Council of Magic:
The King of Puzzlington has sent you to a distant palace to gain the aid of the Council of Magic. As your luck would have it though, spellcasters are a tricky sort.
There are 4 types of spellcasters in Puzzlington: Wizards, Witches, Priests, and Warlocks.
Wizards:
Wizards follow one of two paths: the path of Fire or the path of Water.
Wizards on the Path of Fire always tell the truth when asked a question.
Wizards on the Path of Water always lie when asked a question.
Witches:
Witches come in two styles: Light Witches or Dark Witches.
Light Witches tell the truth during the day and lie at night.
Dark Witches lie during the day and tell the truth at night.
Priests:
Priests worship one of two Gods: Yes, god of life or No, god of death.
When asked a question, instead of answering, priests just say their God's name.
That is, a Priest of Yes will always answer "Yes" to any question.
Warlocks:
Warlocks are unpredictable tricksters.
When asked a question, Warlocks will tell the truth or lie, as they wish.
They will do one or the other, however.
The Council:
The Council of Magic consists of 4 powerful spellcasters. The spellcaster's names are Alice, Bob, Claire and Dave. The Council has one Wizard, one Witch, one Priest and one Warlock; you do not know which Council member is which type of spellcaster. You do not know the Path of the Wizard, Style of the Witch or God of the Cleric.
The members of the Council have full knowledge of each other. That is, they know which member is which type of spellcasters and which sub-type each is. The sub-type of a spellcaster is their Path, Style or God, as appropriate.
You arrive at the palace at noon. You can, once every 12 hours, ask any one member of the Council any one question that can be answered Yes or No (that is, after each question, it switches from night to day or day to night). If a spellcaster is asked a question they can't answer (because they don't know the answer), they remain silent. Priests are an exception to this rule; to them, their god is always the answer, no matter what the question.
Further complicating matters is the Warlock, who hates you; when asked a question, they will choose to tell the truth or lie, whichever they think will hurt you the most.
Your task is to learn the type and sub-type of all Council members as fast as you can.
I know a way to solve this puzzle, but it takes 6 days (12 questions) in the worst case. I'm fairly sure there is a faster way to do it (there is just over 7 bits of information you need to find); but I don't know it. I'd sure like to know it if anyone can find one.
Answer
I think I can do it in:
at most 7 questions
First question:
This borrows some ideas from Gareth McCaughan's answer. He notes the following: "if I ask a witch or wizard "what would you say if I asked you ...?" I always get a truthful answer.". With this in mind, my first question's purpose is to tell whether the recipient is in the (wizard/witch) pair or the (warlock/priest) pair. I ask of A: " If I asked the warlock whether 2+2=4, what would he say? ". If A was in the (witch/wizard) group, he would be silent. If A was in the (warlock/priest) group, he would not be silent, as these 2 always give an answer.
Next 2 questions:
I now ask the same question to B. This tells me what group B is in. In the worst case, I now have A in one group and B in the other group, so I have to ask the same question to C. After this, I know everyone's group, but I don't know anything else (since the warlock always tries to screw up my strategy as much as possible, he will give a different answer to the priest).
Question 4:
Let's say that A,B are (warlock/priest) and C,D are (witch/wizard). There are 2 possibilities. (1st possibility): The only person who hasn't answered a question yet is in the (warlock/priest) group. Call that person X. I then ask of C: "what would you say if I asked you what X would say if I asked him if 2+2=4". If he gives an answer, I know that X is the priest and I know what god he follows (whatever the answer was), and I know who the warlock is. If no answer, then the warlock is X, the priest is the other member of that group and his god is whatever he answered before. (2nd possibility): The only person who hasn't answered a question yet is in the (witch/wizard) group. In this case I ask of C: "what would you say if I asked you what A would say if I asked him if 2+2=4" and again I know everything about the priest and warlock.
Question 5:
I now ask of C: "what would you say if I asked you if you are the wizard" This sorts out who is witch and who is wizard.
question 6 and 7:
These are to determine the types of the wizard and the witch.
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