On 2006-04-03, Daniel Fischer
does anybody know whether in a uniquly solvable sudoku-puzzle guessing is never necessary, i.e. by proper reasoning ('if I put 6 here, then there must be a 3 and thus the 4 must go there...' is what I call guessing) there is always at least one entry determined?
No, it sometimes is, (well, depending on your set of base inference rules -- throwing all possible solutions in and doing pattern matching technically allows no-backtracking solutions). Most people use "eliminate all impossible numbers in a given box (that is, that number occurs in same row, column, or square)", combined with "if there is only one place in this {row, column, square} a number can be, place it." But there are additional common patterns such as "if there are N boxes in a {row, column, square}, each with a subset of N numbers, then eliminate those numbers in the other squares. For example if two boxes in a row both only allow 2 and 3, then 2 and 3 can be eliminated from all the other boxes in that row. These are often worth implementing as they can radically reduce guessing. Also worth doing may be chains of reasoning that can restrict a number to be in a given row or column of a square (or square of a row or column), which can then eliminate it from other places. -- Aaron Denney -><-