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curi
Joined: 05 Aug 2006 Posts: 2 Location: Atlanta, GA USA

Posted: Sat Aug 05, 2006 1:31 am Post subject: 3 theoretical questions 


Denote a basic puzzle as one determining a unique 9x9 square, but also with no superfluous numbers. Denote the 3x3 compartments demarcated by heavy lines as the sections:1,2 and 3 left to right in the top row; 4,5 and 6 in the middle row; and 7,8 and 9 in the bottom row.
1. Every one I've seen has the same number of digits in sections
1 and 9, 3 and 7, 4 and 6, 2 and 8. Has this been proven?
2. The least number of digits I've seen is 17? Is this the minimum?
3. The greatest number of digits is harder as I'm not sure I've
eliminated all superfluous digits. Is the greatest number known?
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Last edited by curi on Fri Feb 04, 2011 1:25 am; edited 1 time in total 

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Marty R.
Joined: 12 Feb 2006 Posts: 5256 Location: Rochester, NY, USA

Posted: Sat Aug 05, 2006 3:30 am Post subject: 


Quote:  1. Every one I've seen has the same number of digits in sections
1 and 9, 3 and 7, 4 and 6, 2 and 8. Has this been proven? 
I don't understand the question: has WHAT been proven? Most published puzzles are symmetrical, but it's not a requirement. Some sources offer asymmetrical puzzles, but I don't see any differences in the approach taken to solve them. 

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keith
Joined: 19 Sep 2005 Posts: 3192 Location: near Detroit, Michigan, USA

Posted: Sat Aug 05, 2006 9:20 am Post subject: 


Quote:  2. The least number of digits I've seen is 17? Is this the minimum? 
Yes, 17 is the least known number of initial clues for a puzzle that has a single, unique, solution. It has not been proved.
You should read the article on Sudoku at Wikipedia:
http://en.wikipedia.org/wiki/Sudoku
and you will find lots of discussion on symmetries, patterns, minimal and maximal puzzles, etc. at this forum:
http://www.sudoku.com/forums/
Keith 

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curi
Joined: 05 Aug 2006 Posts: 2 Location: Atlanta, GA USA

Posted: Tue Aug 08, 2006 1:35 am Post subject: Sudoku Theoretical Questions 


Thanks, Keith. The Wikipedia article was just what I wanted. However, the largest puzzle in which every digit is needed for uniqueness is still not
known.
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