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How small is the smallest X-sdoku?

 
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m_b_metcalf

Joined: 13 Mar 2006
Posts: 210
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Location: Berlin

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PostPosted: Thu Mar 16, 2006 11:51 pm    Post subject: How small is the smallest X-sdoku? Reply with quote

In another thread (http://www.setbb.com/sudoku/viewtopic.php?t=771&mforum=sudoku) I posted an X-sudoku with only 15 givens. Here is another:

Code:

                          8
  9              4         
        4              7   
                 1         
  2              9  3  4   
     8        3           
                           
        3  7               
                          5


Has anyone have any idea how much smaller one can go?

Thanks,

Mike Metcalf
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Ruud
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Joined: 17 Sep 2005
Posts: 708
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Location: Netherlands

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PostPosted: Thu Mar 16, 2006 11:57 pm    Post subject: Reply with quote

How about this one, Mike?

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


13 clues, unique solution.

Ruud.
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m_b_metcalf

Joined: 13 Mar 2006
Posts: 210
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Location: Berlin

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PostPosted: Fri Mar 17, 2006 1:24 pm    Post subject: Reply with quote

Ruud wrote:
13 clues, unique solution.

Ruud.


Ruud,
Thanks. I'll have to try harder! (The smallest in Monckton's book is 16, I believe.)

Regards,

Mike Metcalf
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LangPol

Joined: 20 Mar 2006
Posts: 6
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PostPosted: Mon Mar 20, 2006 1:33 am    Post subject: Reply with quote

Alas, I don't believe that there is a unique solution.

e.g.,

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

2 8 4 | 9 3 7 | 6 5 1
7 3 1 | 5 4 6 | 8 9 2
9 6 5 | 8 2 1 | 4 3 7
------+-------+------
4 5 3 | 7 8 2 | 9 1 6
8 9 6 | 1 5 3 | 7 2 4
1 7 2 | 4 6 9 | 5 8 3
------+-------+------
3 4 9 | 6 1 8 | 2 7 5
5 2 8 | 3 7 4 | 1 6 9
6 1 7 | 2 9 5 | 3 4 8
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Ruud
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PostPosted: Mon Mar 20, 2006 1:49 am    Post subject: Reply with quote

LangPol wrote:
Alas, I don't believe that there is a unique solution.

e.g.,

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


This is Sudoku-X. The diagonals also need to contain digits 1 thru 9.

Ruud.
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