Honestants and swindlecants XI

[Prof. Templeton]

There are three omniscient Gods sitting in a room. The God of the Honesants, the Swindlecants, and the Randomcants. The Gods will only answer Yes/No questions. The Honestants God always answers truthfully, the Swindlecants God always lies and the God of the Randomcants only seems to answer randomly, but in fact will answer with an affirmative only if, one and only one, of the other two Gods would answer with an affirmation, otherwise he will answer with a negative.

You have entered the room and your task is to determine which God is which with only three questions. Unfortunately you don’t know the language of the Gods, only that there are two distinctly different words for Yes and No.

Rules:

• The Gods will only answer Yes or No questions.
  
• The Gods will answer in a single word in their language either an affirmative or a negative.
  
• Each question must be addressed to a specific God. Asking one question of all three Gods is three questions.
  
• You may ask more than one question to a single God.
  
• You may chose your next question(s) based on previous answers.
  
• Because of possible loop conflicts, you may not ask any question about how the God of the Randomcants would answer.
  

The concept for this problem is not of my own making. I will give full credit to the author after an acceptable solution is found.

[Guest]

There are three omniscient Gods sitting in a room. The God of the Honesants, the Swindlecants, and the Randomcants. The Gods will only answer Yes/No questions. The Honestants God always answers truthfully, the Swindlecants God always lies and the God of the Randomcants only seems to answer randomly, but in fact will answer with an affirmative only if, one and only one, of the other two Gods would answer with an affirmation, otherwise he will answer with a negative.

You have entered the room and your task is to determine which God is which with only three questions. Unfortunately you don’t know the language of the Gods, only that there are two distinctly different words for Yes and No.

Rules:

• The Gods will only answer Yes or No questions.
  
• The Gods will answer in a single word in their language either an affirmative or a negative.
  
• Each question must be addressed to a specific God. Asking one question of all three Gods is three questions.
  
• You may ask more than one question to a single God.
  
• You may chose your next question(s) based on previous answers.
  
• Because of possible loop conflicts, you may not ask any question about how the God of the Randomcants would answer.
  

The concept for this problem is not of my own making. I will give full credit to the author after an acceptable solution is found.

Q1: Are you a God? To any God

Y: truth or random

N: Lie

Q2: Same again to a different God

This way we definatly know which one the lieing god is

Q3: Does your name contain the letter O? To the final God

Y: Lie or truth

N: Random

I think this works

[Prof. Templeton]

Q1: Are you a God? To any God

Y: truth or random

N: Lie

Q2: Same again to a different God

This way we definatly know which one the lieing god is

Q3: Does your name contain the letter O? To the final God

Y: Lie or truth

N: Random

I think this works

Remember, you don't know what means "yes" and what means "no". After your second question you could have 2 answers that are the same or two that are different. If they are different you won't have learned anything since you don't know who answered "yes" and who answered "no".

Edit: Well, you will learn something, but not much (of the two Gods they could be H-S, S-H, R-S, S-R).

Edited April 21, 2009 by Prof. Templeton

[Guest]

Are you a Truth Teller?

-All would answer yes, but only ask it to one.

To the same god, Did you just answer Yes?

-Swindlecat would say N, the others would say yes. (Note, the answer will also tell you which of the sounds means Yes and No). If no, ask the same god, while pointing to another, is he/she a honestant? If the answer is Yes you know all three.

If the god said yes to the question "Did you just answer Yes?", then it would either be an honestant or a randomcant. You then ask if he is a roandomcant. If the answer is no, he is a honestant. If it is yes, he is a randomcant, as a swindlecant would have also answered yes, forcing him to answer yes.

[Prof. Templeton]

Are you a Truth Teller?

-All would answer yes, but only ask it to one.

H would truthfully answer "Yes"

S would lie and answer "Yes"

but since both H and S would give affirmative answers, R would answer "No".

Then for the second question, "Did you just answer Yes?" R would have to determine what H and S would do in his situation. H would say "No", S would say "Yes", so R would also say "Yes"

[Guest]

1. Ask one god if they have a H in their name

2. Ask another god if they have a H in their name

3. Ask one of the gods that you should know by now isn't Randomcants if 2 + 2 = 4

[Guest]

H would truthfully answer "Yes"

S would lie and answer "Yes"

but since both H and S would give affirmative answers, R would answer "No".

