On an infinite chessboard player A places the queen wherever he wants. Then player B places the knight wherever he wants. Then the game starts.
One rule is that the square where player A places his queen in the game is removed from the chessboard.
Can A always check-mate B (the both are playing their best strategies)?
A check-mate here is the position in which A attacks knight of B but knight of B has nowhere to jump because the squares on which he 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 knight cannot capture the queen.
So, queen should be careful in she´s strategy because if she removes "too much" squares that would restrict possible movements of her over the board but she can travel long distances.
On the other hand, knight jumps only short distances.