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.

[HoustonHokie]

When the Randomcant considers the answers that the Honestant and Swindlecant would give, how exactly does he evaluate those answers? I see two possibilities:

1. The Randomcant compares the answers he would give if he were an Honestant vs. if he were a Swindlecant.

2. The Randomcant compares the answers the other two gods would give if you turned and asked them the question instead of him.

The reason I ask (and I may be barking up the wrong tree here) is that I'm not sure how the Randomcant would answer the question "Are you sitting in the middle?" or any other question that depends on the relative order of the three gods. Assuming the Randomcant was on one end with the Swindlecant in the middle and the Honestant on the other end, his answer to "Are you sitting in the middle?" with the first method would be yes (H = no, S = yes => R = yes), but his answer with the second method would be no (H = no, S = no => R = no)

[Prof. Templeton]

When the Randomcant considers the answers that the Honestant and Swindlecant would give, how exactly does he evaluate those answers? I see two possibilities:

1. The Randomcant compares the answers he would give if he were an Honestant vs. if he were a Swindlecant.

2. The Randomcant compares the answers the other two gods would give if you turned and asked them the question instead of him.

The reason I ask (and I may be barking up the wrong tree here) is that I'm not sure how the Randomcant would answer the question "Are you sitting in the middle?" or any other question that depends on the relative order of the three gods. Assuming the Randomcant was on one end with the Swindlecant in the middle and the Honestant on the other end, his answer to "Are you sitting in the middle?" with the first method would be yes (H = no, S = yes => R = yes), but his answer with the second method would be no (H = no, S = no => R = no)

From what I understand it would be the first scenario.

[Guest]

From what I understand it would be the first scenario.

If I asked the randomcant, are there two honestants here?

Considering himself as an honestant=yes

Considering himself as a swindlecant=yes

Therefore he would answer no?

[Prof. Templeton]

If I asked the randomcant, are there two honestants here?

Considering himself as an honestant=yes

Considering himself as a swindlecant=yes

Therefore he would answer no?

No. Nothing like that. He is still a Randomcant after all. He would consider, all other things being equal, what would the other two Gods answer if asked the same question, then gives his own answer accordingly. In the above example the Honestant would truthfully say "No" and the Swindlecant would lie and say "Yes", so the Randomcant would answer "Yes".

Edited April 24, 2009 by Prof. Templeton

[Gmaster479]

Yes that it what I percieved it to be which was part of my wrong explanation. Prof. am I on the right track?

[Prof. Templeton]

Since it can be confusing determining what the Randomcant God would respond with I thought I would attempt to clear up some of that confusion. Although it is not necessary to the solution some questions to the Randomcant can seem to have paradoxical answers.

For example: let's assume the Randomcant is in position 1. You ask the question, "Is there an Honestant in position 1?" Since the Randomcant occupies that position H would reply with No and S would reply with Yes, so the answer you would get from the Randomcant would be Yes.

However, if you were to ask the Randomcant God in position 1, "Are you an Honestant?", he would reply No, since if he were an Honestant he would say Yes and if he were a Swindlecant he would also say Yes.

Think of the randomcant as having a virtual Honestant and a virtual Swindlecant living inside of him (or sitting on each shoulder) and he consults these two before answering. Any questions that do not refer directly to the "real-life" Honestant and Swindlecant get deferred to the two virtual Gods inside of the Randomcant. Any questions that refer directly to the "real-life" H and S would defer to the "real-life" Gods. Mostly question about position since we don't know much beyond that. If you are asking the Randomcant God a question and you direct it at him specifically, he would consult with his virtual Gods over the "real-life" ones.

For example: If you were to ask the question, "Are you in position 1?" He would reply Yes because the virtual Honestant inside him would say Yes and the virtual Swindlecant would say no.

Edited April 24, 2009 by Prof. Templeton

[Prof. Templeton]

Yes that it what I percieved it to be which was part of my wrong explanation. Prof. am I on the right track?

Well, there are some holes. As I said previously, you can't use one whole question to determine the meanings of "Yes" and "No" You can have a question(s) that does this, but it should also perform another function at the same time.

• The Gods are omniscient (all knowing)
  
• "Yes" and "No" in their language are distinctly different
  
• You can ask complex questions (would you reply with x, if and only if y, ect.)
  

[Guest]

If you ask all three gods in turn if there is an honestant in "seat a", the answer will be (always):

2 say "yes", one says no. So you would know which is yes, and which is no, but that's about all. You would still not know enough - so the question has to be more complex.

