68 replies to this topic

[Rob_Gandy]

There are 3 smaller, easier puzzles that may serve as hints to building up the answer to this one.

I will post the first one below. Those with pride, feel free to not look.

Spoiler for Hint Puzzle1

Noting their locations, I place two aces and a jack face down on a table, in a row; you do not see which card is placed where. Your problem is to point to one of the three cards and then ask me a single yes-no question, from the answer to which you can, with certainty, identify one of the three cards as an ace. If you have pointed to one of the aces, I will answer your question truthfully. However, if you have pointed to the jack, I will answer your question yes or no, completely at random.

Spoiler for Hint 1 answer

I would ask, "Is the card to the right/left an ace?" If yes pick that one if no pick the other one. Still trying to apply that to the OP though.

[Yoruichi-san]

But we claimed that the other God's know his answer, so therefore with that question you could get the two you ask saying yes , or the two you ask saying no, or different answers for each.

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

[phaze]

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

The way I understand it is they are God's, they know everything, they know both the Random Gods pattern and where he is in that pattern. They know what the Random God will answer even though it be random as if the random God had prepared beforehand a sheet of paper that says the first time I will answer it Da, the second time Da, the third time Ya. Of course the values on the paper are random in every sense that the word "random" is random

[Yoruichi-san]

The way I understand it is they are God's, they know everything, they know both the Random Gods pattern and where he is in that pattern. They know what the Random God will answer even though it be random as if the random God had prepared beforehand a sheet of paper that says the first time I will answer it Da, the second time Da, the third time Ya. Of course the values on the paper are random in every sense that the word "random" is random

Right, but I'm adding an extra hypothetical random, i.e., one that is not on the sheet of paper, that is hypothetically at some point which is randomly determined (and independent of the random god's 'random') if I ask that question what will he say. I.e. if I randomly pick a point on that paper...

And I don't care how omniscient these gods supposedly are...there are some things that are just unknowable...or do I need herr Heisenberg to let loose the hounds? ;P

However, if you want to specify that questions are could be unanswerable are disallowed, fine...

Spoiler for The less fun method...

Ask A, "If I ask you if B is the random god, would you say ja?" If he says ja, then either A or B is the random god. If he says da, either A or C.

Ask the one you know is not the random god, "If I ask you if A is the random god, would you say ja?", if he says ja A is the random god, if da, the other one.

Finally ask one of the non-random gods: "Does ja mean yes?" If ja, he's the truth teller, if da he's the liar.

[mmiguel]

Spoiler for Hint Puzzle #1

If I happen to point to the jack, then your response will convey no information to me since that response depends only on a process (the random yes-no generator) which is completely hidden from me. This is, therefore, a case where I could not learn anything about where an ace may be. I conclude, then, that any answer to this puzzle must depend on trick wording or some such chicanery.

There is a logical solution.

[mmiguel]

Okay, let me get this straight. We're assuming:

1) Random means the god will randomly answer YES or NO regardless of the question, not will randomly answer truthfully or not.
2) The gods all know what random's YES/NO pattern will be.

Spoiler for In that case...

Ask two of them: "If I ask the random god a random number of questions, then ask him 'Is the sky blue', will he answer the ja/da equivalent of YES?

This will tell you who the random god is since only the random god will be able to answer. Ask the one (or one of them if both couldn't answer): "Does da mean YES?" If he answers da, it's the truthteller, if he answers ja, he's the liar.

This is not a paradox, it is a strategy that utilizes the fact that random is random .

Could we really distinguish between someone whose policy is to randomly select yes or no to each yes-no question against someone whose policy is to randomly select to be truthful or false, and then correspondingly select yes or no to each yes-no question?

Spoiler for

I don't really see how the other two gods would be unable to answer.

The only possibilities that I can think of where they might not be able to answer is if the question is bad -> if the question doesn't make sense, if it has no answer, if it has multiple different answers depending on some ambiguous context, or if it is a paradox.

The solution I have in mind does not require asking questions that any god may not be able to answer.

[mmiguel]

What happens when you ask the truth teller or the liar a question they can't answer?

Since that is a topic of interest for many posters, I guess I need to make something up here.
If you ask any god a non-well-formed question which cannot be evaluated as either true or false in the eyes of omniscience...
then there is no rule that you may rely on regarding how they will answer. It's up to them.

Example:
Is the sentence "this sentence is a lie" a true statement?
The gods may answer however they choose in that case (they all act like random).

The OP still applies for well-formed yes-no questions.

[mmiguel]

Spoiler for Hint 1 answer

I would ask, "Is the card to the right/left an ace?" If yes pick that one if no pick the other one. Still trying to apply that to the OP though.

Correct-a-mundo.

Spoiler for Just to state explicitly

Point at a card, and ask if some other card is an Ace.
Say you are pointing at A, and you ask about B (C is the remaining card).
If A = Ace and B = Ace, then he will say Yes ---> Choose B
If A = Ace and B = Jack, then he will say No ---> Choose C
If A = Jack and B = Ace, then he will say ? ---> Doesn't matter which of B or C you choose, you will get an Ace since A is the Jack, so can still follow same rule above.

Here is Hint Puzzle 2:

Spoiler for

Suppose that somehow, you have learned that you are speaking not to Random but to True or False -- you don't know which -- and that whichever god you're talking to has condescended to answer you in English. For some reason, you need to know whether Dushanbe is in Kirghizia or not. What one yes-no question can you ask the god from the answer to which you can determine whether or not Dushanbe is in Kirghizia?

Edited by mmiguel, 19 September 2012 - 05:49 AM.

[mmiguel]

They know his pattern, but since I specify it is random at which point in the pattern I'd ask the question, they cannot know which his answer will be.

How will you choose such a random number?
Will you roll some dice?
What if they know how the dice will happen to land when you decide to roll them?
What if you decide to throw away the first roll and roll a second time --- what if they know how the dice will land at the second time?
What if for each of your possible choices, they know how every coin flip, dice roll, wheel spin, etc will turn out based on having tons of information, the laws of physics, and assuming we live in a world of causes and effects.

Your number can only be 0, 1 or 2 though, since you get 3 questions, and you need to save one question to ask about the sky.

I think trying to find questions that cannot be answered is not that helpful to finding the logical solution to the overall puzzle - but you are doing a good job thinking of possible paths of thought.

Edited by mmiguel, 19 September 2012 - 05:55 AM.

[phaze]

Spoiler for For Hint puzzle 2

What would the other God who is not the random answerer say if I asked him if Dushanbe is in Kirghizia? Take the opposite answer