You are on a treasure hunt, wondering where the "Truth Treasure" is buried. You have no idea where it is buried, so you go Truth Town (made up of only Liars and Knights) because it is famous for holding the treasure's secret location.

When you enter the city, you see two twins and they know each other's types, but you don't. One twin says "(Exactly) one of us is a Knight..." and the other twin says "...and (exactly) one of us is a Liar." You can only ask one question and only to one person. You only care about where the treasure is kept, and obviously a liar would give you a wrong answer, so what should you do?

First, I'd just like to say hello to everyone here. I signed up to this site just a few hours ago, and will say that I'm enjoying it immensely.

Now, on to the solution.

First, let's see if the clues from the question are enough to help us identify each twin's type. For now, we'll assume that twins need not necessarily be of the same type.

Here I'll use "A" to represent the twin who made the first statement in the puzzle question, and "B" to represent the other twin.

There are four possible type configurations:
1. A: Knight, B: Knight
2. A: Knight, B: Liar
3. A: Liar, B: Knight
4. A: Liar, B: Liar

Let's look at each of these in turn.

1. Both twins can NOT be Knights.
Contradicts statements by A and B.

2. A can NOT be a Knight when B is a Liar.
If A's statement is true, B's must be true as well. But if either statement is true, then it contradicts the earlier implication that both twins were Knights.

3. A can NOT be a Liar when B is a Knight.
Similar reasons as 2. Notice that A's statement and B's statement mean essentially the same thing.

4. A and B are both Liars!!
A's statement does not conflict; neither does B's statement. Both statements are lies if both A and B are Liars. This is consistent with Liar behavior, and furthermore, this configuration is the only of the four possible configurations which does not contain contradictions.


Now to put those pesky prevaricators to work! What to ask? Well, do you remember the part of the puzzle question that mentioned that each of the twins knew the other's type? Okay, with that in mind, you might make some progress toward finding that treasure by asking either one of them, "Where would the other twin say the treasure was located?"

The questioned twin (it doesn't matter which because they are the same type, and thus will give identical responses), knowing that:

- the other twin is a Liar
- the other twin would answer with a bogus location
- to say that the other twin's answer would appear something like, "the treasure is located in [x]", where [x] is replaced by any bogus location", would in itself be a statement of truth

Knowing all that, the questioned twin would be forced to disclose the treasure's actual location.


--- Sorry for being so long-winded. I didn't have enough time to write a shorter answer.
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Posted by Joo on 2005-07-07 05:38:05