So what I am thinking is that I need to ask the same question of the first two, and a separate question of the last one. Am I on the right track?

My head hurts... :-)

[Prof. Templeton]

So what I am thinking is that I need to ask the same question of the first two, and a separate question of the last one. Am I on the right track?

Yep.

[Guest]

Hey Prof, if you did not come up with the concept for this one, I'm just wondering, did you solve it personally?

I'm more interested in the actual methods to solve this type of puzzle, rather than just stumbling across the solution by pondering.

P.S. I thought "Can person A answer truthfully more often than person B?" (from an older similar puzzle) was genius.

Regards,

Mick.

[Prof. Templeton]

Hey Prof, if you did not come up with the concept for this one, I'm just wondering, did you solve it personally?

I'm more interested in the actual methods to solve this type of puzzle, rather than just stumbling across the solution by pondering.

P.S. I thought "Can person A answer truthfully more often than person B?" (from an older similar puzzle) was genius.

Regards,

Mick.

Nope, when I found this one it had the solution already posted with it. The person that came up with it has done several variations and is really quite a genius when it comes to logic problems. I think enough hints are out there, now. You need to find a question that will reveal information about which God you are talking to and also information about the words "Yes" and "No".

[Guest]

Would it be reasonable to suppose that we could establish some distinction between the two words prior to having heard either, such as:

"If I asked you....blah blah....would you answer with the shorter of the two words for 'Yes' and 'No'"

That makes the assumption that one is shorter than the other but maybe they could be distinguished otherwise, though alphabetical order seems the only other way and I'm not sure if these gods use the alphabet.

[Brandonb]

I haven't read the answers, but rather just skimmed through PT's posts to see if there has been a correct answer given.

It didn't look that way so I decided to take a stab at it... I'm sorry if someone else has already suggested this.

I'm pretty sure you can figure it out if you line the three up in any order and ask the first "are you the Randomcant?", then ask the second person "are you the Randomcant?", then ask the second person "is the first guy the Randomcant?"

Edited April 25, 2009 by Brandonb

[Prof. Templeton]

Would it be reasonable to suppose that we could establish some distinction between the two words prior to having heard either, such as:

"If I asked you....blah blah....would you answer with the shorter of the two words for 'Yes' and 'No'"

That makes the assumption that one is shorter than the other but maybe they could be distinguished otherwise, though alphabetical order seems the only other way and I'm not sure if these gods use the alphabet.

Yes, quite reasonable.

I haven't read the answers, but rather just skimmed through PT's posts to see if there has been a correct answer given.

It didn't look that way so I decided to take a stab at it... I'm sorry if someone else has already suggested this.

I'm pretty sure you can figure it out if you line the three up in any order and ask the first "are you the Randomcant?", then ask the second person "are you the Randomcant?", then ask the second person "is the first guy the Randomcant?"

If they God were lined up H,R,S or H,S,R you would get the same answers N,Y,Y. Also if the Gods were lined S,H,R you would get the answers Y,N,N which would be indistinguishable from N,Y,Y unless you know what "Yes" and "No" are.

[Brandonb]

If they God were lined up H,R,S or H,S,R you would get the same answers N,Y,Y. Also if the Gods were lined S,H,R you would get the answers Y,N,N which would be indistinguishable from N,Y,Y unless you know what "Yes" and "No" are.

...? I never asked the 3rd one anything.

I asked the 2nd god twice (two different questions), which I thought would distinguish b/w the 1st and 2nd gods and the difference b/w yes and no, and yield responses that would make conversation with the third god irrelevant.

Edited April 25, 2009 by Brandonb

[Prof. Templeton]

...? I never asked the 3rd one anything.

I asked the 2nd god twice (two different questions), which I thought would distinguish b/w the 1st and 2nd gods and the difference b/w yes and no, and yield responses that would make conversation with the third god irrelevant.

Right, I just meant those would be the replies that you would get to your questions. If the first is H, you would get the same answers wheather 2 and 3 were R,S or S,R.

[Brandonb]

Right, I just meant those would be the replies that you would get to your questions. If the first is H, you would get the same answers wheather 2 and 3 were R,S or S,R.

no you don't

If the first is H the response would be Nobo

Then when you asked the second, the reply would have to be Yabadaba OR Nobo (the R would have to answer no, the S would have to answer that yes, they are the Random)

If you then asked the second god if the first was the Random (the 3rd question), you're gonna get the same answer that they gave the for the 2nd answer... however at that point you would now know (all this would determine is the difference b/w yes or no in a charted comparison against starting with the S or R instead of the H).

