# Council of Magic - a palace of deceptive spellcasters

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.
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.

• Ar the other members of the council aware that the warlock hates me? I.e. when I asked a fire wizard on the outer edge of the line the question "Would the person next to you answer 'Yes' if I asked the the question x...". Assuming the person next to him is in fact the warlock: Would the wizard say nothing or would he be able to predict the answer?
– user14478
Sep 2, 2016 at 9:01
• Can I safely assume, for the sake of the puzzle, that witches aren't necessarily female, and warlocks are not necessarily male? Sep 2, 2016 at 13:10
• Just to clarify the not-answering rule: if I ask a question along the lines of "what will ... say if I ask ...", a wizard or witch will reliably remain silent if the person I'm asking about is a warlock? (But I take it a priest will just name his god again.) Sep 2, 2016 at 14:23
• Welcome to puzzling.SE, and thanks for such a great first question! EDIT: second question :) Sep 2, 2016 at 14:30
• How will they react to questions like "Will you answer this question with yes?" (both answers are correct) or "Will you answer this question with no?" (neither answer is correct) Sep 3, 2016 at 8:29

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.

• It can be done in fewer questions than this. Sep 2, 2016 at 20:47
• @user3294068 yeah I just realised it can be cut down to 7. Or do you think it can go lower? Sep 2, 2016 at 21:35
• Ah, I just saw your answer Sep 2, 2016 at 22:08
• Let's say that I am not allowed to ask questions where the reply is silence . Can we still find out everybody's identities ? If yes, then how ? Apr 23 at 12:38

I think I can do it in

10 questions

but I make no guarantee this is optimal. First of all, note that

if I ask a witch or wizard "what would you say if I asked you ...?" I always get a truthful answer. So if I ask "X, what would you say if I asked you what Y would say if I asked him 'Y, what would you say if I asked you ...?'?" and X is a witch or wizard, then he will tell me correctly what Y would say; and if Y is a witch or wizard, what he would say is the truth.

Now, if ... is "what is the name of the priest's god?" then I get a correct answer provided neither of X,Y is the warlock, or if X is the priest. If X is witch or wizard and Y is the warlock, I get silence. If X is the warlock, all bets are off.

OK. So now

I ask that question with (A,B), then (B,C), then (C,D), then (D,A). If one of those pairs is (witch/wizard,warlock) then I get silence from them, anything from (warlock,whoever), and two correct answers. So in this case I know something like "A is witch or wizard, B is warlock, priest's god is (yes/no)".

After that,

I can use A to identify which of C,D is the priest (one question), and then three more questions will sort out the witch and wizard. Total of 8 questions.

That was the easy case. On the other hand,

if none of those pairs is (witch/wizard,warlock) then the sequence is some cyclic permutation of (witch/wiz,wiz/witch,priest,warlock). That way, I get three correct answers and nonsense from the warlock. The warlock will presumably give the same answer as everyone else, so these four questions have told me only what god the priest serves, plus the information already mentioned about the sequence of spellcasters.

So now

I play a similar game but going DCBA instead of ABCD. If I use the exact form of question described above I will get no useful information from the (witch/wiz,wiz/witch) pair, so now I ask "X, what would you say if I asked you what Y would say if I asked him 'Y, what would you say if I asked you in 12 hours whether 2+2=4?'?". The four pairs are, in order but maybe cyclically permuted: (warlock,priest) giving a useless answer; (priest,w/w) giving name-of-god; (w/w,w/w) telling me whether the second w/w is a witch; (w/w,warlock) giving silence.

And now after 8 questions I know

which one is the warlock, I know which one is the priest and what his god is, and I know which of the other two is witch and which is wizard. Now I identify the subtypes of witch and wizard with one question each. Total: 10 questions.

