Tuesday, 21 August 2007

The Next Three Purgatory Puzzles.


Remember, an Angel must tell the truth, A Demon must lie, Only a human can do either, and there is only one of each type on each staircase.

Second Staircase

Person A: I am an Angel

Person B: I am not Human

Person C: Person A is not a demon.

Third Staircase

Person A: I am an Angel

Person B: I am a Human

Person C: I am a Demon

Fourth Staircase

Person A: I am an Angel

Person B: I am a Human

Person C: Person A really is an Angel.

1 comment:

gemoftheocean said...

Second Staircase

Person A: I am an Angel
Person B: I am not Human
Person C: Person A is not a demon.

A: Devil
B: Angel
C: Human

The Angel CAN'T be A, the reason being that if that were so, it leaves devil and human to statements B & C. That being so, the devil couldn't be B, because then he'd be telling the truth, which leaves him with C, which would be a true statement (the angel is not a demon) -- and we know devils don't tell the truth.

Having established that the angel can't be "A" - that leaves him with statement "B" or "C".

The human can be eliminated as A, on the grounds that if he said
"I am an angel" that leaves that the angel would have had to say
C: "Person A is not a human" true enough...but then that leaves with the devil saying "I am not a human" which is a true statement..and the devil can't tell the truth.

Thus, we have established that by elimination

A MUST be the devil.

If B were to lie about himself, that would be okay ... but then that would leave the angel saying A is not a demon, which we know to be false.

ERGO B has to be the angel, an C, by elimination, is the human.

Third Staircase

Person A: I am an Angel
Person B: I am a Human
Person C: I am a Demon

All three are affirmative statements...ergo

A: has to be the Angel, because the angel doesn't lie so B and C would be wrong.

The demon always lies, so he can't say "I am a demon" he must have said
B: I am a human - which fits the condition of lying,

Which leaves our human with "C"

c: "I am a devil" since the human can lie or tell the truth, all three conditions are met.


Fourth Staircase

Person A: I am an Angel
Person B: I am a Human
Person C: Person A really is an Angel.

A: Is the Angel (the human can't say "A", then the angel would have to declare himself to be the human (untrue), or affirm someone else is the angel -- also not possible, given there's only one of each kind.
b: Is the Devil (he can't say "C", because then he'd be telling the truth about the angel.)
c: Is the Human - (he's telling the truth this time)

Geez, there's HOW many staircases?
;-D
[I do love these sorts of puzzles - do you get the LOGIC puzzles put out by Penny Press? fun!]

Karen H. -- San Diego, Ca.