MindTrap 3

Joe has to be a native.

If he were a visitor, his statement that everyone is a native would have to be true. But it can’t be true if he himself is a visitor. There would be at least one visitor–himself. So it’s logically inconsistent to say that Joe is a visitor. He must be a native.

Secondly, we can deduce that his statement is false, since he is a native and a liar. Not everyone is a native.

So Joe is a native, but either Bill or Frank is a visitor–or maybe both.

That’s where the next statement comes in….

Let’s assume that Frank is a native. If Frank is a native, then he is a liar. That means his statement is false. If Frank is a native, it is not true that there is only one visitor. But if Frank is a native, and if Joe is a native, then Bill can’t be a visitor because that would leave only one visitor–because if Frank is a liar, it is not true that there is only one visitor. But if he isn’t a visitor, then he is a native. That would mean they are all three natives. But we have already established that they are not all natives. In other words, it is logically inconsistent that Frank be a native. So he must be a visitor. Let’s see if that works….

If Frank is a visitor, then his statment is true and he is the visitor–and the only one. That makes Bill a native, because since Frank told the truth, there can’t be more than one visitor. This is consistent with what we deduced from Joe’s statement: that not all of them are natives.

So: Joe is a native, Bill is a native and Frank is a visitor.

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