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 ChPicard
 Joined: 12 Mar 2008  Posts: 82  :  Location: Montreal, Canada  Items 

Posted: Fri Oct 24, 2008 9:46 pm Post subject: 5472730538 essentially different grids 


Hi
Ed Russell and Frazer Jarvis tell than there are
5 472 730 538 essentially different grids.
See this page:
http://www.afjarvis.staff.shef.ac.uk/sudoku/sudgroup.html
In the Gordon Royle's list, there are 47924 different 17 given sudokus.
Why can't we find at least a valid 17 given sudoku for each different grid?
Thank you 

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 coloin
 Joined: 05 May 2005  Posts: 97  :   Items 

Posted: Wed Oct 29, 2008 10:58 am Post subject: 


Intriquing.........except the answer is simple.
Most grids have a 19sudoku in them.
Some dont [MC or PT grids]
The PT grid has only SIX [all isomorphic] 20puzzles
Code:  ......78..5.1.9.......2...4..1.4.......8....2.9....5..3..2.......4....63...57....
....56...4.7....2..8.3......3......7..58..........2.4...8...9.....91...3.62......
12...........8.3.6..9....5....6...9...5.....28...3.........4..5.749............18
...4...8..5....3.6....27....3...5......8....2..6....4........75..491....9.......8
.2......94.7.8..........15.....4.8....5.....2.9.7......18.........9...63..2..3...
..3.5.......1.9.2.68.......2......9...58.........3...1...26.....74.....3...5..4..

This is also the reason that most grids dont have a 17sudoku.
There just isnt a combination of clues which hits every unavoidable set.
Its a probability qurk that we get the many 17s.....
It is a step to far to expect to get a 16.
see checker http://math.ie/checker.html
C 

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 ChPicard
 Joined: 12 Mar 2008  Posts: 82  :  Location: Montreal, Canada  Items 

Posted: Sat Feb 14, 2009 1:15 pm Post subject: Do you think THE 16 given sudoku exists? 


coloin wrote: 
This is also the reason that most grids dont have a 17sudoku.
There just isnt a combination of clues which hits every unavoidable set.
C 
Hello
I suppose you tried to find a 16 given sudoku with Checker. Do you think it exists?
What is your strategy?
Thank you 

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 coloin
 Joined: 05 May 2005  Posts: 97  :   Items 

Posted: Thu Feb 26, 2009 8:41 pm Post subject: Re: Do you think THE 16 given sudoku exists? 


Checker was written to check that a grid didnt have a 16. The SF grid with 29 17s, was checked as soon as it was optimized to be feasible. However we cant check all grids in the alloted time.
Most reckon that a 16 doesnt exist, we would certainly have found near relatives by now.
Its tricky to prove though.
There are a finite number of different 17puzzles , it will be tricky too to know that we have found them all !!!
I cant imagine there are many left..but we said that 2 years ago on 35000 !
C 

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