Solve the "Hardest Logical Puzzle Ever

[Russell Berty]

I posted this on another thread but no one has responded. It is truly a great puzzle to work out. So, I am posting it again in its own thread. Enjoy.

The "Hardest Logical Puzzle Ever":

Three gods, A, B, and C, are called True, False, and Random (in some order you do not know.)
True always speaks truly. False always lies. And Random always speaks truly or lies in a completely random manner. Furthermore, they speak their own language. They will respond "da" or "ja" (one means Yes and the other means No but you do not know which is which.)

You may ask three questions in total. Each time you ask one of your questions, it can only be directed at one god. (You can repeat a question to another god but that counts as 2.)

Determine the identities of A, B, and C (i.e. which is True, which is False, and which is Random.)

 

[Russell Berty]

I will be happy to give a hint. Yes, it can be done!

 

[llauren84]

It seems impossible...

 

[Russell Berty]

It is difficult, but not impossible. First try to do the problem assuming that they speak English; that is, they will answer "Yes" or "No". That is the hard part of the problem.

Once you have that solved, your answer can be easily modified for the "da" or "ja" case.

Hint for the "da" or "ja" case: Consider all possible scenarios when you ask the gods the following question,

"Is it true that 1 + 1 = 2 if and only if da means yes"

 

[Dadface]

Russell,your puzzle is making my brain ache with the severest of aches.I'm off to potter around in the garden before it bursts.Nice puzzle though,you rascal.

 

[jamesb-uk]

Do they all know how each of them speaks?

 

[Russell Berty]

Do they all know how each of them speaks?

Yes, they understand each other. And they know who each other are.

 

[Russell Berty]

OK, here is another hint.

Hint: After your first question, you will know one of them that is NOT Random. Moreover, based on the answer to your first question, you will ask your second question to the one that you know is NOT Random.

 

[Russell Berty]

When looking at the case where the gods speak English (Yes or No responses), here is another hint.

Hint: The first question has the following form.

“Is it true that (p and q) or (w and v)?”

Where p, q, w, v are simple statements. From the response to this question, you should be able to determine a god that is not Random.

 

[Kittel Knight]

I will be happy to give a hint. Yes, it can be done!

I think this should be the very last clue...

But it seems you will be happy to show you know the answer to your own puzzle.

Could you please not give any hints more?

 

[davee123]

But it seems you will be happy to show you know the answer to your own puzzle.

Well, it's not his puzzle per se, it was proposed as the "hardest" puzzle some years ago, you can read about it on Wikipedia (but be forewarned, the explanation of the answer is there too!):

http://en.wikipedia.org/wiki/The_hardest_logic_puzzle_ever

DaveE

 

[Kittel Knight]

you can read about it on Wikipedia (but be forewarned, the explanation of the answer is there too!):

Hi Dave,
I want to solve it by myself, and I won't take a look there.

Of course, someone could ask me so why did I read all these posts.

Well, maybe the first post was not ok, and Russell Berty could fix something in the latter posts. So, I read them all.
But I was not expecting any clues. If I wanted them, I would have googled for this puzzle.