### 3.7.156. n-queen

A constraint that can be used for modelling the $n$ -queen problem. Place $n$ queens on a $n$ by $n$ chessboard in such a way that no queen attacks another. Two queens attack each other if they are located on the same column, on the same row or on the same diagonal. A constructive method for arbitrary $n>3$ was first given in [FalkowskiSchmitz86]. An effective heuristics for the $n$ -queen problem was given in  [Kale90]. It consists of starting to place the queens in the center of the chessboard so that they eliminate the maximum number of potential positions.