Funny thing is, I could very well do it, but then I can’t explain how he leaves the room the first time around without the victim noticing.
In any case, it feels like I’m missing something, but let’s just try going over this. Again.
We know the moment the chain was cut, nobody is allowed to be in the room.
We know that the windows in the waiting room couldn’t have been locked by the maid or by the butler after they entered the room, otherwise one would notice.
We know that neither of them would’ve been able to close any of the study windows, since they never entered.
We know that all of the windows were locked by the time police showed up, and until they did, the butler and maid were in the waiting room.
This leads to the simple conclusion that:
The culprit must not be inside the room at the time the chain is broken.
However, we can extend it even further. If the killer is not the maid, it’s impossible to escape the room after the door is broken down. If the killer is the maid, then the next point follows logically enough, anyway:
The culprit must be able to be outside the room after the deed is done, with all the entrances intact, closed and locked.
We know the doors can’t be tampered with. The windows… well, not sure about the windows, so might as well give this a shot: the killer removed the glass from the locked window in the study, allowing him to escape, and then placed the glass back. Alternatively, the study window, when locked, was taken off in its entirety, the culprit left, then put it back.
I’m not expecting much of it, so let’s just assume that gets shot down.
In that case, we can conclude that:
The culprit may only use the door to leave the room.
Therefore, the chain is the next obstacle. We know the chain can’t be tampered with, and we know it can’t be set from the outside, be it either normally or otherwise. Meaning… well…
The chain has to be set from the inside.
Which leaves a contradiction. If you set the chain from the inside, you can no longer leave the room, because you have to use the study windows. Leave through the study windows and you no longer have the ability to lock them. You can’t lock them and hide, because hiding it’s allowed. You can’t lock them after that fact because the only ones who could’ve done it were the sergeant and the police, and we know the window was locked by the time they showed up.
So, the natural solution seems to be to set the chain from inside of the room, while being outside of the room.
Which is to say, through the window in the waiting room.
But then you run into the issue of how that window gets closed. Victim died instantly, so they can’t have done it. Has to be locked by a human hand from the inside, once again bringing up the theory similar to the one with the study windows: either the glass or the window itself was removed, and an object was passed through to set the chain.
The alternative to this is if we assume the chain and the door were both settled at the start, and that the killer never had to enter to do it, but it’s unlikely.
The victim was certainly dead when the body was found, meaning that it couldn’t have been done after the fact. The victim wasn’t killed by a trap because there’s no evidence of it (at first glance, either). The only thing I can think of is that the evidence of the trap from my previous theory did exist when the door was broken down, but was later covered up by the sergeant, who is the killer.
All of this is to say, I’ve kind of reached a dead end. Something’s got to give, I just don’t know what.