FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    solving methods based on conjugate pairs          Sudoku Programmers Forum Index -> Solving sudoku View previous topic :: View next topic   Author Message shoop Joined: 17 Aug 2006 Posts: 35 : Items Posted: Fri Aug 25, 2006 11:21 am    Post subject: solving methods based on conjugate pairs If I understand correctly, the following solving methods are all based on the location of conjugate pairs: coloring fishy cycles nice loops Now my questions are: (1) is it true that fishy cycles generalize simple coloring, and nice loops generalize fishy cycles, and that turbot fish is a special case of fishy cycles? (I might have made this up). (2) I have seen claims that fishy cycles generalise swordfish but I don't see how this can be the case, since as I understand it swordfish is not based on conjugate pairs... example: Code: *..|*..|*.. ***|***|*** ***|***|*** ---+---+--- *..|*..|*.. ***|***|*** ***|***|*** ---+---+--- *..|*..|*.. ***|***|*** ***|***|*** Here, you can use swordfish to eliminate all candidates from rows 2, 3, 5, 6, 8 and 9 but there are no strong links, so I don't see how you could use any of the solving methods mentioned above to get the same result. Sorry for being such a newbie, but I'm really trying to get my head around all of this stuff. I'm sure some of you people out there can answer my questions in the blink of an eye. Cheers! Back to top Jean-Christophe Joined: 19 Mar 2006 Posts: 126 : Location: Belgium Items Posted: Thu Aug 31, 2006 8:24 am    Post subject: Swordfish (or Jellyfish...) Using strong links AKA conjugate pairs are limited to particular cases sometimes refered as "222" (or "2222") Here is a 222 swordfish Code: *..|*..|... ***|***|*** ***|***|*** ---+---+--- *..|...|*.. ***|***|*** ***|***|*** ---+---+--- ...|*..|*.. ***|***|*** ***|***|*** Now, this could be generalized to any swordfish by extending the strong links principle to include up to 3 cells, conjugate "triplets". For jellyfish, up to 4... _________________ Jean-Christophe "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes. Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Thu Aug 31, 2006 11:16 am    Post subject: This is actually the "old" definition for a Swordfish (or Jellyfish). 2-2-2 is the minimal number of candidates that can form a Swordfish. It can go all the way to 3-3-3, in which case there are no strong links at all. Ruud _________________ Meet me at sudocue.net Back to top Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First         Sudoku Programmers Forum Index -> Solving 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