3 Gods questions.
(Q1) to all 3: anything that separates 1 guy from the other 2, such that the 1 guy is Truth or Liar. Easy.
2nd question to the man on his own:
(Q2) "If i asked you "are you the liar" would your answer be 'A'? "
Call the possible responses A and B
If this guy is the truth teller:
- if A=true: he'd answer "no"("B") to "are you the liar", therefore "no" (B) to Q2
- if B=true: he'd answer "no"("A") to "are you the liar", therefore "yes" (B) to Q2
If this guy is the lie teller:
- if A=true: he'd answer "no"("B") to "are you the liar", therefore "yes" (A) to Q2
- if B=true: he'd answer "no"("A") to "are you the liar", therefore "no" (A) to Q2
So the liar will always answer with 'A' to this question, and the truth teller with 'B'
We now know whether the questioned person is truthful or lies, but no whether A or B indicate truth. We can use the same trick on the third question. Point at one of the other Gods and ask:
(Q3) "If i asked you "is that the random God?" would your answer be 'A'? "
If this guy is the truth teller:
*pointing at Random God:
- if A=true: he'd answer "Yes"("A") to "is that the random God?", therefore "Yes" (A) to Q3
- if B=true: he'd answer "Yes"("B") to "is that the random God?", therefore "No" (A) to Q3
*pointing at False God:
- if A=true: he'd answer "no"("B") to "is that the random God?", therefore "no" (B) to Q3
- if B=true: he'd answer "no"("A") to "is that the random God?", therefore "yes" (B) to Q3
If this guy is the lie teller:
*pointing at Random God:
- if A=true: he'd answer "No"("B") to "is that the random God?", therefore "Yes" (A) to Q3
- if B=true: he'd answer "No"("A") to "is that the random God?", therefore "No" (A) to Q3
*pointing at Truth God:
- if A=true: he'd answer "Yes"("B") to "is that the random God?", therefore "no" (B) to Q3
- if B=true: he'd answer "Yes"("A") to "is that the random God?", therefore "yes" (B) to Q3
So, after Q2 we know whether the isolated god from Q1 is true / false, and from Q3 we know which of the other ones is Random.