18er Sudokus with 180° rotational Symmetry

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18er Sudokus with 180° rotational Symmetry

Postby claudiarabia » Mon May 15, 2006 12:06 pm

Where can I find 18er Sudokus with 180° rotational Symmetry. I browsed the forum but the results were quite ample with many pages I can't overview at the moment. Has anybody such?

thanks for your help
Claudia
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Postby ab » Mon May 15, 2006 12:36 pm

here's one I generated:
Code: Select all
...|4..|...
..6|51.|...
.2.|...|7..
-----------
28.|...|...
.9.|...|.3.
...|...|.54
-----------
..3|...|.4.
...|.72|8..
...|..9|...

I got the pattern off the web somewhere, can't remember where, but some guy posted several sudokus with this pattern. This one is different from the ones he posted though:)

Also there's one at this link on page 20:
http://www.geometer.org/mathcircles/sudoku.pdf
ab
 
Posts: 451
Joined: 06 September 2005

Re: 18er Sudokus with 180° rotational Symmetry

Postby Ocean » Mon May 15, 2006 2:13 pm

claudiarabia wrote:Where can I find 18er Sudokus with 180° rotational Symmetry. I browsed the forum but the results were quite ample with many pages I can't overview at the moment. Has anybody such?

thanks for your help
Claudia


This one also has both rotational and reflectional symmetry:
Code: Select all
[sym18]
 . . . | . . . | . 1 .
 . . . | . . 1 | . 2 3
 . . 4 | . 5 . | . . .
-------+-------+-------
 . . . | 6 . . | . 4 .
 . . 7 | . . . | 5 . .
 . 3 . | . . 2 | . . .
-------+-------+-------
 . . . | . 4 . | 6 . .
 8 2 . | 3 . . | . . .
 . 1 . | . . . | . . .


... but it's not minimal. This is the related 'almost symmetrical' 17 (isomorphic to one from Gordon's list of 17s):
Code: Select all
 . . . | . . . | . 1 .
 . . . | . . 1 | . 2 3
 . . 4 | . 5 . | . . .
-------+-------+-------
 . . . | 6 . . | . 4 .
 . . 7 | . . . | 5 . .
 . 3 . | . . 2 | . . .
-------+-------+-------
 . . . | . 4 . | 6 . .
 8 2 . | . . . | . . .
 . 1 . | . . . | . . .


Code: Select all
Some minimal 18s with the same pattern (rotational and reflectional symmetry):

000000010000001023004050000000400050006000700030002000000070400820900000010000000 M18
000000010000001023004050000000600050007000400030002000000080700920400000010000000 M18
000000010000001023004050000000600070005000400030002000000070800820900000010000000 M18
000000010000001023004050000000600070005000800030002000000040600920800000010000000 M18
000000010000001023004050000000600070006000400030002000000070600820400000010000000 M18
000000010000001023004050000000600070008000400030002000000080700720400000010000000 M18
000000010000001023004050000000600070008000900030002000000040600920500000010000000 M18
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby claudiarabia » Mon May 15, 2006 2:44 pm

[quote="ab"]
Code: Select all

...|4..|...
..6|51.|...
.2.|...|7..
-----------
28.|...|...
.9.|.6.|.3.
...|...|.54
-----------
..3|...|.4.
...|.72|8..
...|..9|...


thank you for this nice pattern. It has two solutions as I found out. Thus I changed it a bit. I added a 6 in the center and now it is one-way-defined.

With best regards
Claudia
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Postby ab » Mon May 15, 2006 2:48 pm

claudiarabia wrote:
Code: Select all

...|4..|...
..6|51.|...
.2.|...|7..
-----------
28.|...|...
.9.|.6.|.3.
...|...|.54
-----------
..3|...|.4.
...|.72|8..
...|..9|...


thank you for this nice pattern. It has two solutions as I found out. Thus I changed it a bit. I added a 6 in the center and now it is one-way-defined.

With best regards
Claudia


It only has one solution, you don't need the extra clue in the middle.

If you think otherwise post your solutions here:!:

more links for you:
http://www.csse.uwa.edu.au/~gordon/sudokupat.php?cn=8
http://forum.enjoysudoku.com/viewtopic.php?t=1150&highlight=symmetric+18s
Last edited by ab on Mon May 15, 2006 11:11 am, edited 1 time in total.
ab
 
Posts: 451
Joined: 06 September 2005

Re: 18er Sudokus with 180° rotational Symmetry

Postby claudiarabia » Mon May 15, 2006 2:53 pm

Thank you Ocean,

yes, Gordon's list is realy treasurous. I'll check it out and I'm very happy about your nice figures. It looks like a fly. I'm fascinated by outspoken figures in Sudokus.

With best regards
Claudia
claudiarabia
 
Posts: 288
Joined: 14 May 2006


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