World's Most Difficult Logic Puzzle

@Didymos Thomas,

You have the answer, daleader?

@Didymos Thomas,

Didymos Thomas wrote:

You have the answer, daleader?

http://www.hcs.harvard.edu/~hrp/issues/1996/Boolos.pdf

@Edvin,

Edvin wrote:

My head hurts...

There is a difference between filosawfee and philsosophy, but one example of both is how much time has a person to waste, when all they have is time.

@Didymos Thomas,

(quote) "Three gods A , B , and C are called, in some 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 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. (end quote)

This phrase is ambiguous (to me), quote >>>> "each question must be put to exactly one god" (end quote). <<<<<

I understand the phrase IF the phrase means that questions can be asked of only one god at a time.
The ambiguous part is whether or not all three gods can be asked a question (individually) OR if all three questions MUST be asked of only 1 of the three gods.

I am presuming that the three 'yes/no' questions can be asked of any of the gods AND that the questions may be addressed to any of the three gods but no questions can be asked of two or three gods at once. Am I correct (before I start to answer this)?
In other words, am I able to ask EACH god, if I desire, a question?

I think that I have an emerging answer. But I (kind of, in process) am working out 2 scenarios, but the variables became unwieldly:
1) where all 3 questions MUST be asked of only 1 of the gods (seems impossible) and
2) where any of the 3 questions can be asked of any of the 3 gods (individually), but not simultaneouly.

Can I presume that I can ask all three of the gods (individually) one question each?

INQUIRY SUMMARY:
Is it correct to state that 'any one of the 3 questions may be asked to any god, but no question(s) may be asked to any more than one god at a time'?

.

@Didymos Thomas,

Didymos Thomas wrote:

[L05] The world's most difficult logic puzzle!

From the link:

According to the late philosopher and logician George Boolos, who was a greater teacher and logician at MIT, the hardest (recreational) logical puzzle is one that was invented by the logician and puzzle-master Raymond Smullyan, and modified slightly by the computer scientist John McCarthy. Here is the puzzle :

This puzzle is a very difficult. If you can't solve the problem, don't feel too bad about it. You can read the solution in chapter 29 of Boolos's book Logic, Logic, Logic, published in 1998 by the Harvard University Press. But don't give up so easily!

Logic.
1.There are three god's=true
2.There is a God (A) (B) and (C)=true
3.God (A) answer's correct to a yes or no question=true
4.God (B) answer's False to a yes or no question=true
5.God (C) answer's randomly to a yes or no question=true
6. It is unknown which God is (A), (B), or (C)=true

So therefore logicaly the answer must be

--=(I have determined the identitie's of which god is (A), (B), and (C) are unknown because the fact's 1-6 are true.)=--

This is not a mathmatical problem, therefore if it was you would put it in %'s of which would be more likely to be god (A), (B), and (C), depending on the question's asked to the three unknown god's.

So there is no need to even ask the god's a single question, if you use logic to solve this logic problem ^^

@Didymos Thomas,

I left out #7 which state's all three god's answer in Ja's and Da's=true... but it is not needed when 1-6 are true fact's. also that would be logical.

@No0ne,

Maybe I'm just not understanding it, but as far as I can see the original solution does not work. According to the original solution the first question to ask is: Does da mean yes, if and only if you are true, if and only if B is Random. Now according to the solution no matter whether A is true, false or Random, if he answers Da then C is either true or false; but, if the answer is Ja then B is either true or false.

A is true(or random answering truthfully)

1) Da means yes and B is Random - statement is true and he answers Da.

2) Da means yes and B is not Random - statement is false and he answers Ja.

3) Da means no and B is Random - statement is false and he answers Da.

4) Da means no, he is true, and B is not Random - statement is false and he answers Da???(according to author he should say Ja)

A is false (or random answering falsely)

1) Da means yes, he is not true, and B is random - statement is false and he answers Da.

