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Re: a double diagonal symmetric 19clue-pattern

Postby m_b_metcalf » Sun Jun 03, 2007 5:39 pm

claudiarabia wrote:here it is:

I checked up to d=2 on Claudia's and the first two of Muaricio's, with no success. I think JPF goes to d=3 but it looks hopeless:( . A feature of all these 'puzzles' is that there is one clue value missing.

Regards,

Mike Metcalf
Last edited by m_b_metcalf on Sun Jun 03, 2007 3:21 pm, edited 1 time in total.
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Postby m_b_metcalf » Sun Jun 03, 2007 5:52 pm

JPF wrote:I finally got it:)

Here is a 19 clues-puzzle with vertical symmetry and non diagonal boxes :


Another triumph:!: . I'm still at 20 clues, with rotational symmetery:
Code: Select all
 7 4 9 . . . . . .
 . . . 2 . . . . .
 . . . . . . 6 1 5
 . . . . . . 4 9 .
 . . . 6 . 9 . . .
 . 8 1 . . . . . .
 2 6 5 . . . . . .
 . . . . . 8 . . .
 . . . . . . 9 3 7

Regards,

Mike Metcalf
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Postby JPF » Sun Jun 03, 2007 10:58 pm

May I propose this compromise :

Code: Select all
 1 . . . 2 . . . .
 . . . 3 . . . 4 .
 . . 5 . . . 6 . .
 . 3 . . . 6 . . .
 2 . . . 7 . . . 5
 . . . 4 . . . 8 .
 . . 6 . . . 9 . .
 . 9 . . . 2 . . .
 . . . . 5 . . . 1
SE=7.3

19 clues, diagonal & anti-diagonal symmetry
All the boxes are diagonal.

JPF
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Postby Havard » Sun Jun 03, 2007 11:57 pm

JPF wrote:I finally got it:)

Here is a 19 clues-puzzle with vertical symmetry and non diagonal boxes :

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

SE=6.6

JPF


On a suggestion from Wapati, I took this sudoku and tried to make 17's out of it here: http://forum.enjoysudoku.com/viewtopic.php?t=5461

Hope you don't mind!:)

Havard
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Postby JPF » Mon Jun 04, 2007 10:23 am

Havard wrote:On a suggestion from Wapati, I took this sudoku and tried to make 17's out of it here: http://forum.enjoysudoku.com/viewtopic.php?t=5461
Hope you don't mind!:)

I'm glad that this puzzle can be of any use for finding 17's:)

Here's one puzzle, 23 clues, minimal, with symmetries :

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


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Postby claudiarabia » Tue Jun 05, 2007 8:47 am

JPF wrote:May I propose this compromise :

Code: Select all
 1 . . . 2 . . . .
 . . . 3 . . . 4 .
 . . 5 . . . 6 . .
 . 3 . . . 6 . . .
 2 . . . 7 . . . 5
 . . . 4 . . . 8 .
 . . 6 . . . 9 . .
 . 9 . . . 2 . . .
 . . . . 5 . . . 1
SE=7.3

19 clues, diagonal & anti-diagonal symmetry
All the boxes are diagonal.

JPF


What a nice compromise! Now I think the corner-boxes are more crucial to make a sudoku valid then the others. Before I was thinking that the boxes between the corner-boxes are more difficult to be left with one seed only. For this, with 19 clues only for the whole sudoku, 1 clue for two of the corner-boxes is to few to get a valid sudoku out of it even when the other two have 3 numbers. Maybe Gordon Royle could explain why it is like this. I shall transfer this discussion to the pattern-with-no-sudoku-path.

And your lemniskate is superb! When I take away one clue - app. 3000 solutions!

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Postby ravel » Tue Jun 05, 2007 9:27 am

Dont forget, that your pattern
Code: Select all
. . . . x . . . x
. . . x . . . x .
. . x . . . x . .
. x . . . x . . .
x . . . x . . . x
. . . x . . . x .
. . x . . . x . .
. x . . . x . . .
x . . . x . . . .
is equivalent to this one (swap bands 1 and 2 and stacks 2 and 3):
Code: Select all
. x . . . . . . x
x . . . . x . x .
. . . . x . x . .
. . . . . x . x .
. . . . x . x . .
. . x x . . . . .
. . x x . . . . .
. x . . . . . . x
x . . . . . . x .
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Re: A prize-worth sudoku

Postby m_b_metcalf » Tue Jun 05, 2007 7:35 pm

claudiarabia wrote:As far as I know, 19 is the minimal clue-number from which you can do some horizontal symmetry. Correct me if this statement is overhauled now.