Then for the second question, "Did you just answer Yes?" R would have to determine what H and S would do in his situation. H would say "No", S would say "Yes", so R would also say "Yes"

I missed the one and only one part

[Prof. Templeton]

1. Ask one god if they have a H in their name

2. Ask another god if they have a H in their name

3. Ask one of the gods that you should know by now isn't Randomcants if 2 + 2 = 4

1. Ask one god if they have a H in their name. 2. Then ask another.

H would say "Yes"

S would say "Yes"

R would say "No"

You could have gotten a "Yes" first and a "No" second or a "No" first and a "Yes" second, but you don't know which is which yet. So your third question could be answered "Yes" or "No" and you wouldn't be able to determine who is who or even what "Yes and "No" really are.

[Prof. Templeton]

I missed the one and only one part

That is what makes it hard.

[Guest]

Ask one of the gods:

-are you a mortal? and subsequently ask the same god:

-did you just answer with a negative?

If H: will answer N, Y

If S: will answer Y, Y

If R: will answer Y, N

Now you know what "yes" and "no" are, and you know what one of the gods is.

Next, if the confirmed god is H, point to another of the gods and ask:

-Is he a S? If Y, that god is a S, and the remaining one is a R. If N, that god is a R, and the remaining one is a S.

OR, if the confirmed god is a S, ask someone else:

-are you R? If N, that god is H, and the other one is R. If Y, that god is R, and the other one is H.

OR, if the confirmed god is R, ask someone else:

-are you R? If Y, that god is S, and the other god is H. If N, that god is H, and the other god is S.

Sorry for making it so long! It is probably overcomplicated.

[Guest]

Never mind

Edited April 21, 2009 by psycho

[Prof. Templeton]

Ask one of the gods:

-are you a mortal? and subsequently ask the same god:

-did you just answer with a negative?

If H: will answer N, Y

If S: will answer Y, Y

If R: will answer Y, N

Now you know what "yes" and "no" are, and you know what one of the gods is.

Next, if the confirmed god is H, point to another of the gods and ask:

-Is he a S? If Y, that god is a S, and the remaining one is a R. If N, that god is a R, and the remaining one is a S.

OR, if the confirmed god is a S, ask someone else:

-are you R? If N, that god is H, and the other one is R. If Y, that god is R, and the other one is H.

OR, if the confirmed god is R, ask someone else:

-are you R? If Y, that god is S, and the other god is H. If N, that god is H, and the other god is S.

Sorry for making it so long! It is probably overcomplicated.

You won't know what "Yes" and "No" are after 2 questions since you could have gotten a Y then a N or a N then a Y

Pick one God. Ask if they are an Honestant.

Swindlecant: Yes

Honestant: Yes

Random Cant: No

Ask if they just said Yes

Swindlecant: No

Honestcant: Yes

Randomcant: Yes

Ask if they are a Swindlecant:

Swindlecant: No

Honestcant: No

Randomcant: No

A Swindlecant would answer Yes No No

A Honestcant would answer Yes Yes No

A Randomcant would answer No Yes No

As we can't understand the answers (different language) look for a sound pattern:

S = a b b or 1 followed by 2

H = a a b or 2 followed by 1

R = b a b or alternating pattern

So you can determine 1 of the Gods, but what about the other 2?

[CaptainEd]

I'm having a fundamental problem with the premise of R: Let's just look at one question--the gods are A, B, and C. Never mind that I don't know what the answers mean, I just want to know how they would answer in their native tongue.

Ask A if B is H.

If A is H, answer is No (because B is not H)

If A is S

If B is H, answer is No, because B is H

If B is R, answer is Yes, because B is not H

If A is R,

We don’t know what H would say, if B is H, because A couldn’t be H. Since I can't tell what A would say if B were H, I can't tell whether one and only one god would say Yes.

So, I don’t know what R would say.

Please help explicate the premise!

[Guest]

You won't know what "Yes" and "No" are after 2 questions since you could have gotten a Y then a N or a N then a Y

So you can determine 1 of the Gods, but what about the other 2?

Yep. I realized that just after I posted it and I wasn't quick enough with my retraction.

I'll have to think about this one.

[Guest]

I like your thinking psycho

the rules say that if you were to ask the randomcant your first questions he would say no since BOTH of the other gods would say yes and not just one.

Edit: Sorry I had been typing for a while

Having said that

we need a question that all three answer negative which would be "Are you a lier?"

Whatever they answer is a no and you can ask "Did you just answer yes?" in which case the randomcant and lier would say yes but the truthteller would say no.

