You are the sole survivor of a shipwreck and are drifting in a small raft parallel to the coast of an island. You know that on this island, there are only two tribes of natives: Nobles, kind folk who ALWAYS tell the truth, and Savages, cannibals who ALWAYS lie. Naturally, you want to call out, "Are you a Noble or a Savage?" The man answers the question, but a wave breaks on the beach at that very moment, so you don't hear the reply. The boat drifts farther down along the short when you see another man. You ask him the same question and he replies, pointing to the first man, "He said he was a Noble." Then he continues, "I am a Noble." Your boat drifts further down the shore where you see a third man. You ask him the same questions. The man seems very friendly as he calls out. "They are both liars. I am a Noble. They are savages." The puzzle: IS the data given sufficient to tell you any man's tribe (my prof. says YES it is)? Is it sufficient to tell you each man's tribe?
I am not a philosophy guru...I need some direction please.
The second man's claim: He said he's a noble. I'm a noble.
The third man's claim: They're both lying. I'm a noble.
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The third man has to be lying.
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The first man cannot claim to have been a savage. Why? Savages cannot tell the truth and could have never claimed to be a savage. See? So the first man must have claimed to have been a noble (whether or not he was telling the truth is another matter).
So, the second man must be telling the truth about what the first man claimed to be. Since he told the truth about that, he must also be telling the truth about his own identity.
Now, the third man claims that they're both lying. We've already shown that the first man could have been lying, but that the second man was not.
So,
first man: could be a noble or a savage. second man: is a noble. third man: is a savage.
The second man is absolutely telling the truth, for the simple fact that if he was a liar, he would have said that the first man yelled out that he was a savage. At this point, it's not even important what the first man yelled; he would have said he was a noble, either way. What's important is that the second man said that he yelled out he was a noble, as either a noble or a savage would have done. He has therefore factually recounted what the first man yelled. If he was a savage, he would have told you that the first man claimed he was a savage. So his second statement must be true as well. Therefore the third man has to be lying. The second man isn't lying, which is a lie. He calls himself a noble, which is a lie, and, his final statement actually proves that the first man was a noble, as well, as he claims they are both savages. Therefore, they are both truth-telling nobles, and he is the lying savage. And by the way, your teacher found a horribly racist manner in which to phrase a lateral thinking puzzle.
The second man could be lying when he says "He said he was a Noble."... its entirely possible that the first man said "I am not a savage" or "nice weather we are having" or "I like your raft"
The correct procedure would be to ask "What would one of the savages say, if I asked him if he was a savage"... since the savage would HAVE to say he was a noble, when asked this a savage would HAVE to lie and say that the savage would say he was a savage.... whereas a noble would tell the truth that a savage would say he was a savage...
given just 3 men and 1 question, "are you a savage or noble", you CANNOT tell. Your professor is wrong.
Remember, they are volunteering the "the others lied" parts, not being asked that.