Brain Teasers
Divine Deception
Sailing through a thick fog, you come upon a mysterious island shrouded in mist. A towering volcano in the center of the island pierces the clouds, billowing smoke into the sky. You land your boat and set out to ascend the peak. After an arduous climb, you approach the volcano summit, where lava glows red within a vast crater.
Here, you are approached by three gods and their herald.
Problem
On the summit of this remote volcano, the herald proclaims that you have been selected for a trial. He then lays out the rules for you.
First, you know that one of the three gods always tells the truth, another always lies, and the third will respond to questions randomly. Therefore, let us call the gods True, False, and Random.
Second, the gods speak a different language. They understand all languages perfectly well, but only answer questions with either ja or da, the words for yes and no. You do not know which god is which, and you do not know which word means yes and which word means no.
Finally, you have an existential problem on your hands. You may ask three yes-or-no questions, each one directed to only one god, and only that god will answer with either ja or da. If you can determine the identities of the three gods, they will send you on your way with their blessing, and you can be assured of a prosperous and fulfilled life. If you fail to determine the identities of the gods, however, they will be less generous in their treatment. The volcano pit smokes and glows red beside you.
With your three questions, how do you figure out which god is True, which is False, and which is Random?
Here, you are approached by three gods and their herald.
Problem
On the summit of this remote volcano, the herald proclaims that you have been selected for a trial. He then lays out the rules for you.
First, you know that one of the three gods always tells the truth, another always lies, and the third will respond to questions randomly. Therefore, let us call the gods True, False, and Random.
Second, the gods speak a different language. They understand all languages perfectly well, but only answer questions with either ja or da, the words for yes and no. You do not know which god is which, and you do not know which word means yes and which word means no.
Finally, you have an existential problem on your hands. You may ask three yes-or-no questions, each one directed to only one god, and only that god will answer with either ja or da. If you can determine the identities of the three gods, they will send you on your way with their blessing, and you can be assured of a prosperous and fulfilled life. If you fail to determine the identities of the gods, however, they will be less generous in their treatment. The volcano pit smokes and glows red beside you.
With your three questions, how do you figure out which god is True, which is False, and which is Random?
Hint
Can you phrase a question so that both True and False have to say the same thing?Answer
First, ask the god standing in the middle, "If I were to ask you if the god to your left is Random, would you say ja?"By phrasing questions as hypotheticals, you can ask the gods an embedded question. As long as you ask either True or False, the god will respond with the same word you use ("would you say ja?") if the answer to the embedded question is affirmative, and the opposite word if the answer is negative.
If the god says ja, then there are two possibilities: either the god to his left is Random, and the god speaking is either True or False; or the god speaking is Random. Either way, you know the god to his right is not Random.
Similarly, if the god says da, then there are two possibilities: either the god to his right is Random, and the god speaking is True or False; or the god speaking is Random. In this case, you know the god to the left is not Random.
The next step is to approach the god that you know is not Random, and figure out if he is True or False. Because you still do not know the meanings of ja and da, you need to do this by using the same hypothetical structure, asking, "If I were to ask you if you are True, would you say ja?" If the god is True, they will answer ja. If the god is False, they will answer da. (False's response in this case is essentially either: "no I would not say yes," even though he would; or "yes I would say no," even though he wouldn't.)
Finally, now that you have identified a god as either True or False, you can use the same question structure one last time to identify the other gods (you need to stick to it because you still don't know the meanings of ja and da). Simply ask, "If I were to ask you if the god in the middle is Random, would you say ja?" If the answer is ja, then the god in the middle is Random, and the third god is either True or False (the opposite of the one you have already identified). If the answer is da, then the god in the middle is True or False, and the third god is Random.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments hidden to avoid spoilers.
Follow Braingle!