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]

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

Actually, if the Swindlecant was asked the question he would reply "yes," which means the Randomcant would also reply "yes," making this answer the same as his first two.

Edit: If a was a Randomcant, he would answer yes to both the first and second question. Then when asked the third, he would still answer yes, as he would place each the Honestant and the Swindlecant in his position and as their answers would differ, his would be yes. All answers the same.

If a was a Honestant, he would answer No to both the first two questions, and yes to the last. Thus he would be the Honestant.

Edited April 21, 2009 by psycho

[CaptainEd]

I'm with Plasmid--there are two answers, P and Q. There are only 4 distinguishable sequences of answers, no matter what the questions: PPP, PPQ, PQP, PQQ, and 6 cases to distinguish. If I weren't so awash with coin-weighing, I would think that we can't distinguish 6 cases with only 4 sequences of answers. Sure wish I could prove it (or brilliantly get the answer!)

[Prof. Templeton]

Actually, if the Swindlecant was asked the question he would reply "yes," which means the Randomcant would also reply "yes," making this answer the same as his first two.

Edit: If a was a Randomcant, he would answer yes to both the first and second question. Then when asked the third, he would still answer yes, as he would place each the Honestant and the Swindlecant in his position and as their answers would differ, his would be yes. All answers the same.

If a was a Honestant, he would answer No to both the first two questions, and yes to the last. Thus he would be the Honestant.

You're right. R would answer "Yes" to all three questions wheather the order was R-H-S or R-S-H.

[Guest]

You're right. R would answer "Yes" to all three questions wheather the order was R-H-S or R-S-H.

I just realized it wouldn't mater anyway, as we would know who a was, but unless a is swindlecat, we wouldn't know what b or c were.

Nuts

[Guest]

"...you may not ask any question about how the God of the Randomcants would answer" - I interpret this statement this way: I propose that you are allowed to ask the questions, it is the gods who are unable to give answers.

If you run under the assumption that the gods can *not be able* to answer (give no answer) this is what I can come up with.

Ask god 1:

-If I asked god 2 if he was H, how would he answer?

-If I asked god 3 if he was H, how would he answer?

1) IF god 1 is H, answers are Yes and Silence.

2) IF god 1 is S, answers are No and Silence.

3) IF god 1 is R, answers are Yes and Yes.

Now, in instances 1 and 2 you don't know what yes and no are at this point, but you do know who R is. R is the one identifed by the silence. It could be either god 2 or 3, but lets say it is 3 in this case. So in instance 1 or 2, now ask god 1:

-Are you R?

1) IF god 1 is H, then god 2 is S, and answer is N.

2) IF god 1 is S, then god 2 is H, and answer is Y.

Now, in instance 3, you know that god 1 is R, because he is the only one who could answer both of the questions. Also, you know what yes and no are because R has to answer yes to both of those questions. So, in this instance, now ask god 2:

-What would god 3 say if I asked him if you were H?

1) IF god 1 is H, then god 3 is S, and answer is N.

2) IF god 1 is S, then god 3 is H, and answer is Y.

FIN.

This puzzle is driving me insane...

[Prof. Templeton]

"...you may not ask any question about how the God of the Randomcants would answer" - I interpret this statement this way: I propose that you are allowed to ask the questions, it is the gods who are unable to give answers.

If you run under the assumption that the gods can *not be able* to answer (give no answer) this is what I can come up with.

Ask god 1:

-If I asked god 2 if he was H, how would he answer?

-If I asked god 3 if he was H, how would he answer?

1) IF god 1 is H, answers are Yes and Silence.

2) IF god 1 is S, answers are No and Silence.

3) IF god 1 is R, answers are Yes and Yes.

Now, in instances 1 and 2 you don't know what yes and no are at this point, but you do know who R is. R is the one identifed by the silence. It could be either god 2 or 3, but lets say it is 3 in this case. So in instance 1 or 2, now ask god 1:

-Are you R?

