David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Mon Apr 10, 2006 11:11 pm Post subject: Candidate Lists 


I'm not sure I can explain mandatory pairs, or mutual reception. But I can define candidate lists.
The candidate list for a particular unresolved cell is the set of values that might possibly be placed in that cell without violating the rules of sudoku.
The initial candidate list for an unresolved cell is formed by removing all values already entered in the row, column, and 3x3 box containing that cell from the complete set of symbols {1, 2, 3, ..., 9}.
For example, if r1c1 is unresolved and row 1 contains {1, 2, 3}, column 1 contains {4, 5}, and the top left 3x3 box contains {6, 7}, then the initial candidate list for r1c1 is just {8, 9}.
Most people have to write some candidate lists down while working on a sudoku, especially if it's a tough one. Progress is often made by finding some way to eliminate one or more digits from the initial candidate list for a particular cell.
In general there are only two ways to place the right value in an unresolved cell.
 If the candidate list can be reduced to a single value, that digit must go in this cell ("sole candidate").
 If this cell is the only one in a row/column/box containing a particular candidate, then that digit must go in this cell ("unique in row/column/box").
Ask Alan R about the other terms. dcb 