2)Da means yes, he is not true, and B is not Random - statement is false and he answers Da???(according to author he should say Ja)

3)Da means no, he is not true, and B is Random - statement is false and he answers Ja???(according to author he should say Da)

4)Da means no, he is not true and B is not Random - statement is true and he answers Da???(according to author he should say Ja)

Maybe it's because I am not understanding it too well? I would really appreciate it if someone would explain this to me.

@Didymos Thomas,

Um... if you ask a question to one of them, you would never be able to find out which mean's yes, or which mean's no, because of the fact you would allways have two da's and one ja, or two ja's and one da, you could allways ask a question that would have to be true, like asking if you are a god, the answer must be yes, yet you dont know which god your asking it to. so you dont know if the answer is correct, random, or false therefore there is logicaly no need for the information of da and ja---The reason

1. there are three god's
2. you do not know which god is which
3. therefore if you dont know which god is which, when you ask a question such as (are you god) the answer could be truthfull or false or random, because you dont know which god to give your question to... you only know that there are three, and what kind of answers they will give, you dont know which is which.

you would allways get this if you asked any 3 question's
2 da's and 1 ja
2 ja's and 1 da
because of the fact of the random one prevents a logical dictaction of which is which, from asking a question in a yes or no format...

Dose da mean yes? LOL u dont know which is which, therefore no matter what questions you ever ask all three, you would have to gusse of which is truthfull which is false and which is random! :eek:LOGIC DOSNT GUSSE! >.<! anyways ^.^

I havent looked at the author's answer so if he uses da and ja to solve this logical problem, then i might think that he is cheating in some way by creating a flaw within the presatation of the question, therefore making it a trick question.... and not a logical question...

Logic dosnt gusse... so using da's and ja's would be a gussing game, do the two da's mean yes? or did one ja mean yes and the two da's are the false and random, or are one da the truth and a random, therefore making ja no?... see its a gussen, no logic in using the questions...

The question's throw people off.... Alot of thing's in life will try to throw you off from what is important and what really is not... sadly so dose people's riddle's...

@Didymos Thomas,

If I ask god A, "If I ask God B if he is God B, will he be Lying?"
I ask god B, "Are you god B?"
I ask God C, "Is god A lying about God B?'

Then god A will answer one of three ways.
God B will suggest that god A is doing one of three things, and God C will confirm god A's answer, leaving God B to be the final god.

God A...is God B going to tell me he is God B?
...no.
God B...are you God B?
...no. (he's lying or random)
God C...is God A lying?
...no. (god A is random, god B is Liar and God C is true.)
This works because there are two factors to consider for God C to be random, and since he confirms 2 out of 2 questions, he is no longer random, but predictable and therefore true.

...I think.

@Aristoddler,

Aristoddler wrote:

If I ask god A, "If I ask God B if he is God B, will he be Lying?"
I ask god B, "Are you god B?"
I ask God C, "Is god A lying about God B?'

Then god A will answer one of three ways.
God B will suggest that god A is doing one of three things, and God C will confirm god A's answer, leaving God B to be the final god.

God A...is God B going to tell me he is God B?
...no.
God B...are you God B?
...no. (he's lying or random)
God C...is God A lying?
...no. (god A is random, god B is Liar and God C is true.)
This works because there are two factors to consider for God C to be random, and since he confirms 2 out of 2 questions, he is no longer random, but predictable and therefore true.

...I think.

um...yet you dont know which god is god (B), so you cant ask god (b) you only know that there are three god's, and that one speaks true one speaks false and one will answer randomly, Therefore you dont know which god you are asking the question to...

This logic problem is also related to the concept of tricking a lie detector test...

@Edvin,

What fruitless trash to waste time on when there are so many 'puzzles', the solving of which will benefit mankind and not some tiny ego!
If the only 'puzzle' that you solve in your life is this one, what a waste! (from this perspective, of course)
Really...

@nameless,

nameless wrote:

What fruitless trash to waste time on when there are so many 'puzzles', the solving of which will benefit mankind and not some tiny ego!
If the only 'puzzle' that you solve in your life is this one, what a waste! (from this perspective, of course)
Really...