Because if the 2nd god gave the same answer as the first god... and the first was the H as you proposed, then the 2nd MUST be the R. And if the 2nd gives the opposite answer from the first (and the first is the H as you suggested) then you know that the 2nd MUST be the S.

to summarize... if the first is H (who would answer no), you would either get YY or NN from the 2nd god... and you never ever say anything at all to the third god and never hear any input from him.

EDIT: Wait... I need to work through this again... for some reason I thought the R answered in the NEGATIVE if only one of the others answered in the affirmative (which is completely backwards from the OP)... oops sorry!

Edited April 25, 2009 by Brandonb

[Guest]

Oh dear. I had hoped some kind person would have finished this off after the hint I dropped last night. I guess it falls to me then. This won't be simple and it won't be elegant. Odds are it won't even be correct.

First off we have 6 possible states for the order of the gods. The answers to the questions have 8 possible states, but if we don't know which answer is which that effectively goes down to 4 which isn't enough. So we must distinguish one answer from the other. If we do that on the basis of what they mean then we have to discover what they mean which effectively raises the number of states we have to distinguish between (gods+answer values) to 12. So we must do it on some other basis, which is why I asked the Prof if it was reasonable to assume that we could do so. For example we could call the shorter answer A and the longer B, if we knew they were of different length. Since we don't, we'll have to call the one that goes the first alphabetically A and the other B. Frankly I'm not entirely satisfied with that either. If the answers were something like "which" and "while" (or is that "witch" and "wile" ?) you might run into trouble. So before you set out you'll have to determine an order based on a phonetic alphabet, explain that to the gods, and say that the Yes/No answer which comes first according to that will be denoted A and the other B. Then just hope their answers don't turn out to be a bunch of clicks, whistles, scraping and farting noises.

Anyway, moving on...

The number of distinguishable answer combinations is now 7 (AAA and BBB are indistinguishable since you have to hear both words to know which is which, but we won't use them at all). Here's where my answer gets ugly. I'm sure there's an elegant solution but this isn't it.

I decided things might be a little easier if you could get a straight answer to your questions, so given any question Q, instead of asking Q directly, you ask:

"Would you answer A to Q and are you something other than a truthful Randomcant God?"

If the answer is A then the correct answer to Q is "yes", if B then the correct answer to Q is "no", regardless of which god you are addressing or the meanings of A and B.

Spoiler for more about that:

This is what the Honestant God (call him H) would say if asked a question Q, for both meanings of A and truth values of Q:

A = Y Y N N

Q = T F T F

-----------

H : A B B A

This is the Honestant and Swindlecant gods' response to "Would you answer A to Q?" (note this is the true answer, rather than the spoken answer which would be reversed for the Swindlecant)

A = Y Y N N

Q = T F T F

-----------

H : Y N N Y

S : N Y Y N

Responses to "Are you something other than a truthful Randomcant God?" (true answer)

RH and RS are the Honestant and Swindlecant sides of the Randomcant God's personality.

H : Y

S : Y

RH: N

RS: Y

Combining the above, "Would you answer A to Q and are you something other than a truthful Randomcant God?" (true answer)

A = Y Y N N

Q = T F T F

-----------

H : Y N N Y

S : N Y Y N

RH: N N N N

RS: N Y Y N

"Would you answer A to Q and are you something other than a truthful Randomcant God?" (spoken answer)

A = Y Y N N

Q = T F T F

-----------

H : A B A B

S : A B A B

RH: B B A A

RS: A B A B

Combining the spoken answers from RH and RS to get what R would actually say:

A = Y Y N N

Q = T F T F

-----------

H : A B A B

S : A B A B

R : A B A B

So the answers form an exact match to the real answer to Q. How handy!

AAB:HSR

ABA:HRS

ABB:SHR

BBA:SRH

BAB:RHS

BAA:RSH

So, the first question (to the god on your left) could be:

"Are you the Honestant God, or the Swindlecant God with the Honestant God immediately to your left?"

Of course we ask it indirectly, so it would come out more like:

"Would you give the Yes/No answer which comes first in the aforementioned phonetic alphabet order to the question 'Are you the Honestant God, or the Swindlecant God with the Honestant God immediately to your left?', and are you something other than a truthful Randomcant God?"