• Am I wrong in thinking the 8th question in this scenario gives no additional information? Since the main thing we're trying to identify in the second set of four is the Warlock in Worst Case scenario, if we still haven't found him by silence by question 7, we KNOW we'll find him with silence by question 8. Sep 2, 2016 at 16:00
• The members of the Council have full knowledge of each other. So they know that the warlock will give you the less helpful answer. So there will never be silence. Sep 2, 2016 at 16:02
• @Etoplay, that interpretation was explicitly rejected by the questioner in comments to the question; see above. Sep 2, 2016 at 16:04
• @Chelsea, questions 5-8 also let you distinguish the witch from the wizard. It's very possible that some optimization is possible here, but I don't think just omitting q8 will do. Sep 2, 2016 at 16:06
• @GarethMcCaughan I thought we were using 9-10 to distinguish the witch from the wizard. I agree that more optimization is possible; I'm just trying to understand what additional information we gain from the 8th question specified above. Sep 2, 2016 at 16:10

Here is my solution with the definitly lowest possible number of questions:

5 Questions

Question 1 to Alice:

Has the warlock that I last saw, who is not you, the same gender as the warlock on the council?

## Case 1: Alice stays quiet

That means she is a warlock.

Question 2a to Bob:

Has the wizard that I last saw, who is not you, the same gender as the wizard on the council?

## Case 1.1 Bob stays quiet too:

In that case Alice is a warlock and Bob is a wizard. There are still 16 different possible assignments of type and sub-type after question 2 and we know Bob is a wizard.

Now we ask the last few questions. See below.

In that case Bob is a priest or a witch

Then we ask Bob again: Question 3a:

Has the wizard that I last saw, who is not you, the same gender as the wizard on the council?

Analysis:

If we get the same answer as before then Bob is a priest otherwise he is a witch.
In both cases we know the subtype of Bob.
If Bob is a priest then we know Carol has to be be a witch or a wizard. In that case there are 8 different possible assignments of type and sub-type after question 3.
If Bob is a witch then there are 8 different possible assignments of type and sub-type after question 3

Now we ask the last few questions. See below.

## Case 2: Alice answers the first question

That means she is not a warlock.

Question 2b to Alice:

Has the wizard that I last saw, who is not you, the same gender as the wizard on the council?

Analysis:

If the answer is the same, then Alice is a priest.
If the answer differce, then Alice is a witch.
If there is no answer, then Alice is a wizard.
And we know the subtype of Alice from the first question and there are 24 different possible assignments of type and sub-type after question 2.
If Alice is a wizard or a witch then we can ask the last few questions now.

If Alice is a priest, then we need Question3b to Bob:

Has the warlock that I last saw, who is not you, the same gender as the warlock on the council?

Analysis:

If Bob is silent, then Bob is a warlock and Carol is a witch or wizard (because the priest is alice). If Bob answeres, then Bob is a wizard or witch. In both cases there are still 8 possible assignments of type and sub-type.

Now we ask the last few questions.

# The Last few questions:

The last few questions can only be asked when you know where a wizard or witch is. Those questions are realy, realy, realy complex. I don't think a human could answer them after hearing them once because when the end of the question will be asked then the answer of the question will be forgotten. Each of these last few questions will reduce the possible assignments of type and sub-type to a third.

Let us look on the following statement:

At least one of the following four statements is true:
"The fire Wizzard that I last saw, that is not Alice, or the water Wizzard I last saw has the same gender as the Wizzard on the council."
"The light Witch that I last saw, that is not Bob, or the dark Witch I last saw has the same gender as the Witch on the council."
"The Warlock that I last saw, that is not Carrol, has the same gender as the Warlock on the council."
"The Priest of Yes that I last saw, that is not Dave, or the Priest of No I last saw has the same gender as the Priest on the council."

The analysis for this statement:

The logical value of first sub-statements is unknown if and only if Alice is a fire Wizzard and is true otherwise.
So the truth value to the total statement is unknown if and only if Alice is a fire Wizzard and Bob is a dark Witch and Carrol is a Warlock and Dave is a Priest of Yes.
In all other cases the total statement is true.

For all possible assignment of type and sub-type such a statement can be constructed.
For an assignment of S I will write X(S) for that statement.

