FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    simple logical description of locked candidates          Sudoku Programmers Forum Index -> Solving sudoku View previous topic :: View next topic   Author Message Bob Hanson Joined: 05 Oct 2005 Posts: 187 : Location: St. Olaf College Items Posted: Fri Dec 02, 2005 3:37 am    Post subject: simple logical description of locked candidates oooh, I just stumbled on this: Locked candidate rule: !(r ^ !b) <--> !(b ^ !r) This says, "If candidate k is not possible in the part of a row that is not within a certain block, then candidate k is not possible in the part of that block not within that row. " And vice-versa. You have to like this symmetry! b and r have to intersect, of course. Hmm, in general, for any row and block, then, we have: (r ^ b) ^ !(r ^ !b) <--> (r ^ b) ^ !(b ^ !r) something like that.... _________________ Bob Hanson Professor of Chemistry St. Olaf College Northfield, MN http://www.stolaf.edu/people/hansonr Back to top evert Joined: 30 Aug 2005 Posts: 68 : Location: Amsterdam Items Posted: Mon Dec 12, 2005 11:42 am    Post subject: Is there a conventional name for the three cells that a box and a column/row could have in common? In the grid below 1 can be placed in r1c9. Code: ; ; ; ; ; ; ; ; ; 2;3; ; ; ; ; ; ;8; 4;5; ; ; ; ; ; ;7;  ; ; ; ; ; ; ; ;6;  ; ; ; ; ; ; ; ; ;  ; ; ; ; ; ; ; ;5;  ; ; ; ; ; ; ; ;4;  ; ; ; ; ; ; ; ;3;  ; ;1; ; ; ; ; ;2; The direct logic would be: Within box 1 1 can only be placed in cells 1 and 2. Therefore 1 can be excluded as candidate for all other cells of row 1. Do I understand correctly that this is called locked candidates? Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Mon Dec 12, 2005 12:19 pm    Post subject: evert wrote: Is there a conventional name for the three cells that a box and a column/row could have in common? Several: line-box intersection, minirow & minicolumn, boxrow & boxcolumn. I currently use the term segment. The technique works in 2 directions, from line to box and from box to line. "when all candidates for a specific digit in a row or column are located in the intersection with a single box, that box can be cleared of all other candidates for that digit." reversed, this reads: "when all candidates for a specific digit in a box are located in the intersection with a single row or column, that row or column can be cleared of all other candidates for that digit." Quote: Do I understand correctly that this is called locked candidates? This technique is called "locked candidates" or "line-box interactions" or "block-block interactions" or "row/column-block interactions" or "pointing pairs" and many other creative names. On a more advanced note: Currently, I am looking at this as an example of constraint subsets (size 1): When you can find 2 constraints (A and B), where all possible candidates in constraint A are also present in constraint B, then constraint B can be cleared of all candidates, except those also present in constraint A. For clarification: There are 4 types of constraints, 81 of each type: 1. All candidates for a single cell. 2. All candidates for a digit in a row. 3. All candidates for a digit in a column. 4. All candidates for a digit in a box. The same rule can also be applied to naked and hidden singles. 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