Fully symmetrical puzzles

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

Postby ravel » Mon Jul 17, 2006 10:21 am

Ocean,
i could only find 22 (equivalent) of the 50 hard puzzles in the list (OceanM20). Whats wrong here?
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Postby Ocean » Mon Jul 17, 2006 10:59 am

ravel wrote:Ocean,
i could only find 22 (equivalent) of the 50 hard puzzles in the list (OceanM20). Whats wrong here?


You are right, some of the hard puzzles listed are not in the published list:
1. Those that are not absolutely minimal were deliberately omitted when the 10117-list was compiled. For the specific pattern there were about 300 such puzzles, and several of them turned out to be hard when I checked them recently. (For instance those rated 9.7 and 9.6 can be reduced to 19 clues).
2. After compilation of the 10117-list, another 1000 puzzles were found in this pattern. These extra puzzles are also searched, and some hard from this set are inclued.

Only a small part of the compilation is tested in Explainer, because it's rather time-consuming. So the 'hard list' should be regarded as a sample set, not a complete list.
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Postby ravel » Mon Jul 17, 2006 11:11 am

Thanks,

i have tried to filter hardies in the list with gsf's solver. The linux version seems to give only ratings between 1 and 9. But the problem is that many of my hardest only are 8-rated there and there are about 4000 8-rated in the list, too much for my solver. So many thanks for your work to get short lists with hardies.
PS: Conversely i tested some gsf-9-rated and got less than 8.5 in the Explainer.
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Postby gsf » Mon Jul 17, 2006 1:15 pm

ravel wrote:i have tried to filter hardies in the list with gsf's solver. The linux version seems to give only ratings between 1 and 9. But the problem is that many of my hardest only are 8-rated there and there are about 4000 8-rated in the list, too much for my solver. So many thanks for your work to get short lists with hardies.
PS: Conversely i tested some gsf-9-rated and got less than 8.5 in the Explainer.

try -O -f%r or -O -f%Q (ratings with techniques applied)
these ratings take into account backdoor size/counts
also, this puzzle from ocean's list
Code: Select all
001000200030040050600000007000103000080000030000604000200000006040050080007000100

has backdoor size 2 (up to xy cycles, no uniqueness) -- the first one I've seen
my rating doesn't take this into account -- it should be one of the toughest
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Postby ravel » Mon Jul 17, 2006 1:49 pm

Thanks, but i get
sudoku: -O: unknown option
(downloaded the source today)

The puzzle you mentioned is number 1 in my hardest list:)

%Q (number of backtrack/lookahead guesses) alone gives numbers between 2 and 125 for my list, where this hardest has 14.

[Edit:] When using -o (lower case) i still get 3669 'very difficult' puzzles in OceanM20.
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Postby gsf » Mon Jul 17, 2006 9:17 pm

ravel wrote:Thanks, but i get
sudoku: -O: unknown option
(downloaded the source today)

posted source lags binaries by a few months
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A question

Postby Eioru » Sat Aug 19, 2006 9:15 am

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 )
Thanks everyone find fully symmetric satisfied anyone and it's better to satisfy both two.

I find a fully symmetric puzzle having 3 empty rows and 3 empty lines.
340806012
600502004
000000000
720401069
000000000
460705021
000000000
500103006
870604095
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Re: A question

Postby JPF » Sun Aug 20, 2006 8:14 pm

Eioru wrote:I find a fully symmetric puzzle having 3 empty rows and 3 empty lines.

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

Nice.
Actually, it's an easy pattern.

This one, easy too, has 7 empty units (1 box, 3 rows, 3 cols) and 24 clues :
Code: Select all
 . 1 . | 7 . 2 | . 5 .
 8 . . | 4 . 9 | . . 7
 . . . | . . . | . . .
-------+-------+-------
 3 6 . | . . . | . 8 9
 . . . | . . . | . . .
 4 2 . | . . . | . 7 1
-------+-------+-------
 . . . | . . . | . . .
 9 . . | 2 . 6 | . . 3
 . 3 . | 5 . 1 | . 2 .

[10-2-0-0-0]


There are 3 non equivalent patterns with 20 clues and 7 empty units :
[0-2-6-0-0]
[0-4-6-0-0]
[0-6-4-0-0]

Here is one [0-4-6-0-0] ~ [26-0-0-0-0] for example :
Code: Select all
 x . x | x . x | x . x
 . . . | . . . | . . .
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 . . . | . . . | . . .
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 . . . | . . . | . . .
 x . x | x . x | x . x

[26-0-0-0-0]


It is more than probabble that these 3 patterns don't have any valid puzzles.

Last point, it's not clear to me if a fully symmetical pattern can have 4 empty boxes + 1 empty row + 1 empty col. :

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



I was not able to get less than 8 solutions.
Code: Select all
385000967412000538679000412000807000000000000000309000927000684548000391136000725


Any idea ?

