In a remote island there are only two types of people live on the island, Knights and Liars. Knights always tell the truth. Liars always speak falsely.

A group of six inhabitants, comprising Abe, Ben, Cal, Dan, Eric and Frank, was busy in a discussion. A visitor from a nearby city approached them and asked them what type each of them belonged to. Their reply were as follows:

   Abe: None of us is a knight.
   Ben: At least three of us are knights.
   Cal: At most three of us are knights.
   Dan: Exactly five of us are knights.
   Eric: Exactly two of us are knights.
   Frank: Exactly one of us is a knight.

Determine the type of each of the six inhabitants from the aforementioned statements.

Abe is definitely a liar because no knight would say that there are no knights. If Dan is a knight, then there are 5 knights, so everybody except Abe is a knight. However, that would make Eric a liar. Therefore, Dan is a liar. If Frank is a knight, then he is the only knight. However, Cal would be telling the truth. Therefore, Frank is a liar. Now, we know that there are at most 3 knights, so Ben is a liar and Cal is a knight. Since Frank is a liar, there is not only one knight, so Eric is a knight.

Posted by Math Man on 2013-01-14 19:40:23