Recently, in one of the old book on programming came across the following problem: to place on the chessboard 5 queens so that each free field was attacked by at least one queen. This problem is called the problem of the dominant queens. I have not seen the implementation of this task in Maple. Naturally to solve this problem for an arbitrary board N by N. I have 2 variants to solve the problem, but I am not going to to present them yet, so that everyone can enjoy the independent decision. Especially the interesting case is the case of the board 6 by 6, when the solution is unique (certainly up to symmetry).
Of course, it is interesting for each board N by N to find the minimum number of queens that satisfy the above condition. It seems that for arbitrary board N by N the exact value of this number is not known. I do not know any other way of solving the problem as a brute force method.