1) IF god 1 is H, then god 2 is S, and answer is N.

2) IF god 1 is S, then god 2 is H, and answer is Y.

Now, in instance 3, you know that god 1 is R, because he is the only one who could answer both of the questions. Also, you know what yes and no are because R has to answer yes to both of those questions. So, in this instance, now ask god 2:

-What would god 3 say if I asked him if you were H?

1) IF god 1 is H, then god 3 is S, and answer is N.

2) IF god 1 is S, then god 3 is H, and answer is Y.

FIN.

This puzzle is driving me insane...

Excellent effort, but the rule is that you aren't even allowed to ask the questions. You would end up with a "If I say he will say "Yes", then he will say "No" and if I say he will say "No", then he will say "Yes"" scenario. Best to be avoided all together.

[Guest]

Just to make sure - the Randomcant is giving "Logical Exclusive OR" answers, right? If both say yes - he says no. If both say no - he says yes. If one says yes, he says no?

Thanks for clarifying!

Love your puzzles, btw.

[Prof. Templeton]

Just to make sure - the Randomcant is giving "Logical Exclusive OR" answers, right? If both say yes - he says no. If both say no - he says yes. If one says yes, he says no?

Thanks for clarifying!

Love your puzzles, btw.

Yes. He is giving logical Exclusive Or responses. If only 1 truth, he says true. If both are true or false, he says false.

[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.

I still think this works, not everytime but it works

[Gmaster479]

I still think this works, not everytime but it works

I think Prof. T is looking for a full-proof answer. You even say that with luck it will work.

As for me I am still wrapping my brain around this one. The first ones were easy compared to this

[Prof. Templeton]

I still think this works, not everytime but it works

It looks like it may work for 2 out of the 6 possible cases. But we're looking for a guarenteed solution. I'll admit this is a tough one.

Edited April 22, 2009 by Prof. Templeton

[plasmid]

Consider the gods to be in a circle and ask this question to each god. Are either of the following statements true: (1) you are a Swindlecant AND either you or the Swindlecant god is to the right of the Honestant god, or (2) you are an Honestant AND you are about to answer this question with the equivalent of "no"?

Honestant:

Part 1: That's clearly false. The truth or falseness of the statement posed by the question will depend entirely on the second part.

Part 2: If his answer were "yes", the second part and the entire statement would be false: unacceptable

If his answer were "no", the second part and therefore the entire statement would be true: he should have answered "yes" and it's therefore unacceptable.

So the Honestant god cannot answer.

Swindlecant:

Part 2: That's clearly false. The truth or falseness of the question will depend entirely on the first part.

Part 1: If he is to the right of the Honestant, then the entire statement is true and he answers "no".

If he is to the left of the Honestant, then the entire statement is false and he answers "yes"

Randomcant: The Honestant cannot answer this question, so the Randomcant will answer "yes" if a Swindlecant would answer "yes" and will answer "no" if a Swindlecant would answer "no".

Part 2: This is false, so the truth or falseness of the question depends on the first part.

Part 1: A swindlecant would consider the first half of part 1 true, and the second half of part 1 would be true no matter how the gods are arranged. So the statement would be true and a swindlecant would answer "no", and the Randomcant god will therefore always answer "no".

So at the end of it all, we can identify the Honestant god because he is silent. The Randomcant will always answer "no", so if both speaking gods give the same answer then they both said "no", which is only possible if the Swindlecant god is to the right of the Honestant god. If the two speaking gods gave opposite answers then the Swindlecant answered "yes", so the Swindlecant god is to the left of the Honestant god.

[Prof. Templeton]

Consider the gods to be in a circle and ask this question to each god. Are either of the following statements true: (1) you are a Swindlecant AND either you or the Swindlecant god is to the right of the Honestant god, or (2) you are an Honestant AND you are about to answer this question with the equivalent of "no"?

