TITLE: Sudoku puzzles and propositional logic
QUESTION [6 upvotes]: I am currently reading about how to solve Sudoku puzzles using propositional logic. More specifically, they use the compound statement 
$$\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$$
where $p(i,j,n)$ is the proposition that is true when the number
$n$ is in the cell in the $ith$ row and $jth$ column, to denote that every row contains every number. I know that this is what the entire compound statement implies, but I am trying to read each individual statement together. Taking one single case, does 
$$\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$$
say that in the first row, the number one will be found in the first column, or second column, or third column, etc?

REPLY [3 votes]: Although expressible as propositional logic, for practical solutions, it is computationally more effective to view Sudoku as a Constraint Satisfaction Problem. See Chapter 6 of Russell and Norvig: Artificial Intelligence - A Modern Approach, for example.