Many famous mathematicians studied mathematical chess problems, such as, Thabit, Euler, Legendre and Gauss.
A domination (or covering) problem involves finding the minimum number of pieces of the given kind to place on a chessboard such that all vacant squares are attacked at least once.
The minimum number of dominating kings is 9, queens is 5, rooks is 8, bishops is 8, and knights is 12.
The domination problems are also sometimes formulated as requiring one to find the minimal number of pieces needed to attack all squares on the board, including occupied ones.
[9] This is done with the pieces' normal legal moves during a game, but alternating turns is not required.
In the second one the positions of bishops must be exchanged with an additional limitation, that enemy pieces do not attack each other.