Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Logic problem

This isnt anything for school etc.

I found this in a forum I frequent:

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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 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.

CLARIFICATIONS:

* It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

* What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

* Whether Random speaks truly or not 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.

* Random will answer 'da' or 'ja' when asked any yes-no question.

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The problem looks very intimidating and I didnt really know even how to start... Anyone? I also dont know the answer.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Logic problem

I haven't solved it yet, but I've found a way of eliminating one of the problems:

Say your question is (for example) "Are you random?"
Now mix the words around until you get a statement instead of a question.
You now have "You are random."
Below this, place "Da means yes."

Finally, ask "Is exactly one of these statements true?"

A "Ja" to that question translates to a "Yes" to the original question (and Da goes to No).

So now we can solve the problem ignoring the language barrier.

Edit: And solved.
Hint: Use the first question to find a God that is definitely not Random (although you don't know which of the remaining two it is).

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Why did the vector cross the road?
It wanted to be normal.