I’m unlikely to try to solve it, but are you looking for an answer like “if the king starts here, you can do it with N queens placed at...”, or “no matter where the pieces start, you can do it with N queens”? Are you limiting positions to those which could theoretically be achieved in a legal game of 4D chess?
(By that last one, I mean that on a 2D board, you could have a king in the corner and a queen directly adjacent above and beside it, and that would be mate. But you can’t ever have that position in a legal chess game. If something like that turns out to be the optimal, would you accept it?)
It’s the worst case scenario for queens, of course. Just as you ask how to mate the solitary black king with the white king and a white rook in 2D chess. The mating method should always work.
If it doesn’t always work, which means that there is a position from where the mate isn’t possible … then that number of queens isn’t the answer we are looking for.
I’m unlikely to try to solve it, but are you looking for an answer like “if the king starts here, you can do it with N queens placed at...”, or “no matter where the pieces start, you can do it with N queens”? Are you limiting positions to those which could theoretically be achieved in a legal game of 4D chess?
(By that last one, I mean that on a 2D board, you could have a king in the corner and a queen directly adjacent above and beside it, and that would be mate. But you can’t ever have that position in a legal chess game. If something like that turns out to be the optimal, would you accept it?)
No, unless the queen is defended by some other piece, otherwise the king could just capture it. Or am I missing something?
Ah, I was unclear: I meant two queens, one each above and beside.
It’s the worst case scenario for queens, of course. Just as you ask how to mate the solitary black king with the white king and a white rook in 2D chess. The mating method should always work.
If it doesn’t always work, which means that there is a position from where the mate isn’t possible … then that number of queens isn’t the answer we are looking for.
To answer the other question: there exists a checkmate with two queens. Just pin the king into a corner with one, and guard that queen with another.
But can you actually pin a noncooperative king there with only 2 queens? You can in 2D, but hardly in 3D and even less in 4D.