# World's Most Difficult Logic Puzzle

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Tue 15 Jan, 2008 12:32 pm
[L05] The world's most difficult logic puzzle!

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 :

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.

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!

Aedes

Sun 20 Jan, 2008 08:59 pm
@Didymos Thomas,
Hard one! I'll have to think about it.

Didymos Thomas

Sun 20 Jan, 2008 09:01 pm
@Aedes,
Yeah, it is tough. I haven't had much time for it, but the time I have spent has been basically fruitless.

Edvin

Mon 25 Feb, 2008 03:11 am
@Didymos Thomas,

Vasska

Mon 25 Feb, 2008 03:34 am
@Didymos Thomas,
Let's recapture

You've got three God's which we for now call:
• A
• B
• C

They are in no particularly order named:
• Truth
• False
• Random

They give as their names state either
• A truthful anwser
• a false or true answer

They give anwsers as yes or no but we don't know which words are used. (Ja is Yes in my language but i think that's just a coincidence)
• Da
• Ja

And then i am completely lost. Since their is no way of knowing a god speaks the truth or the false unless you can find the words to make three questions that provoke the real answers. Which is the hard part ^^

Edvin

Mon 25 Feb, 2008 06:24 am
@Vasska,
I can't believe that there is an sollution to this puzzle. I just can't. What botheres me though is his choice of response for the three: da and ja. Why those?

Vasska

Mon 25 Feb, 2008 07:03 am
@Edvin,
Edvin wrote:
I can't believe that there is an sollution to this puzzle. I just can't. What botheres me though is his choice of response for the three: da and ja. Why those?

It's to make the puzzle even harder. If it were Yes and No you at least would have known what they would have said. Now even if they speak the truth you can still be dazed by the fact that the Ja could be Yes or No.

It sure is a difficult one.

Edvin

Wed 27 Feb, 2008 12:54 pm
@Didymos Thomas,
Ok. I'm losing it. Somebody give a clue?

Didymos Thomas

Wed 27 Feb, 2008 02:42 pm
@Didymos Thomas,
I have absolutely no clue as to the solution.

Edvin

Wed 27 Feb, 2008 03:40 pm
@Didymos Thomas,
Gah! This is a dangerous puzzle of fiendish design. Undoubtably designed to make people feel stupid, then go insane.

de Silentio

Sun 2 Mar, 2008 12:54 pm
@Didymos Thomas,
Nice.

When I ask my three questions, who am I asking them to? For example, can I ask the God who is False if he is God B?

Edvin

Sun 2 Mar, 2008 02:04 pm
@de Silentio,
Only yes no questions I've of late given the puzzle a new aproach. I've given up, letting the subconcius do all the work. Sooner or later it's bound to solve it. Somehow.:cool:

de Silentio

Sun 2 Mar, 2008 05:38 pm
@Didymos Thomas,
Quote:
Only yes no questions

That would be a yes/no question. Me: "God False, are you God B?" "God False: No (or yes)"

Didymos Thomas

Sun 2 Mar, 2008 06:07 pm
@Didymos Thomas,
Ah, but how do you know which God (A,B, or C) is God False? We might ask each of them "Are you God False/True/Random" and then ask them all a control or series of control questions: "Can pigs fly?", for example.

de Silentio

Sun 2 Mar, 2008 06:18 pm
@Didymos Thomas,
That was why I was wondering Who I can ask a question to. Do I know which God is God B, or am totally oblivious to which God is A,B, or C AND which God is True, False, or Random.

When I ask the three questions, are they blanket questions? Who answers them? Must I first label the Gods 1, 2, and 3, so I know which God I am asking the question to?

Didymos Thomas

Sun 2 Mar, 2008 07:53 pm
@Didymos Thomas,
There are three Gods, arbitrarily labeled A, B, and C. One of them is GT, one GF, and another GR. Each question must be directed at a single God, either A, B, or C.

The possibility I suggest above would not work - I forgot that we can ask only 3 questions.

And of course, the Gods will respond with either "ja" or "da", for "yes" or "no"; however we do not know if ja is yes or no, or if da is yes or no.

Let's first figure out what we do know:

These are the possible solutions I can come up with
A= T B= F C= R
A= F B= R C= T
A= R B= T C= F

Tue 4 Mar, 2008 06:56 am
@Didymos Thomas,
it is not that hard just thing ppl. Trust me the trick is da and ja! And asking the same question from all three! By same mean the same format just different wording! Remmber use Ja and DA!

Doobah47

Tue 4 Mar, 2008 07:26 am
@Didymos Thomas,
If you ask the random will he alternate between da and ja or will it be totally random?

Tue 4 Mar, 2008 08:30 am
@Doobah47,
Doobah47 wrote:
If you ask the random will he alternate between da and ja or will it be totally random?
totally random! Whenever you guys fully gave up let me know and I post the answer. I almost got it right. I gave the best hint I can possibly give without giving to much away. If you guys want more hint I can give you one more but that tells the answer in my opinion
!

Tue 4 Mar, 2008 08:46 am
@de Silentio,
de Silentio wrote:
That was why I was wondering Who I can ask a question to. Do I know which God is God B, or am totally oblivious to which God is A,B, or C AND which God is True, False, or Random.

When I ask the three questions, are they blanket questions? Who answers them? Must I first label the Gods 1, 2, and 3, so I know which God I am asking the question to?

you well obviously see them and ask them. They well not move so yea mentally you can lable them as whatever you want. Say give them automatic lable as A, B, C in any order. Your task is to say whether God A is telling the truth, false, or random answer and so on for the other two. Labeling is in any order you feel like!

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