Math game...

[agua.]

That's correct. These seem to have been way too easy. Let's try a harder one...

There are thee men. One of them always tells the truth, one always lies and the third sometimes lies and sometimes tells the truth. You do not know who is who. You may ask exactly 3 yes or no questions. Each question must be directed at only one of the men . You may ask the same man more than one question. After asking 3 questions, you should be able to know who is who.

There's one more catch. The men all understand English, but they will answer in their own language, in which yes and no are "da" and "ja". You don't know which means yes and which means no.

Good luck

The TOG​

Ok ok I've had a thinky dink.

The men are a) , b), c) who are either truth T , lie L , or truth + lie T+L

1. I ask a) " are you L" . The only person that can answer this question with a "yes" is T+L. Both T and L will answer "no"

2. I ask a) "are you T" . The only person who can answer this with a "no" is T+L. Both T and L will answer with "yes"

3. If the answer to 1. was "yes" I ask b) if a) answered the first question truthfully. Only L will answer "yes" and this means a) = T+L, b) = L, c) = T else a)=T+L, b) T, c) L

or

3. If the answer to 2. was "no" I ask b) if a) answered the question truthfully. Only L will answer "yes" and this means a) = T+L b)= L c) =T else a)=T+L b) = T c) =L

Oh hang on I've forgotten what happens if in 1. a) answers "no" and if in 2. a) answers "yes"

I'll be back. ( maybe :D )

 

[agua.]

Oh man i just realised I should be asking questions if they're T+L . Back to the drawing board.

 

[Sparkey]

Kill all three.
Ask, "Are you dead?"
The one who replies, "Yes" is the truth-teller.



At first glance there looks to be a total of 3! (6) possible outcomes between True (T), False (F) and Random (r):

TFr, TrF, FTr, FrT, rTF, rFT <---- meaning we can find a solution.

However, Random's answers may be either True (t) or False (f) -AND- his responses don't have equal probability: ('Ambiguous' is a better name for him.)

TFt, TFf, TtF, TfF, FTt, FTf, FtT, FfT, tTF, fTF, tFT, fFT

So now we see that there are a total of 12 possible outcomes. Therefor, no set of 3 questions can determine a solution.

But if we are to set the impossibility aside and accept that there is a solution we still must remember that "each question must be directed at only one of the men."

To begin, I suggest that we might line the three subjects up, side-by-side, all in a row, and ask the first,

"Are you standing in the middle?"​

If the answer is YES - we can eliminate him from the truth teller category.
If no, we ask the person on the other end, "Are you standing in the middle?"

I've not completed the questions but there is no rule that says we can't change our question according to the answer given. So I'm thinking the task is to prepare a series of questions that are triggered by the information we get in response. The more I work on it though, the more I come back to the possibility of impossibility.

But maybe this will serve as groundwork for others to complete? G'luck. The final (non-required) condition that was given (that the yes/no responses can't be understood due to language barrier) serves to reinforce my initial conclusion:

My best guess: The solution is that there is no solution.

 

[TOG]

I'm pretty sure this is possible, although I haven't figured it out yet. It's similar to another well known puzzle. You are in a room with two doors, one of which leads to a great treasure, whereas the other leads to certain death. There is a man standing by each door. One of the men always lies and the other always tells the truth. You don't know who is who nor who stands by which door. You can ask one question of only one man and then you have to know which door to pick. Since you probably all already know this one, I'll just point out the answer...

If I asked the other man which door leads to the treasure, what would he say?

If you ask the liar, he'll point to the door that leads to death, since he'll lie about what the truth teller would say. If you ask the truthful one, he'll also point to the door to death, since he'll tell the truth about what the liar would say. You then pick the other door.

I think this one might be similar. Maybe we should not ask "What do you say", but rather "What would <someone else> say". At least, that's my current line of thinking.

The TOG​

 

[Sparkey]

That's all well and good if we speak the same language and we can make sense of the answer. The fact that the author of the riddle included that part suggests that he's having a bit of fun with us.

My way of thinking is that it is the most difficult logic problem simple because most don't try to prove that the only solution is "there is no solution". That's an acceptable solution to logic problems too. We have not been given sufficient information to determine the solution -AND- we have not been given any way to discover it.

Since the subjects can understand I suppose we could say, "Tap once for yes, twice for no..." but that defeats the purpose of the rule. To me it's easier to accept the terms and conclude there is no solution. I've tried to plug the question into Google but didn't find a satisfactory answer. The closest I found was the whole 3! (6 possible) and the revised 12 possible situations.

Given that, there is no solution even if we could understand the answers.