And the next statement we look at:

Alice is not a fire Wizzard or Bob is not a light Witch or Carrol is not a Warlock or Dave is not a Priest of Yes.

And its analysis:

This is false when Alice is a a fire Wizzard and Bob is a light Witch and Carrol is a Warlock and Dave is a Priest of Yes.
In all other cases the statement is true.

For all possible assignment of type and sub-type such a statement can be constructed. For an assignment of S I will write Y(S) for that statement.

Now we come to the actual question:

What would you answer if I asked you "Is an odd number of the following statements false: $X(S_1), ..., X(S_{\frac{1}{3}n}), Y(S_{\frac{1}{3}n+1}), ..., Y(S_{\frac{2}{3}n})$"

For example when there wasn't an answer to the first question and the second and third answer was yes then the following assignment of type and sub-type are possible:
$S_1$: warlock, priest of Yes, fire wizard, light witch
$S_2$: warlock, priest of Yes, fire wizard, dark witch
$S_3$: warlock, priest of Yes, water wizard, light witch
$S_4$: warlock, priest of Yes, water wizard, dark witch
$S_5$: warlock, priest of Yes, light witch, fire wizard
$S_6$: warlock, priest of Yes, dark witch, fire wizard
$S_7$: warlock, priest of Yes, light witch, water wizard
$S_8$: warlock, priest of Yes, dark witch, water wizard

The question then would be:

What would you answer if I asked you "Is an odd number of the following statements false:
'At least one of the following four statements is true:
"The warlock that I last saw, that is not Alice, has the same gender as the Warlock on the council."
"The Priest of Yes that I last saw, that is not Bob, or the Priest of No I last saw has the same gender as the Priest on the council."
"The fire wizard that I last saw, that is not Carol, or the water Wizzard I last saw has the same gender as the Wizzard on the council.
"The light witch that I last saw, that is not Dave, or the dark Witch I last saw has the same gender as the Witch on the council."
',
'At least one of the following four statements is true:
"The warlock that I last saw, that is not Alice, has the same gender as the Warlock on the council."
"The priest of Yes that I last saw, that is not Bob, or the Priest of No I last saw has the same gender as the Priest on the council."
"The fire wizard that I last saw, that is not Carol, or the water Wizzard I last saw has the same gender as the Wizzard on the council.
"The dark witch that I last saw, that is not Dave, or the light Witch I last saw has the same gender as the Witch on the council."
',
'Alice is not a warlock or Bob is not a priest of Yes or Carrol is not a water wizard or Dave is not a light witch.',
'Alice is not a warlock or Bob is not a priest of Yes or Carrol is not a water wizard or Dave is not a dark witch.',
'Alice is not a warlock or Bob is not a priest of Yes or Carrol is not a light witch or Dave is not a fire wizard.'

For that question there won't be an answer when one of $S_1, ... S_{\frac{1}{3}n}$ is the correct assignments of type and sub-type.
The answer will be Yes if one of $S_{\frac{1}{3}n}+1, ... S_{\frac{2}{3}n}$ is the correct assignments of type and sub-type.
The answer will be No if one of $S_{\frac{2}{3}n}+1, ... S_{n}$ is the correct assignments of type and sub-type.

By successively cutting the possible assignments of type and sub-type in third, there will be only one possible assignment after the fifth question and that one will be the solution.

## P.S.

There is the answer mu for yes-no questions. It is the answer if the question assumes wrong things. For example "Did you stop beating your wife?". If that answer would be allowed for questions like "Has the wizard the same gender as the fire wizard on the council?" when there is no fire wizard then the puzzle could maybe solved with 4 questions.

