King + Queen vs. King is perhaps the most basic winning endgame and known to be mate in at most ten moves. However, I am wondering if there is any sequence of premoves that guarantees checkmate? For concreteness, is this possible in the following position?
[Title "White to move and checkmate using only premoves"]
[fen "7K/6Q1/8/8/8/3k4/8/8 w - - 0 1"]
To clarify, this series of premoves would need to result in checkmate regardless of black's response.
The answer is "No". The problem boils down to a combination of the initial smallest square the black king can be confined to being too large and the white king being too far away to limit how far the black king can wander in the square.
For instance, the smallest square the king can be confined to is by moving the white queen to e5. It then takes 3 moves at least to move the white king to a square where it can protect the queen while the queen makes the black "prison" smaller. However in 3 moves the white king takes to get to either f5 (intending Qe4) or e6 (intending Qd5) the black king could have moved to b4 in the case the white king moved to f5, or d2 in the case the white king moved to e6. Then the black king would escape the closing down of the box.
Here's what I mean:
[Title "White can't predict / force where the black king goes"]
[fen "7K/6Q1/8/8/8/3k4/8/8 w - - 0 1"]
1. Qe5 Kc4 2. Kg7 Kd3 3. Kf6 Kc4 (3...Kd2 4. Ke6 Kd3 5. Qd5 Ke3) 4. Kf5 Kb4 5. Qe4 Kc5
