Originally posted by bobbob1056th
A. "This is not the door to go through unless the sign on the adjacent door is true"
B. "Exactly two of these signs are false"
C. "This is the door to open unless the sign on the adjacent door is false"
A. "No fewer than 2 of these signs are false"
B. "None of these signs are false"
C. "Go through either this do ...[text shortened]... ast one of these signs is false"
C. "If door A is not the one to go through, then door B is"
3rd door: B
A is saying: B false => not door A, B true => door A
C is saying: B true => door C, B false => not door C
If B were true, then A and C are false and with the above we have from A (being false): not door A, and from C (being false) : not door C, leaving door B as the solution
If on the other hand, B were false then there are two options: A and B are both true, or both false. If both true, then with B false the two are stating: not door A (says A) and not door C (says C) leading again to door B. If both are false, however, we have a contradiction: A says not A, but it is false, hence door A. But C says not C, but it is false , hence door C. But it cannot be both A and C, hence A and C are not false at the same time.
4th door: B
B is false. If it were true then it would contradict itself. Given that, A must be true, because if it were false, it would be true together with the false B.
So, with A true, C must be false. C states that it is either door C or door A (the true one). Hence it is the third one: door B.
5th door: C although with a degree of uncertainty (if A true and B false)
B is true. If not it would be true which is a contradiction. Three options:
- A false and B false cannot happen: from A (false) follows it has to be door C. But from C (false) follows that if it were door C (i.e. not A) then it is door B, which contradicts
- A true and B false: A says it is not door C, hence A or B; if A then from C (false) no conclusion can be drawn (no statement about what happens if A is the door). Assuming it is a clear solution, though, then A is not the door then C leads us to B, but it is false, hence it must be C
-A false and C true: A false leads to door C. But from C follows that if it is door C (not door A) then it is door B which is a contradiction.