Sudoku puzzles and propositional logic 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?

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.