If no: Then you know the truthteller and can ask the same god "Is he (pointing at one of the others) a swindlecant?" and he will tell you the truth and you know all 3.

If yes: Ask the same god "Is he (pointing at one of the others) a swindlecant?" only the lier would say yes and the randomcant would say no and this is where i am stuck.

Edited April 21, 2009 by zzembower

[plasmid]

It almost seems like you can prove that this is an impossible problem. If you number the gods #1, #2, and #3, there are six different possible arrangements

1H, 2S, 3R

1H, 2R, 3S

1S, 2H, 3R

1S, 2R, 3H

1R, 2H, 3S

1R, 3S, 2H

The gods will reply with a word whose meaning you don't know. Without loss of generality, we can call the first word you hear in response to a question "A". If you hear a different response on any subsequent question, we can call that response "B". There would be four different possible patterns of responses

AAA

AAB

ABA

ABB

which wouldn't be enough to ensure that you could distinguish between six possible arangements of the gods.

Which leads me to ask, is it allowed to ask a god a question like "If I were to ask you this question, would your answer be the equivalent of "no"?" such that the Honestant would have to be silent or take some other third course of action?

[Guest]

Ask one of the gods:

-are you a mortal? and subsequently ask the same god:

-did you just answer with a negative?

If H: will answer N, Y

If S: will answer Y, Y

If R: will answer Y, N

Now you know what "yes" and "no" are, and you know what one of the gods is.

Next, if the confirmed god is H, point to another of the gods and ask:

-Is he a S? If Y, that god is a S, and the remaining one is a R. If N, that god is a R, and the remaining one is a S.

OR, if the confirmed god is a S, ask someone else:

-are you R? If N, that god is H, and the other one is R. If Y, that god is R, and the other one is H.

OR, if the confirmed god is R, ask someone else:

-are you R? If Y, that god is S, and the other god is H. If N, that god is H, and the other god is S.

Sorry for making it so long! It is probably overcomplicated.

Your first two questions would go the way you describe, but it in no way gives you any information unless you were lucky enough to ask the Swindelcant god.

You'd have no way to differentiate between H and R, nor would you know which question means yes and which means no.

[CaptainEd]

I have another question about the premise.

"Because of possible loop conflicts, you may not ask any question about how the God of the Randomcants would answer."

Does this mean:

(a) you may not ask anybody "How would R answer...? or

(b) you may not ask anybody "How would B answer", given that B might be R.

[Guest]

Your first two questions would go the way you describe, but it in no way gives you any information unless you were lucky enough to ask the Swindelcant god.

You'd have no way to differentiate between H and R, nor would you know which question means yes and which means no.

Yeah, it figures. I thought I was getting someplace, too. Must ponder more.

Makes me wonder if figuring out what "yes" and "no" are is not needed.

[Prof. Templeton]

I'm having a fundamental problem with the premise of R: Let's just look at one question--the gods are A, B, and C. Never mind that I don't know what the answers mean, I just want to know how they would answer in their native tongue.

Ask A if B is H.

If A is H, answer is No (because B is not H)

If A is S

If B is H, answer is No, because B is H

If B is R, answer is Yes, because B is not H

If A is R,

We don’t know what H would say, if B is H, because A couldn’t be H. Since I can't tell what A would say if B were H, I can't tell whether one and only one god would say Yes.

So, I don’t know what R would say.

Please help explicate the premise!

Well, R's answers depend on what H and S would respond with. So if we are asking if God "B" is an Honestant and "B" was, in fact the Honestant:

H would reply "Yes"

S would reply "No"

R would reply "Yes" since only one of the reponses from the other two Gods was a "Yes".

If God "B" is not an Honestant then:

H would reply "No"

S would reply "Yes"

R would reply "Yes" since only one of the reponses from the other two Gods was a "Yes".

R's answers are only dependent on what H and S would answer if given the same question. So in your example above R would give you 2 seperate answer that depended on if "B" was the Honestant or if he wasn't. For this question R's replies happen to be the same in both cases. If you walked up to God "A" and asked "Is God B is an Honestant", if "A" was the Randomcant you would get the same answer wheather "B" was or wasn't. Have I made it more confusing?

H...S...R

Y...Y...N

Y...N...Y

N...Y...Y

N...N...N

[Prof. Templeton]

I have another question about the premise.

"Because of possible loop conflicts, you may not ask any question about how the God of the Randomcants would answer."