• You only see a council member when you ask them a question. Also, gender to name assignments might not be the same in Puzzlington (e.g. Alice could be a guy). Mu leads to silence. Sep 4, 2016 at 15:03
• I assumed that I see the whole council at the beginning and that everybody knows I have seen the whole council. It doesn't matter what gender Alice has, as long as Alice has the same gender as Alice. And that should be always true. Sep 4, 2016 at 20:42
• Took me a while to understand this answer, but it's correct in every particular, and is the minimum possible as you say, because log(base3) 192 = 4.78, and there are 192 possible states at the beginning. Deserves more upvotes. Sep 5, 2016 at 12:42
• I had a very hard time following our original conclusion that Alice is a warlock if she says nothing, as a warlock must say yes or no. I believe you are working on the presumption that anyone that is suppose to tell the truth or lie is forced to say nothing in the event of question that is neither true nor false, due to false premise? I would explain that presumption at the beginning of the question to help understand your conclusions. I would argue that the response value of a 'mu' can not be presumed to be nothing, but I like the question enough to upvote as it works if your axiom is true May 19, 2017 at 15:44

I can do it in 7 simple questions.

I do not make any assumptions about what a priest would do if asked a question they don't know the answer to (they might answer anyway) and I do not assume a warlock would answer a question if remaining silent would be more devious.

1. A: "Is the last Wizard I saw, who is not you, a Fire wizard?"
2. B: "Is the last Wizard I saw, who is not you, a Fire wizard?"
3. C: "Is the last Wizard I saw, who is not you, a Fire wizard?"
4. D: "Is the last Wizard I saw, who is not you, a Fire wizard?"

I do assume that, while I am addressing the question to only one mage, that I can see all of them at once during or immediately before asking the questions. I also assume they cannot read my mind or otherwise magically know things about what's in my head. If these assumptions are wrong, then the questions above would need rewording.

The wizard won't know who I'm talking about, and will therefore remain silent. The priest and witch will know I'm talking about the wizard on the council (since they see me looking at him/her), and will answer, according to above. The warlock will tell the truth, lie, or remain silent.

If the warlock answers, then only one person remained silent, and that person must be the wizard. Ask:

1. Wizard: "Is it day time?"

The fifth question will come at noon, so a yes will indicate a fire wizard, while a no will indicate a water wizard. Next ask (if B is the wizard, substitute D instead):

1. Wizard: "If I asked B right now if you are a water wizard, what would they say?"

If B is the warlock, the wizard would not be able to predict their answer, and would remain silent.

If B is the priest, they would give the same answer they gave the last time, which a fire wizard would tell you truthfully and a water wizard would lie about.

If B is the witch, they would give the opposite answer they gave the last time, since both questions were asked at night, and the questions have opposite truth value.

Now you know whether B is the witch, warlock, or priest. Next pick one of the remaining types and ask:

7: Wizard "Is C a witch/priest/warlock?"

After these questions, you will now know which mage is which type. You can tell whether the witch is a light or dark witch based on their answer and the time of day when you asked it. Likewise for the priest.

If the warlock remained silent Two mages remained silent, and two mages gave answers. The silent two are the wizard and warlock, the other two are witch and priest. Assume A and B are the silent two.

5b: "Is the last Witch I saw, who is not you, a Light Witch?"

The witch would remain silent, while the priest would give the same answer they gave previously. Now you know who the witch and priest are:

6b: Witch: "Is it night?"

Since it will be midnight at this time, a light witch would say "no", and a dark witch would say "Yes".

7b: Witch: "Is A the wizard?"

A light witch will tell the truth, while a dark witch would lie. Now you know who everyone is. Based on the witch's previous answer, you know whether the wizard is a fire or water wizard.

Summary:

This approach asks the warlock precisely one question. No matter whether the warlock answers truthfully, lies, or remains silent, we can determine which mage is which within 7 questions, and based on their answers tell which type each is.

• Allow me to clarify: Priests always name their god, no matter what the question; the Warlock chooses truth or lies, not yes, no or silence; you only see a council member when asking them a question. You are correct that they can not read minds. Thank you for forcing me to clarify; it helps me refine my puzzles. Sep 2, 2016 at 21:04
• "...what Would they say" is not Really a yes/no question Sep 3, 2016 at 15:04
• @bmyguest The exact wording I used was "question that can be answered Yes or No". For example, "What god does the Priest worship?" or "What would ... say if I asked ...?" is fine. Sep 3, 2016 at 15:26

This answer does not make any assumptions about whether I have seen all council members before, or what the council members know about whom I've seen.

