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At least how many "opened" numbers?

 
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dixonhsiao

Joined: 28 Jan 2007
Posts: 5
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PostPosted: Tue Jan 30, 2007 3:28 pm    Post subject: At least how many "opened" numbers? Reply with quote

So far we know that,in a normal 3*3 grid sudoku problem,

there is at least 17 "opened" numbers are given,so we can solve the puzzle

with unique solution.I'd like to ask that at least how many is it for those

exotic sudokus ?for example those with grid 5*5 or even 10*10 ?


------------
begging for answer.... Smile
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m_b_metcalf

Joined: 13 Mar 2006
Posts: 210
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Location: Berlin

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PostPosted: Tue Jan 30, 2007 6:40 pm    Post subject: Re: At least how many "opened" numbers? Reply with quote

dixonhsiao wrote:
So far we know that,in a normal 3*3 grid sudoku problem,

there is at least 17 "opened" numbers are given,so we can solve the puzzle

with unique solution.I'd like to ask that at least how many is it for those

exotic sudokus ?for example those with grid 5*5 or even 10*10 ?


17 for 9x9 is not proven, only highly likely. I've seen 16x16 with 70 givens. I've generated 25x25 with about 250 but lower is certainly possible. My minimal 100x100 has 6196 but fewer is also possible. It takes so long to make these monsters that no-one is going to find a minimum experimentally and there is no theory to hint at an answer.

Regards,

Mike Metcalf
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Pat

Joined: 06 Sep 2006
Posts: 128
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PostPosted: Thu Feb 01, 2007 3:35 pm    Post subject: re: minimum number of clues - box-size 4x4 Reply with quote

m_b_metcalf wrote:

    I've seen 16x16 with 70 givens


amazing!
the best i've seen so far was 77
    could you please point me to a 70-clue example?
    thanks!!
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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 Feb 01, 2007 4:06 pm    Post subject: Re: re: minimum number of clues - box-size 4x4 Reply with quote

Pat wrote:
m_b_metcalf wrote:

    I've seen 16x16 with 70 givens


amazing!
the best i've seen so far was 77
    could you please point me to a 70-clue example?
    thanks!!


Sorry, my error (and that explains why I couldn't find it). My own best effort is 85 (edit below).

Regards,

Mike Metcalf

Code:

  .  .  .  .  .  .  .  .  .  .  .  .  7  .  .  .
  .  .  .  .  .  .  .  .  .  .  .  2  .  . 15  .
  .  .  8  . 11  .  .  .  .  .  .  .  .  . 13  .
  . 10  .  .  .  .  8  .  .  . 12  .  6  3  .  .
  4  .  .  .  .  . 15  . 14  .  .  .  . 12  .  .
  .  .  .  .  3  .  .  . 16  1  .  . 11  .  . 14
  . 12 13  .  9  .  .  5  .  . 15  .  .  .  .  7
 10  6  .  1  .  .  .  .  .  .  .  7  3  .  .  .
  .  .  . 14  .  .  2  .  .  .  .  .  . 13  . 11
  .  1  4 16  .  6  . 12  2  . 14 10  .  .  .  .
  . 13  .  . 15  5  .  .  6  .  .  3  .  4  .  .
  .  9 11  .  . 13  .  . 12  .  5  8  .  2  1  3
  .  .  .  4  . 14 13  .  7  . 10  .  . 15  8  1
 16  .  .  9  .  .  6  .  .  .  8  .  .  .  . 13
  .  .  2  .  . 12 16  7  5  .  9  .  .  . 10  .
 15  3  .  . 10  1  .  .  .  2  .  .  . 16 11  .
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