Nobody attempted to answer this before - so why won't one of you give it a go ?
It's really really tough !!!!!
Loads of you purport to have a brain - why not prove it ?
You're stuck in Purgatory...
The Place where angels always tell the truth , demons lie and humans can do either....
After climbing all those stairs you feel a call of nature and run off to use the facilities....
You flush, wash your hands and then pull the door to the toilet exit - it's locked !
You turn round.
Five other entities are grinning at you - you've been locked in and one [or more] of them has a key.
They will only hand the key over if you identify the person or persons who have the key ?
To do this you have to work out the ontological identity of the individual...
ask the wrong person[s] and you'll be stuck in there forever...
Now you think this should be easy enough - Angel , demon, human etc.....
But these Humans are different : They are all university academics so will lie/tell the truth in special ways
At least One is a Philosopher ; a Philosopher will alternate between making a true statement and a false statement then back to a true statement, false statement...and so on...[n.b. you don't know whether the first statement will be true or false]
At least One is an Agnostic ; an Agnostic likes to fit in ; so will copy the previous speaker; if they lie he will lie too, if they tell the truth he will tell the truth too...and so on.
At least One is an Atheist; The Atheist will always do the opposite to the previous speaker ; if they lie he will tell the truth, if they tell the truth, he will lie !
An Angel will always tell the truth, A Demon will do nothing but lie.
But then something occurs to you !!! Do angels or demons need to use a toilet ?
maybe there are more than one of certain types? maybe there are demons or angels here but one can't be sure ??
You are only allowed to ask all five of them, as a group , five questions.
You realise that the easiest way to work this out is to find a pattern - the agnostic copies which means you'll find two truths or two lies together: So you ask the five of them :
"#1 Who is an Agnostic ?"
A: "B isn't an agnostic"
B: "C isn't an agnostic"
C: "E isn't an agnostic"
D: "A isn't an agnostic"
E: "D isn't an agnostic"
Ooooops...now the question has been asked the people start walking around...quickly you ask
"#2 Who is an Angel ?"
B: " I am ! "
E: " I am ! "
C: " I am ! "
A: " I am ! "
D: " I am ! "
They start walking around again; in sheer desperation you ask
"#3 Ok , who stole the key ?"
C: " I didn't !"
B: " I didn't !"
D: " I didn't !"
A: " I didn't !"
E: " I didn't !"
Again they change places: You start pulling your hair: You ask
"#4 Ok how many of you stole the key ? "
D: "Well only one of us..."
A: "Actually there were two of us.."
C: "Um, there were three of us who did it..."
E: "There were four of us who took the key"
B: "Ok we all did it ! "
They swap places again ! There is a tiny glimmer of hope but maybe you don't know it yet - you
ask your final question :
"# 5 Who did it ?"
E: "B did it !"
B: "D did it !"
D: "A did it !"
C: "E did it !"
A: "C did it !"
Now maybe you don't know it yet; but you can work out who stole the key, and the identity of each person...
So ask the person [or persons] for the key and unlock the door.