I need up to 6 questions, but in many cases only 5, and in a few cases even just 4. In any case, it beats the currently accepted answer which needs 7 questions.

I'm not sure whether this can be improved upon under those conditions.

Here's my strategy:

First question: Alice, if I asked you what Bob would say if I asked him what he would say if I asked him what you would say if I asked you what you would say when I asked you whether you are a wizard, what would you say?

Possibility 1: No answer to question 1 (-).

This means that either Alice or Bob is the warlock and neither is the priest. Explanation: If Alice remains silent, she is certainly not a priest, because priests always answer. Also there are only two possibilities why Alice would not answer: Either Bob is the warlock, and thus she does not know what he would answer, or Bob would not answer. In the latter case, Bob is no priest, and the only reason why he would not answer is that he doesn't know what Alice would answer because Alice is the warlock.

So in summary, we now know either Alice or Bob is the warlock, and either Claire or Dave is the priest.

Case (-), second question: Claire, if I asked you what Alice would answer if I asked her at day whether Bob is a warlock, what would you say?

Possibility 1.1: Again no answer (--).

Now we know Alice is the warlock. Also we know that Dave is the priest.

Case (--), third question: Bob, if I asked a council member, who is Alice if you are a witch, and who is you if you are a wizard, what got the priest prays to, what would be the answer I get?

Possibility 1.1.1: Again no answer (---).

Bob is a witch, as only in that case he's be compelled to say what Alice would say, which he can't as she is a warlock.

Case (---), fourth question: Bob, if I asked a council member, who is Alice if you are a light witch, and who is you if you are a dark witch, which god the priest prays to, What would you answer?

Possibility 1.1.1.1: Again no answer (----).

We now know that Bob is a light witch.
To summarize, up to here, we know that Alice is a warlock, Bob is a light witch, Claire is a wizard, and Dave is a priest. We don't know yet the subtypes of Claire and Dave, and since there are four possibilities, we need two questions to find out.
Case (----), fifth question: Bob, which god does the priest pray to?
Case (----), sixth question: Bob, is the wizard on the path of fire?
Since Bob is a light witch, and the fifth question is asked on a day, we will get a truthful answer. Also, the sixth question is asked at night, so the answer will be wrong; of course the correct answer is easily derived from that knowledge.

Possibility 1.1.1.2: Fourth question answered with Yes or No.

Bob is a dark witch. And since in that case the question takes on the special form "What would you say if I asked you …", the answer is truthful. So we now know the god Dave prays to. We also now know that Claire must be a wizard. The only missing bit is Claire's subtype. But we can use the next question to ask that from Bob directly. We know how to interpret his answer, as we know his type

Possibility 1.1.2: Third question answered with Yes or No.

Bob is a wizard, and Claire is a witch. Again, the question takes the special form "If I asked you …" and therefore the answer is truthful, so we know the god of the priest. We can use the fourth and fifth question to determine the subtypes of Bob and Claire by asking Bob (using the "If I asked you …" form to uncover Bob's subtype).

Possibility 1.2: Second question answered with Yes (-Y).

We now know that Bob is the warlock. Furthermore we know that either Claire is a Yes priest, or both Claire and Alice are saying the truth at night (one is a fire wizard, the other dark witch), or both are lying at night (one is a water wizard, the other a light witch).

Case (-Y), third question: Alice, if I asked a council member who is Bob if Claire is a priest, and who is you otherwise, what he would say if I asked him whether you are a wizard, what would he answer?

Possibility 1.2.1: third question not answered (-Y-).

Since Bob is the warlock, we now know Claire is a Yes priest. We don't yet know which of Alice and Dave is the wizard, and what are the subtypes of the witch and the wizard.

