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Scott Cram Inner circle 2678 Posts |
You go to an island withe 3 tribes. You wish to establish trade with the tribes on this island.
These 3 tribes have an unusual characteristics. Each tribe is known as either a "truth-telling" tribe, or a "lying" tribe. In the truth-telling tribes, every member always tells the truth. In the lying tribes, every member always lies. Obviously, you prefer to do business only with the truth-telling tribes, but you don't know which is which, or how many truth-telling vs. lying tribes there are. As it happens, you run across the 3 tribal chiefs, and so you ask them whether they're truth-tellers or liars. Chief 1: "I'm a . . . " (You can't hear the rest, because the waves on the beach crash loudly right at that moment) Chief 2: "He said he's a truth-teller, and he is." Chief 3: "No! They're both liars. I'm the truth-teller!" After that, all three chiefs leave, and you don't get another chance to speak with them. Based on this one encounter, which tribe or tribes always tell the truth, and thus are the ones you want to establish trade with? |
Alessandro Scotti Loyal user Italy 263 Posts |
I think that after Chief 3 speaks there are really only two possibilities: liar, liar, truth-teller and truth, truth, liar. However, no matter what he is, Chief 1 always has to tell "I am a truth-teller" and Chief 2 can only confirm this if he is a truth-teller too (otherwise he would say "He said he's a liar, and he is.") So both 1 and 2 tell the truth, while 3 is a liar.
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Scott Cram Inner circle 2678 Posts |
Correct, Alessandro!
Here's a simpler way to describe it. When Chief 1 says what he is, we know he HAS to be saying that he's a truth-teller (A truth-teller would say he's a truth teller, and a liar would also say that he was a truth-teller). Chief 2 states that Chief 1 said that he was a truth-teller. We know that must be true, so we now know that Chief 2 is a truth-teller. Since truth-telling Chief 2 says that Chief 1 is a truth-teller, we then know that Chief 1 is a truth-teller. Chief 3 states that Chiefs 1 and 2 are both liars, and we know that's not true, so we know that Chief 3 is a liar. His claim to be a truth-teller further verifies that (after all, he can't say that he's a liar). |
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