On an infinite chessboard, player A places the queen wherever they want. Then, player B places the knight wherever they want. Finally, the game starts.
The main rule is that any square where player A places their queen is removed from the chessboard.
Can A always check-mate B (if the both are playing their best strategies)?
A check-mate here is a position in which A attacks B’s knight, giving it nowhere to jump because the squares on which it can jump are all removed.
The second rule is that queen cannot "go over" (cannot "hover over") the removed squares, and cannot attack the knight "over the removed squares".
The third rule is that the knight cannot capture the queen.
So, the queen should be careful in her strategy, because if she removes "too many" squares, that would restrict her possible movements over the board, even though she can travel long distances.
On the other hand, the knight jumps only short distances.