### 3.7.86. Dominating queens

A constraint that can be used for modelling the dominating queens problem. Place a number of queens on a $n$ by $n$ chessboard in such a way that all squares are either attacked by a queen or are occupied by a queen. A queen can attack all squares located on the same column, on the same row or on the same diagonal. Values of the minimum number of queens for $n$ less than or equal to 120 are reported in [OstergardWeakley01]. They are in fact all either equal to $⌊\frac{n+1}{2}⌋$ or to $⌊\frac{n+1}{2}⌋+1$.