Hmm. It’s not completely trivial…considering that the answer requires some very specific parameters, so let’s nitpick. ;-)
The second part of the question is not fixed, though, fully. It’s important that you worded it differently than I did. Mine was “Would it be a lie if I said that you would say the door on the right leads to death and damnation?” That second “would” is the deciding factor. Whether or not the door on the right leads to D&D is inconsequential, because whatever the answer, the answer to the overall question will tell which is which.
So, if the door on the right does lead to D&D, then if telling the truth (T), the man would say that it leads to D&D, and if lying (L) the man would say that it does not lead to D&D. So, the man must determine what he would say, and is only judging whether or not he would agree with me. And because what I’m asking him to tell me is if the statement I would make about what he would say would be a lie, if T and it’s DR, he would say it’s not a lie because he would say DR because that’s the truth; and if L and it’s DR, he would say it’s not a lie because he would say it’s not DR because he would lie – but he’s going to lie about his lie, and because our answers are yes/no and focused on one door, the same answer is given by both and we know that DR leads to D&D.
Extreme shorthand:
Q1 – Would it be a lie to say you said X (where X is the answer to Q2)
Q2 – Would you say that DR = D&D
When DR = D&D
T answers Q2 yes (because it is true), and Q1 no (because it is not a lie)
L answers Q2 no (because he would say DL = D&D if in fact DR = D&D), and Q1 no (because it would be a lie to say L would answer Q2 in that manner, but L would lie and say his Q2 answer would be yes).
When DL = D&D
T answers Q2 no (because it is untrue), and Q1 yes (because it is a lie and he would say it was)
L answers Q2 yes (because he would say DR = D&D if in fact DL = D&D), and Q1 yes (because L would answer Q2 in that manner described, but that would be a lie, and L would lie that his initial answer would be “yes” and say his Q2 answer would be no).
Let’s try reversing it…“If I claimed that you would say the door on the right (DR) leads to D&D, would you agree?”
Q1 – “Would you say that DR leads to D&D?”
Q2 – “If I claimed that you would, would you agree?”
If DR leads to D&D:
Q1 – T answers yes, L answers no.
– Because T would say that, L would say the opposite.
Q2 – T answers yes, L answers yes.
– Because T agrees that this is what he would say, and would tell the truth about it. L, on the other hand, would say DR does not lead to D&D because it does. Therefore, in truth he would disagree that he would say that. He does not say that, but because the question is now if he would agree that it’s something that he would say, because he would disagree, he will say that he agrees. L would state that he agrees because he actually disagrees. Therefore, both would agree.
If the left door (DL) leads to D&D:
Q1 – T answers no, L answers yes.
– Because T would say that it doesn’t, L would say the opposite.
Q2 – T answers no, L answers no.
– Because T disagrees that this is what he would say, and states the truth that no, he would not agree because he would not tell a lie. L, on the other hand, would say DR does lead to D&D because it does not. Therefore, in truth he would agree that he would say that. Because the question is now if he would agree that it’s something that he would say, and because he would agree, he will say that he no, he does not agree. Therefore, both would disagree.
And in true anal form, a graph!
Answers to Q2 (original above) – “Would you say that DR = D&D?
T – states truth, L = states lies, Y = Answers Yes, N = Answers No, DL = D&D means Left Door is D&D, DR = D&D means Right Door is D&D.
************************************
Door..I DR = D&D I DL = D&D I
************************************
T . . ..I . . . . Y . . .I . . . .N . . ..I – - Both the truth
************************************
L . . . I . . . . N . . .I. . . . Y . . ..I – - Both a lie
************************************
Now, Q1 – Would it be a lie to state your answer to Q2 would be yes?
************************************
Door..I DR = D&D I DL = D&D I
************************************
T . . ..I . . . . N . . .I . . . .Y . . ..I – - (States that it is not a lie when DR = D&D, so
************************************ – - – the statement DR = D&D is true and I go
L . . . I . . . . N . . .I. . . . Y . . ..I – - – through DL. States that it is a lie when DL
************************************ – - – = D&D, so I go through DR).