FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    5472730538 essentially different grids          Sudoku Programmers Forum Index -> The mathematics of sudoku View previous topic :: View next topic   Author Message 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 Back to top 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 19-sudoku in them. Some dont [MC or PT grids] The PT grid has only SIX [all isomorphic] 20-puzzles 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 17-sudoku. 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 Back to top 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 17-sudoku. 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 Back to top 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 17-puzzles , 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 Back to top Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First         Sudoku Programmers Forum Index -> The mathematics of sudoku All times are GMT Page 1 of 1   Jump to: Select a forum Sudoku----------------Solving sudokuSetting sudokuProgramming sudokuThe mathematics of sudokuExotic sudoku Library----------------PuzzlesSoftwareSudoku elsewhere Not sudoku----------------Random thoughtsForum feedback  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 Igloo Theme Version 1.0 :: Created By: Andrew Charron