You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:
Door A: It’s behind B or C
Door B: It’s behind A or D
Door C: It’s in here
Door D: It’s not in here
Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?
If your psychic powers are good enough to tell you that three are false and only one is true, then
why couldn't your psychic powers just give you the right answer?
A can't be true because if A is true then D is false but D being false contradicts A being true.
B must be true because if B is true then D is false, and if D is false then it must be behind D.
C is false because C being true would conflict with D being false
D is false because D being true conflicts with B being false.
C/D can't be true because then either A or B would also be true.
A can't be true because then either C or D would be true.
B is true. It can't be behind A because D would be true, so it is D, for which there are no contradictions.
If D, then !A && !B && !C.
!A && !B == !(b || c) && !(a || d) == !b && !c && !a && !d.
If D isn't the correct answer, then no door is the correct answer.
I prefer the reasoning that says that the spirit is behind the door which has only one reference.
Both B and D refer to A; A and D refer to B; A, C and D refer to C; only B refers to D. Therefore
the spirit is behind D.