dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

3 theoretical questions

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> General discussion
View previous topic :: View next topic  
Author Message
curi



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

PostPosted: Sat Aug 05, 2006 1:31 am    Post subject: 3 theoretical questions Reply with quote

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?
________
universal health warehouse


Last edited by curi on Fri Feb 04, 2011 1:25 am; edited 1 time in total
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sat Aug 05, 2006 3:30 am    Post subject: Reply with quote

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.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sat Aug 05, 2006 9:20 am    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
curi



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

PostPosted: Tue Aug 08, 2006 1:35 am    Post subject: Sudoku Theoretical Questions Reply with quote

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.
________
Toyota TS010 history
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> General discussion All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group