FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    Medusa chain strength          Sudoku Programmers Forum Index -> Solving sudoku View previous topic :: View next topic   Author Message Pep Joined: 27 Nov 2005 Posts: 10 : Location: Bath, UK Items Posted: Sat Dec 03, 2005 8:35 pm    Post subject: Medusa chain strength If I understand Medusa chains correctly, there are strong chains where all the implications from one node to the next also work in the reverse direction, and weak ones where they work only one way. Consider a cell C where r meets c meet, and therein we have either a 9 or not. And suppose that there is one other cell in the box, B, containing C which has a 9, say at D. Then there is a strong inference between C and D for 9. Now look at another case of a B where D and E both contain 9 as well as C. Both D and E are in the same box and a row, say R. And in columns K,L respectively. And suppose each of R, K and L contain only one other 9. Now the links between C and D, and between C and E are weak. But the link between the 9 in R and the two cells D and E _together_ is strong, and so is the one through B because the two cells D and E can be treated as a single entity in this case. Either exactly one is a 9 or none is. Do I understand the situation properly? Back to top Bob Hanson Joined: 05 Oct 2005 Posts: 187 : Location: St. Olaf College Items Posted: Sat Dec 03, 2005 9:17 pm    Post subject: OK, I think I'm following you. Yes, I think that's pretty much the idea. Quote: Consider a cell C where r meets c meet, and therein we have either a 9 or not. And suppose that there is one other cell in the box, B, containing C which has a 9, say at D. Then there is a strong inference between C and D for 9. Code:   :   c B :  \: ..9C.....r..   :\   : 9D   :  \ Yes, that's correct. Quote: Now look at another case of a B where D and E both contain 9 as well as C. Both D and E are in the same box and a row, say R. And in columns K,L respectively. And suppose each of R, K and L contain only one other 9. Code:     K     L     |     | R---9D----9E---     |.   .|     | . . |     |  9C |     |     |     |     |     9     9     |     | Quote: Now the links between C and D, and between C and E are weak. But the link between the 9 in R and the two cells D and E _together_ is strong, and so is the one through B because the two cells D and E can be treated as a single entity in this case. Either exactly one is a 9 or none is. I would NOT recommend thinking about 9D and 9E as one entity. They have different properties with respect to their OTHER candidates in their same cells. One will be TRUE and the other FALSE. By the way, because 9C has a weak link to both parities of this chain (call them A and a), it can be eliminated. The Medusa idea focuses on "marks" or "possibilities" rather than "cells." The strong links are D(F)<==>E(T) and E(F)<==>D(T) and the weak ones are only D(T)==>C(F). What makes it useful is that a FALSE can drive a TRUE -- that's the value of a strong connection. My first attempt at discussion of X-cycles, Y-cycles, and the relation to 3D Medusa is at http://www.stolaf.edu/people/hansonr/sudoku/top95-analysis.htm#medusa _________________ Bob Hanson Professor of Chemistry St. Olaf College Northfield, MN http://www.stolaf.edu/people/hansonr 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