The answer will be A or B but you won't know which it is until you've heard both responses.

Then (to the same god):

"Are you the Randomcant God, or the Honestant God with the Swindlecant God immediately to your left?" (again, wrapped as above)

Finally (to the god on your right):

"Are you the Honestant God, or the Swindlecant God with the Randomcant God immediately to your right?" (likewise)

By now you should have heard examples of both responses so you can figure out which is A and which is B, look up the combination in the above table and bish bash bosh you're there. Easy really.

Apologies in advance for the huge number of errors I have no doubt made here. Actually looking at it now I think I've technically infringed the "you may not ask any question about how the God of the Randomcants would answer" rule since I'm asking gods about their own answers. Maybe the question wrapper could be done better, but unfortunately I'm just about to reach the end of my attention sp

So now we'll invent a one-to-one mapping between answer combinations and god order and try to ask questions that result in that mapping. This is messy but pretty trivial.

[plasmid]

Brilliant move, octopuppy!

An implementation need not be too convoluted.

1. (Ask to god #1) Are exactly one of these statements true? A) The alphabetically first of your words for "yes" and "no" means "no". B) You are the god of the Honestants.

2. Same question to god #2.

3. To whichever of god #1 and god #2 gave the alphabetically first answer (if they both gave the same answer, ask whichever you prefer): Are exactly one of these statements true? A) The alphabetically first of your words for "yes" and "no" means "no". B) You are a god.

Spoiler for And the logic behind it:

1. The replies from each of the gods would be:

Honestant if "yes" comes first: A is false and B is true, so exactly one statement is true, answer with the word for yes – answer with alphabetically first word.

Honestant if "no" comes first: A is true and B is true, not exactly one statement is true, answer with the word for no – answer with the alphabetically first word.

Swindlecant if "yes" comes first: A is false and B is false, not exactly one statement is true, lie by answering with the word for "yes" – answer with the alphabetically first word.

Swindlecant if "no" comes first: A is true and B is false, exactly one statement is true, lie by answering with the word for "no" – answer with the alphabetically first word.

Randomcant if "yes" comes first: both Honestant and Randomcant answered with "yes" (the first word) so answer with "no" – answer with the alphabetically second word.

Randomcant if "no" comes first: both Honestant and Randomcant answered with "no" (the first word) so answer with "yes" – answer with the alphabetically second word.

Final result: Both Honestant and Swindlecant would answer with the first word, Randomcant would answer with the second word. (Of course, at this point since you've only heard one answer, you don't know whether it's the first or second word.)

2. Same logic, but now if both answers were the same you know that god #3 is the Randomcant (and that the answer you heard was alphabetically first). If the answers were different, you know that the one who gave the alphabetically second answer was the Randomcant. Either way, you know who the Randomcant is

3. You're now asking either the Honestant or Swindlecant, so the possibilities are

Honestant if "yes" comes first: A is false and B is true, so exactly one statement is true, answer with the word for yes – answer with alphabetically first word.

Honestant if "no" comes first: A is true and B is true, not exactly one statement is true, answer with the word for no – answer with the alphabetically first word.

Swindlecant if "yes" comes first: A is false and B is true, exactly one statement is true, lie by answering with the word for "no" – answer with the alphabetically second word.

Swindlecant if "no" comes first: A is true and B is true, not exactly one statement is true, lie by answering with the word for "yes" – answer with the alphabetically second word.

Final result: Honestant answers with the alphabetically first word, Swindlecant answers with the alphabetically second word. You already know from the first two questions which word is alphabetically first.

So who wrote the riddle, prof?

[Prof. Templeton]

to Octopuppy for seeing a way to a solution. He is close enough to get the credit. I had considered including in the OP that the Gods used an alphabet like everyone is acustom to, but thought it would be to large of a hint. Plasmid is correct in that a simpler solution can be found. Utilizing an alphabetical word arrangement solution is also subject to debate as the OP never says the Gods have a similar alphabet stucture only that the words are distinctly different. The original creator of this puzzle (whose name is Eric Yeh and has made several variations on this type of logic problem) intended to tap into the omniscience of the Gods with a solution similar to this...

Spoiler for solution:

Ask God "A", "Is your word for "Yes" the word that I would find the most asthetically pleasing immediately upon hearing the second word?"