Honestant:

Part 1: That's clearly false. The truth or falseness of the statement posed by the question will depend entirely on the second part.

Part 2: If his answer were "yes", the second part and the entire statement would be false: unacceptable

If his answer were "no", the second part and therefore the entire statement would be true: he should have answered "yes" and it's therefore unacceptable.

So the Honestant god cannot answer.

Swindlecant:

Part 2: That's clearly false. The truth or falseness of the question will depend entirely on the first part.

Part 1: If he is to the right of the Honestant, then the entire statement is true and he answers "no".

If he is to the left of the Honestant, then the entire statement is false and he answers "yes"

Randomcant: The Honestant cannot answer this question, so the Randomcant will answer "yes" if a Swindlecant would answer "yes" and will answer "no" if a Swindlecant would answer "no".

Part 2: This is false, so the truth or falseness of the question depends on the first part.

Part 1: A swindlecant would consider the first half of part 1 true, and the second half of part 1 would be true no matter how the gods are arranged. So the statement would be true and a swindlecant would answer "no", and the Randomcant god will therefore always answer "no".

So at the end of it all, we can identify the Honestant god because he is silent. The Randomcant will always answer "no", so if both speaking gods give the same answer then they both said "no", which is only possible if the Swindlecant god is to the right of the Honestant god. If the two speaking gods gave opposite answers then the Swindlecant answered "yes", so the Swindlecant god is to the left of the Honestant god.

Hmmm. Some of these questions would be considered "imdeterminable" and cannot be answered. They would therefore not be valid questions, since the Gods will only answer yes/no questions I suspect none of the gods would answer. You would be asking questions with 3 answers and not 2. I admire your determination however.

[Gmaster479]

Start off assuming you know the 2 words for 'Yes' and No' but don't know which is which

To #1: Are you a God?

H: Yes (so)

R: Yes (so)

S: No (la)

To #2: Did he just answer 'la' (or 'so', whichever one isn't what you got out of the first God)

1= H, R would say: No (Y,N)

1= R, H would say: Yes (Y,N)

1= H, S would say: Yes (Y,Y)

1= R, S would say: Yes (Y,Y)

1= S, H would say: No (N,N)

1= S, R would say, No (N,N)

In the Blue Case, both answers are the same so they have to both be yes's, therefore #3 is the S God. So you ask #1, "Are you not the Honestant God" The Honestant God will answer 'No' or 'la', a different answer, so you know it goes H, R, S and if he answers the same, it will be R, H, S.

The red and green cases are different. Sure they are different based on Yes and No but not knowing what is yes and what is no makes this tricky. You know after hearing two of the same answers that the last God is either an Honestant or a Randomcant.

So ask the #3 God "Are you not the Honestant God?" R answers yes and thats the 3rd time you've heard the same answer, then it goes H, S, R. If it is a new answer you would know it would be S, H, R.

If the God answers no and you hear the same thing 3 times you know its S, R, H. If you hear something different, then it is R, S, H.

So you are probably thinking. "You heard the same thing 3 times and a new answer in 2 cases so how can you tell the difference?"

Go based on the answer of the 3rd question. An honestant god could only be in the 3rd spot and answer the same as before if the first guy was lying. So that means 'la' is no and 'so' is yes. The Random God can only be in the 3rd spot if the first person was an honestant, so that means the first answer means 'yes' (so) and the other one means 'no'. (This is what I mean by having to know the 2 words without hearing them as part of your answer)

So: Y, N, Y = H, R, S

1, 2, 1

Y, N, N = R, H, S

1, 2, 1

Y, Y, Y = H, S, R

1, 2, 3'

Y, Y, N = R, S, H

1, 2, 3

N, N, N = S, R, H

1, 2, 3

N, N, Y = S, H, R

1, 2, 3

EDIT: I hope this is close is some way

Edited April 22, 2009 by Gmaster479

[Guest]

EDIT: I hope this is close is some way

Start off assuming you know the 2 words for 'Yes' and No' but don't know which is which

To #1: Are you a God?

