Obviously we can all mate a king when we have a king and a queen. Making that a bit more challenging,
You have an empty board with your king and queen on it, say, you start with king a e1 and queen at d1. Your opponent start with his king at e5. After that, on each move your opponent marks the king's move secretly - a legal move but one you don't know. Is it still possible to force a mate?
Using a three-dimensional board, 8 x 8 x 8. King and queen vs king. The king can move in any of the surrounding 26 squares, and the queen in any of the 26 directions as far as there is room. Can the king and the queen force a mate?