 

[TOG]

I checked just now on Wikipedia. There is a solution. I didn't read it, but I saw the first question, and it is kinda like the one I proposed above, but a bit more complicated. Since I now know the first question, it's only fair to let the rest of you know. Here it is...

Does da mean yes if and only if you are False, if and only if B is Random?
​

Like I said, maybe we should stick to English to begin with. But for anyone who wants to try, the original puzzle has a solution and that's the first question. The Wikipedia article also said "The Hardest Logic Puzzle Ever is a logic puzzle invented by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996." So you can look it up in your old copies of The Harvard Review of Philosophy. You do still have those lying around somewhere, don't you?

The TOG​

 

[Sparkey]

Oh! I get it. This is another case where I am wrong. That's not all that strange to me. TOG, thanks for the assurance but I think that minds greater than mine may be required here.

Hmmmm... I wonder what 'da' actually means. The reason that I mention this is it could just as easily mean no, right? Adding two if-conditionals to a false statement doesn't make it true. But maybe that's just because I'm used to computer logic?

"Da"

It seems safe enough to go to Wiki and if you don't scroll down you don't see the answer. Your computer resolution may vary. Your actual mileage may also vary. But here's the question as posed there:

The Hardest Logic Puzzle Ever is stated as follows:

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Boolos provides the following clarifications: a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely

 

[agua.]

Oh! I get it. This is another case where I am wrong. That's not all that strange to me. TOG, thanks for the assurance but I think that minds greater than mine may be required here.

Hmmmm... I wonder what 'da' actually means. The reason that I mention this is it could just as easily mean no, right? Adding two if-conditionals to a false statement doesn't make it true. But maybe that's just because I'm used to computer logic?

"Da"

It seems safe enough to go to Wiki and if you don't scroll down you don't see the answer. Your computer resolution may vary. Your actual mileage may also vary. But here's the question as posed there:

The Hardest Logic Puzzle Ever is stated as follows:

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Boolos provides the following clarifications: a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely

TOG, thanks for the assurance but I think that minds greater than mine may be required here.

Man Sparrow if you're giving up on it I'm wasting my time :D

 

[Sparkey]

I haven't looked at the solution, although I'm glad there is one, but I'm afraid that if I do I won't be able to understand it.

Let's give it a reasonable amount of time and we should let you have the honors, right? That way you can 'splain it to us.

 

[agua.]

I haven't looked at the solution, although I'm glad there is one, but I'm afraid that if I do I won't be able to understand it.

Let's give it a reasonable amount of time and we should let you have the honors, right? That way you can 'splain it to us.

I'm still trying to work it out mate. I can't get my head around the implications of the random person because it mucks up my line of questioning and seems to lead to too many variables. Or maybe I'm over thinking it like your son's sequence :D

 

[agua.]

Ok I'm taking a dig using Sparrow's clever idea.

Line them up in a row. A, B ,C

Q1. @ A . Are you standing on the left ? Yes = T or TL No = L or TL
Q2. @ B. Is A standing on the left ? Yes = T or TL No = L or TL
Q3. ( if Q1 = yes & Q2 = yes ) @ C ( C must be L ). Is T standing on the left ? Yes ~ A =TL B=T C=L No ~ A=T B=TL C = L
Q3. ( if one of Q1 or Q2 = no ) @ A or B ( the one where = yes ) Are you L ? Yes ~ A =TL B=L C=T No ~ A= L B = TL C =T ( or vice vesra etc )
Q3. ( if Q1 = no & Q2 = no ) @ C ( C must be truth ) Is L standing on the left. Yes ~ A = L B=TL C= T No ~ A=TL B=L C=T

Chicken dinner ?

 

[TOG]

Ok I'm taking a dig using Sparrow's clever idea.

Line them up in a row. A, B ,C

Q1. @ A . Are you standing on the left ? Yes = T or TL No = L or TL
Q2. @ B. Is A standing on the left ? Yes = T or TL No = L or TL
Q3. ( if Q1 = yes & Q2 = yes ) @ C ( C must be L ). Is T standing on the left ? Yes ~ A =TL B=T C=L No ~ A=T B=TL C = L
Q3. ( if one of Q1 or Q2 = no ) @ A or B ( the one where = yes ) Are you L ? Yes ~ A =TL B=L C=T No ~ A= L B = TL C =T ( or vice vesra etc )
Q3. ( if Q1 = no & Q2 = no ) @ C ( C must be truth ) Is L standing on the left. Yes ~ A = L B=TL C= T No ~ A=TL B=L C=T

Chicken dinner ?