H: Yes (so)

R: Yes (so)

S: No (la)

To #2: Did he just answer 'la' (or 'so', whichever one isn't what you got out of the first God)

1= H, R would say: No (Y,N)

1= R, H would say: Yes (Y,N)

1= H, S would say: Yes (Y,Y)

1= R, S would say: Yes (Y,Y)

1= S, H would say: No (N,N)

1= S, R would say, No (N,N)

In the Blue Case, both answers are the same so they have to both be yes's, therefore #3 is the S God. So you ask #1, "Are you not the Honestant God" The Honestant God will answer 'No' or 'la', a different answer, so you know it goes H, R, S and if he answers the same, it will be R, H, S.

The red and green cases are different. Sure they are different based on Yes and No but not knowing what is yes and what is no makes this tricky. You know after hearing two of the same answers that the last God is either an Honestant or a Randomcant.

So ask the #3 God "Are you not the Honestant God?" R answers yes and thats the 3rd time you've heard the same answer, then it goes H, S, R. If it is a new answer you would know it would be S, H, R.

If the God answers no and you hear the same thing 3 times you know its S, R, H. If you hear something different, then it is R, S, H.

So you are probably thinking. "You heard the same thing 3 times and a new answer in 2 cases so how can you tell the difference?"

Go based on the answer of the 3rd question. An honestant god could only be in the 3rd spot and answer the same as before if the first guy was lying. So that means 'la' is no and 'so' is yes. The Random God can only be in the 3rd spot if the first person was an honestant, so that means the first answer means 'yes' (so) and the other one means 'no'. (This is what I mean by having to know the 2 words without hearing them as part of your answer)

So: Y, N, Y = H, R, S

1, 2, 1

Y, N, N = R, H, S

1, 2, 1

Y, Y, Y = H, S, R

1, 2, 3'

Y, Y, N = R, S, H

1, 2, 3

N, N, N = S, R, H

1, 2, 3

N, N, Y = S, H, R

1, 2, 3

i don't think you would be able to tell if the same answer three times in a row was nonono or yes yes yes... so it could be HSR or SRH

...i can't find a solution and mathimatically it doesn't seem possible, i'm really curious about the answer

Edited April 23, 2009 by varnejm

[Guest]

I dont have the answer yet but I think the way this problem needs to start out is finding what the word for yes or no is.

I think you need to come up with a question that all 3 would answer yes or no to. Once you have that then you can ask 2 questions to figure out who is who.

I am not smart enough to come up with a paradoxal yes or no question. Good luck.

[Prof. Templeton]

I dont have the answer yet but I think the way this problem needs to start out is finding what the word for yes or no is.

I think you need to come up with a question that all 3 would answer yes or no to. Once you have that then you can ask 2 questions to figure out who is who.

I am not smart enough to come up with a paradoxal yes or no question. Good luck.

It's true you have to determine what "yes" and "no" are but you can't waste one whole question on it. That would leave you with only 2 questions and 2² = 4 determinations and 3! = 6 posibilities for the Gods positions. You're first question should therefore actually perform 2 tasks.

[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.

This is a question but didn't want to give any clues away so it's in a spoiler. I just wanted to confirm my understanding of the problem.

You state that the randomcant will answer with an affirmative, if one of the other two gods would answer with an affirmation. Yet the other two gods (1 Honesants 1 Swindlecants) will answer opposite of each other. Therefore one of their answers would ALWAYS be affirmative, meaning the randomcant will ALWAYS answer affirmative, or have I misunderstood your wording?

[Prof. Templeton]

This is a question but didn't want to give any clues away so it's in a spoiler. I just wanted to confirm my understanding of the problem.

