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.

If there were no knights, Abe would be a knight: a contradiction.
If there were 1 knight, Frank and Cal would be knights: a contradiction.
If there were 2 knights, they would be Eric and Cal. This is possible.
If there were 3 knights, only Cal and Ben would be knights: a contradiction.
If there were 4 knights, only Ben would be a knight: a contradiction.
If there were 5 knights, only Dan and Ben would be knights: a contradiction.
If all 6 were knights, only Ben would be a knight: a contradiction.

So there are two knights: Eric and Cal.

Posted by Charlie on 2013-01-14 13:31:21