What is the minimum number for rotational symmetry? Here is 18:
Code: Select all
 1 2 3 . . . . . .
 . . . 4 5 6 . . .
 . . . . . . . . .
 . . . . . . 4 1 7
 . . . . . . . . .
 8 6 5 . . . . . .
 . . . . . . . . .
 . . . 1 9 8 . . .
 . . . . . . 5 2 6  SE 2.0

Regards,

Mike Metcalf
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Re: A prize-worth sudoku

Postby Mauricio » Wed Jun 06, 2007 9:16 am

m_b_metcalf wrote:
claudiarabia wrote:As far as I know, 19 is the minimal clue-number from which you can do some horizontal symmetry. Correct me if this statement is overhauled now.

What is the minimum number for rotational symmetry? Here is 18:


And here a minimum 20 clue for full symmetry:
Code: Select all
1 . .|. . .|. . 2
. 2 .|. . .|. 3 .
. . 4|. 5 .|6 . .
-----+-----+-----
. . .|6 . 7|. . .
. . 8|. . .|9 . .
. . .|3 . 1|. . .
-----+-----+-----
. . 6|. 3 .|8 . .
. 7 .|. . .|. 1 .
2 . .|. . .|. . 3


Sudokus with full symmetry have 4n or 4n+1 clues, so the next possible lower number of clues for a sudoku with full symmetry is 17, which I do not think it is possible.
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Re: A prize-worth sudoku

Postby Havard » Wed Jun 06, 2007 10:20 am

Mauricio wrote:Sudokus with full symmetry have 4n or 4n+1 clues, so the next possible lower number of clues for a sudoku with full symmetry is 17, which I do not think it is possible.


Well, if you could make a 18 with the property: "take away one clue to make the pattern have full symmetry", I could start a search with that 18 as a seed?:)

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Re: A prize-worth sudoku

Postby JPF » Wed Jun 06, 2007 11:52 am

Mauricio wrote:And here a minimum 20 clue for full symmetry:
Code: Select all
1 . .|. . .|. . 2
. 2 .|. . .|. 3 .
. . 4|. 5 .|6 . .
-----+-----+-----
. . .|6 . 7|. . .
. . 8|. . .|9 . .
. . .|3 . 1|. . .
-----+-----+-----
. . 6|. 3 .|8 . .
. 7 .|. . .|. 1 .
2 . .|. . .|. . 3
Sudokus with full symmetry have 4n or 4n+1 clues, so the next possible lower number of clues for a sudoku with full symmetry is 17, which I do not think it is possible.

For more about fully symmetric puzzles, see here

JPF
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Re: A prize-worth sudoku

Postby m_b_metcalf » Wed Jun 06, 2007 12:22 pm

JPF wrote:
Mauricio wrote:Sudokus with full symmetry have 4n or 4n+1 clues, so the next possible lower number of clues for a sudoku with full symmetry is 17, which I do not think it is possible.

For more about fully symmetric puzzles, see here

Yes, but I was wondering about rotational (crossword) symmetry. And is something like the following conceivable?
Code: Select all
 1 2 3 . . . . . .
 . . . 4 . 6 . . .
 . . . . . . . . .
 . . . . . . 4 1 7
 . . . . 2 . . . .
 8 6 5 . . . . . .
 . . . . . . . . .
 . . . 1 . 8 . . .
 . . . . . . 5 2 6    15670 solutions

Regards,

Mike Metcalf
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Re: A prize-worth sudoku

Postby Mauricio » Wed Jun 06, 2007 2:21 pm

m_b_metcalf wrote:What is the minimum number for rotational symmetry? Here is 18:


I was very lucky to found "randomly" this puzzle:
Code: Select all
1 . .|. . .|. . 2
. 3 .|4 . 5|. . .
. . .|. . .|6 . .
-----+-----+-----
. . 5|. . .|7 . .
. . .|3 . 8|. . .
. . 6|. . .|2 . .
-----+-----+-----
. . 2|. . .|. . .
. . .|9 . 1|. 3 .
7 . .|. . .|. . 4


I said "randomly", as my search was not so random, I was looking selectively for something else and this puzzle popped out. It is my first 18, BTW.
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Re: A prize-worth sudoku

Postby Mauricio » Thu Jun 07, 2007 8:17 am

m_b_metcalf wrote:Yes, but I was wondering about rotational (crossword) symmetry. And is something like the following conceivable?

Do you mean sudokus with 17 clues and rotationally symmetric?
I scanned gordon's list searching for sudokus that are equivalent to a pattern with 17 clues and rotationally symmetric, and none appeared.
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Re: A prize-worth sudoku

Postby m_b_metcalf » Thu Jun 07, 2007 11:57 am

Mauricio wrote:Do you mean sudokus with 17 clues and rotationally symmetric?
I scanned Gordon's list searching for sudokus that are equivalent to a pattern with 17 clues and rotationally symmetric, and none appeared.

Yes, that's what I meant. Thanks for doing the search. Are there any other symmetric 18-clues puzzles, or are these two the first to be published?

Regards,

Mike Metcalf
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