Ah you got to that one eh? I actually figured out who the culprit was on a hunch because the specifics on figuring out who it is slipped my mind. Gut feelings FTW.
I managed to write down the notes Elizabeth gave me.
It's rather clever really.
What you basically know about the culprit at first.
He's lying, he's acting alone and the others will tell the truth
It's broken down to pattern figuration. Which statements from the suspects contradict each other -- figuring that out will rule out enough suspects to find the true criminal.
Elizabeth says: The culprit is someone in my family (Theo, Elizabeth or Margaret)
If Elizabeth lies. Then the culprit is Marie. But she can't lie because if she lies, she's the culprit. It's also invalidated by 2 previous statements, such as "Part of my family" and "will tell the truth".
Margaret and Marie came as a pair, they backed each other up with their testimony despite not having been together the whole time.
If one of them is lying, they're basically also stating that the other did it. So it's invalidated by two points again.
Lastly we have Theodore who claims it'd be the workings of his sister Elizabeth, a likely story at first, but given that none of it contradicts what anyone else has said, then he's obviously lying and thus he's the true culprit. It's quite well thought out.