Case (-Y-), fourth question: Alice, if I asked a council member who is Bob if you are a wizard, and who is you otherwise, what he would say if I asked him whether the with is a light with, what would be the answer?

Possibility 1.2.1.1: Fourth question not answered (-Y--)

Alice is a wizard, and Dave is a witch. We don't know the subtypes, but using the "What would you say if …" form, we can query both in the fifth and sixth question to either Alice or Dave.

Possibility 1.2.1.2: Fourth question answered Yes or No.

Alice is a light which (Yes) or a dark with (No). We still need to find out the subtype of Dave, which we can do with a direct fifth question to Alice.

Possibility 1.2.2: Third question answered Yes (-YY).

Alice is a wizard, and Claire is a with. Moreover the subtypes of Alice and Claire are linked as described above. So what remains is to figure out the subtypes of Alice and Dave (the latter being the priest), which can be done by directly asking Alice (using the "What would you say" form, of course) in the fourth and fifth question.

Possibility 1.2.3; Third question answered No (-YN).

Alice is the witch and Claire is th wizard. Otherwise it's just like the case before; again we need two further questions to Alice to determine the subtypes of Alice and Dave (again, Claire's subtype is linked to Alice's as described above).

Possibility 1.3: Second question answered No (-N).

We again know that Bob is the warlock. Furthermore we know that either Claire is a No priest, or exactly one of Claire and Alice is saying the truth at night (one is a fire wizard, the other light witch, or one is a water wizard, the other a dark witch).

The subcases here are completely analogue to the subcases for (-Y), with three to four more questions asked for a total of five to six questions.

Possibility 2: First question answered Yes or No (Y or N).

Now we know that neither Alice nor Bob is the warlock. We moreover can already exclude some further possibilities about Alice and Bob, however I'll defer that analysis for later.

Case (Y or N), second question: Alice, if I would ask you what Claire would answer if I asked her at daytime what she would say if I asked her whether Dave is the warlock?

Possibility 2.1: You get no answer (Y- or N-).

Now we know that Claire is the warlock.

Case (Y- or N-), third question: Alice, if I asked a member of the Council, which is Claire if you are a Priest, and you otherwise, whether Bob is a priest, what answer would I get?

Possibility 2.1.1: You again get no answer (Y-- or N--).

Now we know that Alice is the priest, and from the answer to the first question, we know her subtype. We still don't know whether Bob is the wizard or the witch, and which subtypes the wizard and the witch are.

Case (Y-- or N--), fourth question: Bob, if I asked a member of the council, who is Claire if you are a witch, and who is you otherwise, whether the wizard is on the path of fire, which answer would I get?

Possibility 2.1.1.1: You get no answer (Y--- or N---).

You now know that Bob is a witch. You still need to figure out the subtypes of Bob and of Dave, the wizard. This you can do with two more simple "What would you say if I ask you" questions to Bob, for a total of 6 questions.

Possibility 2.1.1.2: You get either Yes or No.

You know that Bob is a wizard, and his subtype. You still have to figure out whether Dave is a light or a dark witch, which you can get from a direct fifth question to Bob.

Possibility 2.1.2: On the third question you get Yes (Y-Y or N-Y).

You now know that Bob is the priest. Furthermore, from the first answer, you know which god Bob prays to. The last two to three questions are then exactly as in possibility 2.1.1, except of course the roles of Alice and Bob are exchanged.

Possibility 2.1.3: On the third question you get No (Y-N or N-N).

You now know that Dave is the priest (but not of which god). Moreover, from the first question, you know whether Alice is the wizard (Y-N) or the witch (N-N), so all types of the council members are now known. What remains to find out is the subtypes of each.

Case (Y-N or N-N), fourth question: Alice, if I asked a member of the council which is Clair if the priest prays to Yes, and you otherwise, whether the wizard in on the way of fire, what would be the answer I get?

Possibility 2.1.3.1: You get no answer (Y-N- or N-N-).

You now know that Dave prays to Yes. You still need to figure out the subtype of the witch and the wizard, which you can get through "What you you say if I ask you" questions to Alice.

