Lost in the woods, you finally happen upon a rickety old bridge across a deep ravine. The ravine is too steep to go down and climb back up. You need to know if the bridge is safe. As 'luck' would have it, you recognize that on the other side of the bridge is that dreadful town, "Knight-and-Liarville". Everyone who lives there is a knight (who always tells the truth) or a liar (who always lies). You are tired and you've been lost in Knight-and-Liarville before. You see three men on the other side of the bridge.

You shout out: "Are you a knight?"

The first man says something, but you can't hear what he said.

The second man shouts, "He said he was a knight."

The third man shouts, "No, he didn't. He said he was a liar."

Which man do you ask to find out whether or not the bridge is safe?

The key in this problem is that a knight will always tell the truth and a liar will never tell the truth. Thus, the only response anyone will make to the question "Are you a knight?" is yes. There are only two types of people. A knight will tell the truth, that he/she is a knight, while a liar will lie and state that he/she is a knight. So the unintelligible response of the first man is an answer stating that he is a knight.

Thus, the shout of the second man "He said he was a knight." is the truth, and the second man is necessarily a knight.

Similarly, the shout of the third man "No, he didn't. He said he was a liar." is a lie, and the third man is necessarily a liar.

With this knowledge in hand, we can safely ask either the second or the third man whether the bridge is safe. We must simply realize that if we ask the second man, his answer will be the truth, whereas if we ask the third man, his answer will be a lie--that is, if he states the bridge is safe, it is in actuality unsafe and vice versa.

Posted by Timothy on 2004-03-26 19:48:43