There are a couple of minor flaws. The first is that the first two questions are ambiguous, since you didn't specify whether it was on your left or his left. We can safely ignore that and assume that it is understood by all which is being referred to. The second flaw is in your third question. Everything works if either the first two are answered the same way or if the third answer is "Yes", but look at this possibility.

Q1 @ A - Are you standing on the left?
A1 from A - YES

Q2 @ B - IS A standing on the left?
A2 from B - NO

Q3 @ A - Are you L?
A3 from A - NO

Based on answer 1, we know that A is either the one who always tells the truth or the one who sometimes tells the truth and sometimes lies. He is not the one who always lies. We know that both his answers were truthful, but we don't know whether it was because he always tells the truth or because he just happened to tell the truth those two times. If A is the one who sometimes lies, then B is the one who always lies. But if A is the one who always tells the truth, then B could still be either the one who always lies or the one who sometimes lies. There are three possible conclusions from this...

A = T, B = L, C = TL
A = T, B = TL, C = L
A = TL, B = L, C = T

Sorry, no chicken for you tonight.

The TOG​

 

[agua.]

 

[TOG]

I have been working on it, and my questions are a little different, but I got it to where if the first answer is yes, then you only need one more question to know who everybody is, and if the first answer is no and the second is yes then you need a third question to know who everybody is. But if the first two answers are no, then you need a total of 4 questions to figure it out. It still needs a little more work.

The TOG​

 

[agua.]

Cool TOG so you think I should disregard the line of questioning I was using ?

 

[agua.]

Oh and can the questions have 2 or more caveats in them that a true answer would require all of them to be true ?

 

[TOG]

Cool TOG so you think I should disregard the line of questioning I was using ?

Your line of questioning isn't so different from mine. Like I pointed out, whether someone is on the left is a bit ambiguous, so I used the question "Am I wearing a baseball cap" and assumed that I was. Both are simply questions to which we know the answer. You asked "Are you L?". I asked "Is one of the others the one who always tells the truth?". Slightly different answer, but pretty much the same thinking behind it. And like I said, mind doesn't completely work either. Here it is if you want to figure out what's wrong with it...

The three men are Andy, Ben and Carl. Abbreviations are T = always answers truthfully, F = always answers falsely, R = answers randomly, Rt = answers randomly and is telling the truth, Rf = answers randomly and is lying.
Assume you are wearing a baseball cap.

Ask Andy: "Is one of the others the one who always tells the truth?"

If Andy = T, then he will answer NO, since neither of the others is T
If Andy = F, then the correct answer is YES, but he will lie and answer NO
If Andy = Rt, then he will answer YES, since one of the others is the T
If Andy = Rf, then the correct answer is YES, but he will lie and say NO

If Andy says "Yes", then ask Ben: "Am I wearing a baseball cap?"

You already know that Andy = R, so...
If Ben says "Yes", then
Andy = R
Ben = T
Carl = F

If Ben says "No", then
Andy = R
Ben = F
Carl = T

That's if you're lucky enough to get a "YES" to the first question. Then you need only 2 questions to find out who's who. But if Andy says "No"...

Ask Ben: "Is one of the others the one who always tells the truth?" (See above for possible answers.)
If Ben says "Yes", then you know he's is R and Andy is F...
Andy = F
Ben = R
Carl = T

You still only need two questions and you know everything. But...

If both Andy and Ben say "No", then you haven't ruled anything out and have to figure everything out from your last question. I don't see a way of doing that. I need to modify at least one of my questions, but I'm not sure which one. Maybe both. I haven't checked what happens if I reverse the order of the questions.

The TOG​

 

[TOG]

YAY!!!! I figured it out!!!! WOO HOO!!!

Next question... Do I reveal the answer or do I give you another day or so to figure it out? Here's a hint... You were on the right track back in post #171, but the first two questions should be directed toward the same person, and the second question (which depends on his answer to the first) has multiple parts that have one answer (all parts have to be true for the whole question to be true).

The TOG​

 

[Sparkey]

YAY!!!! I figured it out!!!!

Next question... Do I reveal the answer or do I give you another day or so to figure it out?

Go right ahead, as far as I'm concerned. Question to you though, does your solution include the Non-English responses? That's that part that convinced me to give up.

I'm thinking that the first question needs to be designed to identify one (either one) of them who is NOT the random dude.

 

[TOG]

No, my solution doesn't include the non-English responses. It may help people get on the right track though. Since agua. was trying to figure it out, I'll wait till he responds before I give the answer. It still took quite a while to figure out, even with English answers.

The TOG​