The New Sudoku Players' Forum

[m_b_metcalf]

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

[m_b_metcalf]

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

[JPF]

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

[Havard]

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

[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!

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 .
 . . . . . . . . .



JPF

[claudiarabia]

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!

Claudia

[ravel]

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 .


[m_b_metcalf]

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

[Mauricio]

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.

[Havard]

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?

Havard

[JPF]

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

[m_b_metcalf]

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

[Mauricio]

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.

[Mauricio]

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.

[m_b_metcalf]

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