Possibility 2.1.3.2: You get a "Yes" or "No".

You no know that Dave prays to No, also you know the subtype of the wizard. You only need to find out the subtype of the witch, which you can get through a direct question to the wizard.

Possibility 2.2: The answer to the second question is the other one than the first (YN or NY). You know that Alice is not the priest (otherwise she would have given the same answer twice). Also you know that Dave is the warlock (as you've excluded it for Alice, Bob and Claire). Again, I'll leave further analysis for later questions.

Case (YN or NY), third question: Alice, if I'd ask a person that is Dave if Bob is a priest, and which is you otherwise, whether the witch is a light which, what answer would I get?

Possibility 2.2.1: No answer (YN- or NY-).

You have identified Bob as the priest, and from the first answer, you know his god. Furthermore, from the second answer you know whether Claire is lying during the day.

Case (YN- or NY-), fourth question: Alice, if I asked a member of the council which is Dave if you are a wizard, and you otherwise, whether the wizard is on the path of fire, what answer would I get?

Possibility 2.2.1.1: No answer (YN-- or NY--).

We know Alice is a witch and Claire a wizard; from the second question we also now Claire's subtype. So all we need to figure out is the subtype of Alice, which we can get by asking Claire directly.

Possibility 2.2.1.2: Yes or No.

We know Alice is a wizard, and from the answer also her subtype; also from the second answer we know the subtype of Claire. In other words, we know everything, and a fifth question is not needed in this case.

Possibility 2.2.2: Yes or No to the third question.

Bob is not the priest, therefore through exclusion we now know Claire is the priest, and from the second answer we know her god. Moreover, from the first question we now can tell whether Alice of Bob is the wizard (the other one is the witch), and we further know from the third question the subtype of the witch. All we need to figure out is the subtype of the wizard, which we can find out by a direct question to the witch.

Possibility 2.3: Same answer to the first two questions (YY or NN).

From the fact that Alice answered both questions, we know that Dave is the warlock. Furthermore, we know the god of the priest: If Alice is the priest, her answer is always her god. If Bob is the priest, Alice's first answer was Bob's god, If Claire is the priest, Alice's second answer was Claire's god. Furthermore, if Bob is the priest, we know whether Claire says the truth during the day, and if Claire is the priest, we know whether Alice is a wizard.

Case (YY or NN), third question: Bob, If I asked a member of the council which is Dave if you are a priest, and you otherwise, whether Alice is a priest, what would be the answer?

Possibility 2.3.1: No answer (YY- or NN-).

Bob is the priest.

Case (YY- or NN-), fourth question: Alice, if I asked a council member who is Dave if you are a wizard and you otherwise, whether the witch is a light witch, what would the answer be?

Possibility 2.3.1.1: No answer (YY-- or NN--).

Alice is a wizard, and Claire a witch. Claire's subtype can be obtained from the answer to the second question, so the only thing that remains to be figured out is the subtype of Alice, which can be done by a direct fifth question to Claire.

Possibility 2.3.1.2: Answer Yes or No.

Alice is a with, and from the answer you get her subtype. Also, Claire is a wizard, and the subtype is determined from the second question. So we already know everything about the council, no fifth question required.

Possibility 2.3.2: Yes to the third question (YYY or NNY).

Alice is the priest. We still have to figure out the types and subtypes of Bob and Claire.

Case (YYY or NNY), fourth question: Bob, if I asked a member of the council who is Dave if you are a wizard and you otherwise, whether the wizard is on the path of fire, what would the answer be?

If Bob doesn't answer, he is the wizard, and we need to find out both his and Claire's subtype with two further questions to Bob of the type "If I asked you whether …". If Bob answers, we know that Claire is the wizard and her subtype, so we need just one other straightforward question to Claire to figure out Bob's subtype.

Possibility 2.3.3: No to the third question (YYN or NNN).

Claire is the priest, and Alice is the wizard. We need to further "If I asked you" questions to Alice to figure out her and Bob's subtype.