3.7.89. Dominating queens

A constraint that can be used for modelling the dominating queens problem. Place a number of queens on an 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]. Most of them are in fact either equal to ⌊n+1 2⌋ or to ⌊n+1 2⌋+1. Values n=3 and n=11 are the only two values below 120 for which the previous assertion is not true since we only need in these two cases ⌊n 2⌋ queens.