JPF
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Postby Eioru » Wed Aug 23, 2006 3:26 am

I can't find puzzle with this pattern

xooxoxoox
ooxoooxoo
oxoooooxo
xooxoxoox
ooooooooo
xooxoxoox
oxoooooxo
ooxoooxoo
xooxoxoox
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Postby JPF » Wed Aug 23, 2006 6:46 am

Eioru wrote:I can't find puzzle with this pattern

xooxoxoox
ooxoooxoo
oxoooooxo
xooxoxoox
ooooooooo
xooxoxoox
oxoooooxo
ooxoooxoo
xooxoxoox

Here is one :

Code: Select all
[SM24 18-4-0-2-0]

 9 . . | 1 . 5 | . . 7
 . . 5 | . . . | 6 . .
 . 1 . | . . . | . 5 .
-------+-------+-------
 8 . . | 7 . 3 | . . 2
 . . . | . . . | . . .
 7 . . | 5 . 6 | . . 3
-------+-------+-------
 . 5 . | . . . | . 1 .
 . . 2 | . . . | 4 . .
 3 . . | 9 . 2 | . . 5



In this thread you can find this one from ab (20 clues, minimal) as well :

Code: Select all
#09 ab
[M20  2-4-0-2-0 ]

 . . . | 4 . 5 | . . .
 . . 9 | . . . | 8 . .
 . 7 . | . . . | . 4 .
-------+-------+-------
 3 . . | 9 . 8 | . . 6
 . . . | . . . | . . .
 8 . . | 3 . 2 | . . 5
-------+-------+-------
 . 5 . | . . . | . 9 .
 . . 7 | . . . | 4 . .
 . . . | 5 . 1 | . . .

2-4-0-2-0   2-8-4-2-0   4-2-0-2-0   8-0-2-2-0   16-2-4-2-0   16-8-2-2-0


JPF
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Postby Eioru » Sat Aug 26, 2006 10:07 am

Can I get the pattern of the Ocean's hardest puzzles.Thanks.
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Postby daj95376 » Sat Aug 26, 2006 4:22 pm

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

They are symmetrical around the /-diagonal.
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Fermion's fully-symmetrical puzzles

Postby Pat » Sun Jul 29, 2007 12:24 pm

Fermion (2006.Jun.15-16) wrote:

      [ 32 clues ]
Code: Select all
 4 . . | . . . | . . 6
 . . 9 | 7 . 6 | 2 . .
 . 8 . | 4 . 9 | . 3 .
-------+-------+------
 . 2 6 | 1 . 3 | 4 9 .
 . . . | . . . | . . .
 . 1 4 | 5 . 7 | 6 2 .
-------+-------+------
 . 4 . | 8 . 1 | . 5 .
 . . 5 | 2 . 4 | 8 . .
 2 . . | . . . | . . 1


      [ 32 clues ]
Code: Select all
 . . . | . 1 . | . . .
 . . 9 | 7 . 6 | 2 . .
 . 8 . | 4 . 9 | . 3 .
-------+-------+------
 . 2 6 | 1 . 3 | 4 9 .
 9 . . | . . . | . . 7
 . 1 4 | 5 . 7 | 6 2 .
-------+-------+------
 . 4 . | 8 . 1 | . 5 .
 . . 5 | 2 . 4 | 8 . .
 . . . | . 3 . | . . .



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Postby JPF » Sun Jul 29, 2007 9:40 pm

Nice puzzles:)

If you like a bit harder :

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

ER=8.3


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

ER=8.9

Actually, it is not too difficult to build up a full symmetrical puzzle with 32 clues.

Challenge :
for each pattern, find fully symmetrical 20,24,28 clues puzzles having a pattern included in it (sub pattern)

Example : from the first pattern, here's a 28 clues, minimal :
Code: Select all
 . . . | . . . | . . .
 . . 1 | 2 . 3 | 4 . .
 . 4 . | 5 . 6 | . 7 .
-------+-------+-------
 . 6 4 | 7 . 5 | 3 1 .
 . . . | . . . | . . .
 . 1 8 | 6 . 4 | 2 5 .
-------+-------+-------
 . 5 . | 4 . 1 | . 2 .
 . . 9 | 3 . 2 | 1 . .
 . . . | . . . | . . .

ER=8.9
it's a sub pattern of pattern 2 as well.

JPF
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Postby Eioru » Tue Jul 31, 2007 10:58 pm

Code: Select all
..5.2.4..
.4.....5.
6...8...2
...6.9...
1.3...5.7
...3.5...
8...6...1
.7.....4.
..9.3.8..


ER=6.9 and
1 x Unique Rectangle type 1
1 x Unique Rectangle type 2
1 x Unique Rectangle type 3
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