You state that the randomcant will answer with an affirmative, if one of the other two gods would answer with an affirmation. Yet the other two gods (1 Honesants 1 Swindlecants) will answer opposite of each other. Therefore one of their answers would ALWAYS be affirmative, meaning the randomcant will ALWAYS answer affirmative, or have I misunderstood your wording?

The Honestant and Swindlecant will answer some questions the same. Ex. "Are you an Honestant?" Both will answer "Yes".

[plasmid]

Consider the gods to be in a circle and ask this question to each god. Are either of the following statements true: (1) you are a Swindlecant AND either you or the Swindlecant god is to the right of the Honestant god, or (2) you are an Honestant AND you are about to answer this question with the equivalent of "no"?

Honestant:

Part 1: That's clearly false. The truth or falseness of the statement posed by the question will depend entirely on the second part.

Part 2: If his answer were "yes", the second part and the entire statement would be false: unacceptable

If his answer were "no", the second part and therefore the entire statement would be true: he should have answered "yes" and it's therefore unacceptable.

So the Honestant god cannot answer.

Swindlecant:

Part 2: That's clearly false. The truth or falseness of the question will depend entirely on the first part.

Part 1: If he is to the right of the Honestant, then the entire statement is true and he answers "no".

If he is to the left of the Honestant, then the entire statement is false and he answers "yes"

Randomcant: The Honestant cannot answer this question, so the Randomcant will answer "yes" if a Swindlecant would answer "yes" and will answer "no" if a Swindlecant would answer "no".

Part 2: This is false, so the truth or falseness of the question depends on the first part.

Part 1: A swindlecant would consider the first half of part 1 true, and the second half of part 1 would be true no matter how the gods are arranged. So the statement would be true and a swindlecant would answer "no", and the Randomcant god will therefore always answer "no".

So at the end of it all, we can identify the Honestant god because he is silent. The Randomcant will always answer "no", so if both speaking gods give the same answer then they both said "no", which is only possible if the Swindlecant god is to the right of the Honestant god. If the two speaking gods gave opposite answers then the Swindlecant answered "yes", so the Swindlecant god is to the left of the Honestant god.

If we're not allowed to take this route, then I get the feeling we're about to be hornswaggled with something as silly as a female firefighter that will let you go around calling her a "fireman" without getting a whalloping.

The OP says that we have to address each question to a specific god. Allright, then. My first question is: "God of the Honestants, are you a god?" Whoever pipes up is the god of the Honestants. Similar strategy for the other two bozos.

[Prof. Templeton]

If we're not allowed to take this route, then I get the feeling we're about to be hornswaggled with something as silly as a female firefighter that will let you go around calling her a "fireman" without getting a whalloping.

The OP says that we have to address each question to a specific god. Allright, then. My first question is: "God of the Honestants, are you a god?" Whoever pipes up is the god of the Honestants. Similar strategy for the other two bozos.

No hornswaggling. A valid solution does exist. And it was "firefighter".

[Guest]

No hornswaggling. A valid solution does exist. And it was "firefighter".

Yep. The Prof. took advantage of our paradigms with precision. I'd be impressed, but around here it's a regular occurance.

[plasmid]

No hornswaggling. A valid solution does exist. And it was "firefighter".

Hmm, it sure was. I guess that

that I can sure get fooled easily. And I revise my previous answer: I should've first asked "Swindlecant god, are you a god?" Then "Randomcant god, are you a god?" Then "Honestant god, are the Astros going to beat the spread in their next game?"

[Guest]

Hmm, it sure was. I guess that

that I can sure get fooled easily. And I revise my previous answer: I should've first asked "Swindlecant god, are you a god?" Then "Randomcant god, are you a god?" Then "Honestant god, are the Astros going to beat the spread in their next game?"

Has anyone solved this one yet?

I am thinking of jumping in...

[Guest]

Has anyone solved this one yet?

I am thinking of jumping in...

Not solved yet, but be warned ...your head will hurt trying!!!