In an island there are three types -- knights, liars and knaves. Knights always speak the truth, liars always speak falsely and, knaves strictly alternate between a true statement and a false statement - albeit not necessarily in this order.

A visitor to the island was faced with three such inhabitants Al, Ben and Cal and he wanted to find out their types.

The visitor’s questioning went as follows:

Visitor: Al, which sort are you?
Al: I am a knight.
Visitor: Ben, what are you?
Ben: I am a liar.
Visitor: So, Ben, was Al lying?
Ben: No.
Visitor: Cal, what sort are you? What is Al?
Cal: I am a knight. Al is a knave.

Which is which?

Only a knave can claim to be a liar, so Ben is a knave.  Since Ben's 1st statement was a lie, his 2nd is true, so Al is not lying, so Al is a knight. Therefore Cal's 2nd statement is a lie.  Therefore, Cal is not a knight, so his 1st statement is a lie also.  Since Cal has lied twice in a row, Cal is a liar.  Also, his pants are on fire.

Posted by Steve Herman on 2014-01-20 10:44:11