:34 pm

Well done...that is good.

The significance of the search for a fully symetrical 36.:?:

[Ive just realized there cant be a pattern for 34 or 35 clues] [I cant be the only one !] [I have just read page 1 of this thread.......! impressive study]

Well....the first minimal 36puzzle that was made we were exceptionally fortunate for it was symetrical about the diagonal.:!:
Code: Select all
 *-----------*
 |..3|..6|78.|
 |..6|78.|12.|
 |78.|12.|45.|
 |---+---+---|
 |.31|.64|8..|
 |.64|8..|2..|
 |8..|2..|5..|
 |---+---+---|
 |312|645|...|
 |645|...|...|
 |...|...|...|
 *-----------*


So if this is possible.........What pattern[s] do you have in mind ?

i think the step up from 33 clues to 36 clues is huge.......and it is a lot easier to make puzzles by removing clues from high clue puzzles.

Therefore.......have you tried ?
Starting from Havards set of 38s
Scramble the rows and boxrows a few hundred times
Get the puzzle which has the most clues coinciding with your puzzle template.

If you can get 31-32 clues to line up.......you might have a chance
to go on to make a puzzle approaching the 36 clue template.

You might have to go in stages,32,33,34,35........

I will try the above to see how close I can get....

C

ps A tip I gave Havard......not sure if he used it......
Any more than 6 of one clue value gives a non minimal puzzle !!!
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Postby JPF » Tue Aug 28, 2007 5:52 pm

Congratulations, Mauricio !

Excellent ; a nice and great puzzle.:)

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Postby Mauricio » Thu Aug 30, 2007 1:11 am


If you are just looking for isomorphs of fully symmetrical puzzles, it can be done very fast: First compile a list of all possible fully symmetrical patterns (there are relatively few patterns), and then check if your puzzle is isomorphic (patternwise) to one of that list.
coloin wrote:Therefore.......have you tried ?
Starting from Havards set of 38s
Scramble the rows and boxrows a few hundred times
Get the puzzle which has the most clues coinciding with your puzzle template.

If you can get 31-32 clues to line up.......you might have a chance
to go on to make a puzzle approaching the 36 clue template.

You might have to go in stages,32,33,34,35........

Have you done that already? I will be surprised if you could match more than 28 clues. As for the pattern I'd pick, it would be a pattern such that several of its 32 clues subpatterns have many possible (thousands) minimal sudokus, but I have not done a exhaustive search on the 32's, just a few patterns (7 I think, and several others I could not construct).
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Postby Mauricio » Fri Aug 31, 2007 7:45 am

I know the following puzzle is not fully symmetrical, and it is only a 34, but it has horizontal+vertical symmetry, 2 clues shy of a fully symmetrical puzzle and ER 9.2:
Code: Select all
#34 clues, minimal, horizontal + vertical symmetry, ER 9.2
+-------+-------+-------+
| . . . | . 1 . | . . . |
| . . 1 | 2 . 3 | 4 . . |
| . 2 3 | 5 . 6 | 1 7 . |
+-------+-------+-------+
| . 3 8 | . 2 . | 5 1 . |
| . . . | 8 . 5 | . . . |
| . 4 5 | . 3 . | 8 2 . |
+-------+-------+-------+
| . 6 4 | 3 . 2 | 7 8 . |
| . . 2 | 1 . 7 | 6 . . |
| . . . | . 6 . | . . . |
+-------+-------+-------+
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Postby coloin » Fri Aug 31, 2007 10:52 am

Excellent...I think that is way to progress

I made a lot of difficult puzzles with 29 and 30 clues, but no more. It seems the template choice is critical !!!!!

I wonder if Havard is keen to try to make the ultimate in snowflake puzzles !!!!

I will try to extend your puzzle if I may ?

There just isnt enough room !!!!
The lack of an empty row is also potentially making it difficult !
This is not going to be easy !

I think it is difficult to go straight to the template......perhaps make a 35 with 32/36 of the clues from the template and move sideways to the template from that.

C
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Postby Mauricio » Fri Aug 31, 2007 8:32 pm

coloin wrote:I think it is difficult to go straight to the template......perhaps make a 35 with 32/36 of the clues from the template and move sideways to the template from that.

I could not add more clues to the template, so I took coloin's words.
The following are 17 35's which each one (should) has at least 33 clues of the following pattern (I'd be very grateful if someone can do variations to the puzzles and match more clues):
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 . | . . . |
+-------+-------+-------+

Code: Select all
000010000001203400052604170007030540500002006036040782063401857005308600000000000
000010000001203400052604170007030540500002006063040782036401857005308600000000000
000000000102304500043506210017050840000807000058041720036108470001405600000060000
001020000002304100030105260074000580300508007085040630017403826003602700000000000
001020000002304100035106270084000650300605008056040730010403527003702800000000000
000000000102304500043506210017050840000708000058041720036107480001405600000060000
001020000002304100030501260074000580300805007085040630017403826003206700000000000
001020000002304100035601270084000650300506008056040730010403527003207800000000000
000000000102304500043506210017030840000708000038041720056107480001403600000060000
000000000102304500043506210017050480000708000058041720036107840001405600000060000
000000000001203450032405160067040380000708000048036710025607830006304500000050000
000000000102304500034506210017040830000708000048031720056107380001403600000060000
000000000102304500043506210017030480000708000038041720056107840001403600000060000
000000000001203450032405160067020380000708000028036710045607830006302500000050000
000000000102304500034506210017040380000708000048031720056107830001403600000060000
000000000001203450023405160067030280000708000038026710045607820006302500000050000
000000000102304500043506210017030480000708000038041720056103870001407600000060000

And 2 36's, each one has 32 matching clues:
Code: Select all
001000000002304150003105264067030480000708000038046720015607840006403500000050000
001000000002304150004105263067040380000708000048036720015607830006403500000050000

36's, 33 matching clues
Code: Select all
005010000002304560003506214017030480000708000038040720056107840001403600000060000
005010000002304560004506213017040380000708000048030720056107830001403600000060000
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re: equivalent _patterns_

Postby Pat » Sun Sep 02, 2007 9:50 am

Mauricio wrote:If you are just looking for isomorphs of fully-symmetrical puzzles,
it can be done very fast:
    First compile a list of all possible fully-symmetrical patterns (there are relatively few patterns),

    and then check if your puzzle is isomorphic (patternwise) to one of that list.

good point, Mauricio!

so we should use Ruud's canonicalization,
to be able to recognize equivalent patterns

~ Pat
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Postby Mauricio » Thu Sep 06, 2007 8:42 pm

One more clue (r7c6):
Code: Select all
+-------+-------+-------+
| . . . | . 1 . | . . . |
| . . 1 | 2 3 4 | 5 . . |
| . 2 6 | 5 . 7 | 4 1 . |
+-------+-------+-------+
| . 3 4 | . . . | 6 2 . |
| 2 1 . | . . . | . 5 4 |
| . 6 8 | . . . | 1 3 . |
+-------+-------+-------+
| . 8 2 | 7 . . | 3 4 . |
| . . 3 | 1 2 8 | 7 . . |
| . . . | . 4 . | . . . |
+-------+-------+-------+
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