Alex, Bert, and Carl know a secret two digit number. It is known that one of them is a knight who always tells the truth, one is a liar who makes all false statements, and one is a knave who alternates between true and false statements. Each one of them makes statements about the number as follows:

Alex:
1: One digit is 1.
2: The sum of the digits is 8.
3: Bert's second statement is false.

Bert:
1: One digit is 3.
2: The difference of the digits is 4.
3: Exactly one of Carl's statements is true.

Carl:
1: One digit is 6.
2: Alex's first statement is false.
3: The first digit is larger.

What is the secret number?

37

Posted by Andre on 2010-05-24 18:14:46