Does this mean:

(a) you may not ask anybody "How would R answer...? or

(b) you may not ask anybody "How would B answer", given that B might be R.

I would have to say both would not be allowed unless you know that "B" is not the Randomcant.

[CaptainEd]

Well, R's answers depend on what H and S would respond with. So if we are asking if God "B" is an Honestant and "B" was, in fact the Honestant:

H would reply "Yes"

S would reply "No"

R would reply "Yes" since only one of the reponses from the other two Gods was a "Yes".

If God "B" is not an Honestant then:

H would reply "No"

S would reply "Yes"

R would reply "Yes" since only one of the reponses from the other two Gods was a "Yes".

R's answers are only dependent on what H and S would answer if given the same question. So in your example above R would give you 2 seperate answer that depended on if "B" was the Honestant or if he wasn't. For this question R's replies happen to be the same in both cases. If you walked up to God "A" and asked "Is God B is an Honestant", if "A" was the Randomcant you would get the same answer wheather "B" was or wasn't. Have I made it more confusing?

H...S...R

Y...Y...N

Y...N...Y

N...Y...Y

N...N...N

I don't buy that this is well defined. H and S can't answer the same question in the same circumstances. Here are the six cases: (AB) = HR, HS, RH, RS, SH, SR

what would H say if I asked if B were H? There would be two cases HR, and HS. In both those cases, A(ie.H)'s answer would be No. However, if I ask R whether B is H, the two cases are different from A's cases: RH and RS. In the first case, B is H, but A could never have inhabited that case because A is H, so "how A would have answered" is not defined. Similarly, how would S have answered in the case RS? Since S couldn't have inhabited that condition, S's answer is not defined.

I think the intent of the premise might be achieved if, instead of saying that R responds Yes if exactly one of the other gods would say Yes, we say that R responds yes if any Honestant would say the opposite of any Swindlecant.

Edited April 21, 2009 by CaptainEd

[Guest]

Ask first 2 gods same known question.

Am I a Male?

Am I a Male?

with luck you get the same word meaning the first 2 gods are H and R and you know what word = yes.

Ask the last god while pointing to first god, is this an honastant?

If he says yes then the gods are R H S, if he says a differant word then they are H R S

It's not solid but it works with luck.

[Guest]

Ask a if b is honestant.

Ask a if c is honestant.

If answers are different, a is swindlecant. Ask if a is swindlecant. Match false answer to responses to the first question to determine what b and c are. For example, if answers are “ug” and “oh” respectively, and he is asked if he is a swindlecant and he answers “oh,” we know that “oh” means no and “ug” means yes. Which means c is honestcant and b is randomcant. And vis a versa.

If answers are the same, ask a if it is a honestant. If their answer is different from the first two answers, they are an honestant. If they are the same, it is a randomcant.

[Prof. Templeton]

I don't buy that this is well defined. H and S can't answer the same question in the same circumstances. Here are the six cases: (AB) = HR, HS, RH, RS, SH, SR

what would H say if I asked if B were H? There would be two cases HR, and HS. In both those cases, A(ie.H)'s answer would be No. However, if I ask R whether B is H, the two cases are different from A's cases: RH and RS. In the first case, B is H, but A could never have inhabited that case because A is H, so "how A would have answered" is not defined. Similarly, how would S have answered in the case RS? Since S couldn't have inhabited that condition, S's answer is not defined.

I think the intent of the premise might be achieved if, instead of saying that R responds Yes if exactly one of the other gods would say Yes, we say that R responds yes if any Honestant would say the opposite of any Swindlecant.

I think I understand what your getting at. In your cases where "A" is the randomcant (RH and RS) H would answer "Yes" and "No" respectively, because in RH "B" is the Honestant and in RS "B" is not the Honestant. I think you have to look at what H and S would reply with if they were in R's position (figuratively), even if the question is about themselves. I hope that clears it up.

[Prof. Templeton]

Ask a if b is honestant.

Ask a if c is honestant.

If answers are different, a is swindlecant. Ask if a is swindlecant. Match false answer to responses to the first question to determine what b and c are. For example, if answers are “ug” and “oh” respectively, and he is asked if he is a swindlecant and he answers “oh,” we know that “oh” means no and “ug” means yes. Which means c is honestcant and b is randomcant. And vis a versa.

If answers are the same, ask a if it is a honestant. If their answer is different from the first two answers, they are an honestant. If they are the same, it is a randomcant.

Both Honestant and Randomcant would answer "No" to the last question.