Honestant will reply with whichever word you would find more pleasing to the ear.

Swindlecant will reply with whichever word you would find least pleasing to the ear.

Randomcant will reply with whichever word means "Yes"

Ask God "A", "Is your word for "No" the word that I would find the most asthetically pleasing immediately upon hearing the second word?"

If the answers to the two questions are the same, then God "A" in the Randomcant and his answer means "Yes".

If the answers are different and you find the answer word to question 1 more pleasing, God "A" is the Honestant.

If the answers are different and you find the answer word to question 2 more pleasing, God "A" is the Swindlecant.

If God "A" is the randomcant you now know what "Yes" is and can determine the other two Gods by asking one of them a factual question (is 2+2 equal to 4). otherwise you know which God is "A" and what the two words and what they mean so, you need to ask God "A" another question that will order to other two Gods such as "If I were to ask you wheather God "B" was the Randomcant, would you respond with "Yes"?".

And your done.

[Guest]

to Octopuppy for seeing a way to a solution. He is close enough to get the credit. I had considered including in the OP that the Gods used an alphabet like everyone is acustom to, but thought it would be to large of a hint. Plasmid is correct in that a simpler solution can be found. Utilizing an alphabetical word arrangement solution is also subject to debate as the OP never says the Gods have a similar alphabet stucture only that the words are distinctly different. The original creator of this puzzle (whose name is Eric Yeh and has made several variations on this type of logic problem) intended to tap into the omniscience of the Gods with a solution similar to this...

Spoiler for solution:

Ask God "A", "Is your word for "Yes" the word that I would find the most asthetically pleasing immediately upon hearing the second word?"

Honestant will reply with whichever word you would find more pleasing to the ear.

Swindlecant will reply with whichever word you would find least pleasing to the ear.

Randomcant will reply with whichever word means "Yes"

Ask God "A", "Is your word for "No" the word that I would find the most asthetically pleasing immediately upon hearing the second word?"

If the answers to the two questions are the same, then God "A" in the Randomcant and his answer means "Yes".

If the answers are different and you find the answer word to question 1 more pleasing, God "A" is the Honestant.

If the answers are different and you find the answer word to question 2 more pleasing, God "A" is the Swindlecant.

If God "A" is the randomcant you now know what "Yes" is and can determine the other two Gods by asking one of them a factual question (is 2+2 equal to 4). otherwise you know which God is "A" and what the two words and what they mean so, you need to ask God "A" another question that will order to other two Gods such as "If I were to ask you wheather God "B" was the Randomcant, would you respond with "Yes"?".

And your done.

That's a great puzzle, probably the hardest one here that I've actually managed to do. Even when you figure out how it might be possible it still remains extremely slippery, hence the brutal nature of my solution.

Eric Yeh's way of distinguishing the answers is clever but what if my tendency to find things pleasing is affected in some small way by the order in which I hear them (or by which God is speaking them)? My way of using a phonetic alphabet is also flawed since there can still be ambiguity about the right way to spell a word. Anyone got a better way? Unless the gods speak identically I think it's a bit of a dodgy area.

I like the way the Eric Yeh solution manages to differentiate between 7 cases (in the case of one god order you also find out what both words mean)

However if the Randomcant doesn't come first you will not know what the words mean so your example question wouldn't work, you'd have to ask something like "If I were to ask you whether God 'B' was the Randomcant, would you respond with '[insert more pleasing word]'?".

[Prof. Templeton]

Right you are. I was trying to post some of it by memory alone.

the Gods know your tendencies.

[Guest]

the Gods know your tendencies.

...if my preference was affected by order of hearing the words, that breaks the solution. If for example both words are incredibly beautiful, then I will probably prefer the first one I hear (since I will have become slightly desensitised by the time I hear the second). How then will I know if I am talking to a Swindlecant? Even if the gods know this and foresee that I will speak to the Swindlecant first, there is no way the Swindlecant can give a dishonest answer, since the first question is now equivalent to "Is 'Yes' the answer to this question?"

[Gmaster479]

Wow that was a good puzzle. Good job octopuppy. I guess that whole omniscent thing was key

[Guest]

i worked hard on this riddle and have come up with this answer

ask one of the three gods these 2 questions

(1) are you god of randomcants?

(2) what would the honestants god say if i asked him the sme question?

ask any of the other 2 gods the (2) question again

tell me if you want an explanation......

Edited November 28, 2011 by Arjit Saraswat