You may justly say what is fruitless, and a waste of time for you, yet you are not everyone els... for you do not know what they have defined as fruitfull or fruitless, or even what would be a waste of time for them..

Life dose not bare any fruit nor dose it have a point to it, nor is there such a thing as (time) to waste..

For the point fruit life will ever bare is the fruit we make, for the only point life will have is the one we say it has, therefore making it have a point...

And there is no such thing as wasting time... hence time is the perception of light, the thing you speak of is the time that we take from are self's to give to other's, hence we dont waste any time, for we share, take, and give each other's time to one another. For that is what i have defined..

So Thank you for your time, in reading this comment posted
And because of your slander like comment, i have taken some of my time to give further understanding on why you should not type in such a manner, it is best to tell why it is a waste of time to your self, and why it would be for the other parties... the reason why simple, if you dont the only thing you will prove, is that your point of view of the comment's is curved to your perception, and is as one sided as a contract for the U.S.A Army Smile

Anyway's if you still belive that they wasted there time, and so did i, on thinking about that so called puzzle(it was very ezy and not even a puzzle by my standerds) Then you had just wasted your time reading them, and posting a comment.

Bcause you should give there comment's the same amount of respect as you would want your own to have... It's called do onto another as want done onto one's self... just dont lie to your self... And thats why you shouldnt post such comment's like that. Because people's perception seem to be far off from the one that you displayed -.-

@Edvin,

'Answer this question twice if you are Random, are you Random.' The puzzle may already be solved if Random gives two opposing random responses, as false must answer twice to be false. Random cannot not answer twice as no second response is not a response to the question unless you are True. True has given you the word for "no".

@urangutan,

I had this all wrong

@No0ne,

No0ne wrote:

Logic.
1.There are three god's=true
2.There is a God (A) (B) and (C)=true
3.God (A) answer's correct to a yes or no question=true
4.God (B) answer's False to a yes or no question=true
5.God (C) answer's randomly to a yes or no question=true
6. It is unknown which God is (A), (B), or (C)=true

So therefore logicaly the answer must be

--=(I have determined the identitie's of which god is (A), (B), and (C) are unknown because the fact's 1-6 are true.)=--

This is not a mathmatical problem, therefore if it was you would put it in %'s of which would be more likely to be god (A), (B), and (C), depending on the question's asked to the three unknown god's.

So there is no need to even ask the god's a single question, if you use logic to solve this logic problem ^^

Also, this is why lie detector's are flawed, mainly the one's that you are not straped into... They work off of shoty software that is bound to the problem of "da's&Ja's"...

@Edvin,

Three gods A , B , and C are called, in some 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 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.

This is just how a lie detector operator would do to find out which sign means false, and which means true...

Yet, this puzzle allso points out the flaw in the perception of the operator that interpets the da's, Ja's, and random.

@No0ne,

No0ne;13943 wrote:

You may justly say what is fruitless, and a waste of time... blah... blah... blah....

Crap! Crap! And more crap!
In grade school there was something going around that you might have appreciated.
It was a card that asked; "How do you keep an idiot busy? Turn over..".
On the other side it said; "How do you keep an idiot busy? Turn over.."
Try it, enjoy! It should keep you busy for quite awhile...
Pfffft!

@nameless,

Solutions to logic puzzles often employ useful techniques and occasionally require the creation of new ones. I would say that had you been spending your time solving a very difficult puzzle,you would have done something far more useful for human kind than spout insults and inane opinions about puzzles on an internet forum. You do not want to appear a hypocrite do you? Smile

@Didymos Thomas,

Several months ago I gave this one a lot of thought after being presented with it on another online forum. It made me brain hurt and I didn't figure it out.

@nameless,

nameless wrote:

Crap! Crap! And more crap!
In grade school there was something going around that you might have appreciated.
It was a card that asked; "How do you keep an idiot busy? Turn over..".
On the other side it said; "How do you keep an idiot busy? Turn over.."
Try it, enjoy! It should keep you busy for quite awhile...
Pfffft!

This side, that side...What did it say on the inside???

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