Alex, Bert and Carl are all different types. One is a knave, one is either a knight or liar, and one is a doubleton. A doubleton is a type similar to a knave, except that a doubleton's truth pattern is two true statements followed by two false statements repeatedly.

From the statements below, determine who is the doubleton.

Alex:
1. I am a knight.
2. Bert is the doubleton.
3. Carl is the knave.

Bert:
1. I am the knave.
2. Carl is the doubleton.
3. Alex is a liar.

Carl:
1. I am a liar.
2. Alex is the doubleton.
3. Bert is a knight.

Carl's third comment is proven false by Bert's first comment. 

Carl's first comment cannot be true. Therefore, Carl is not a liar or knight, and cannot be a doubleton since his first and third comments are lies. Carl is a knave. 

From Carl's second comment (true) - Alex is a doubleton.

This means that Bert is not the knave or the doubleton, and must be either a knight or liar.

Bert's first statement is not true.  Bert is not a knight. Bert is a liar.

Alex: Doubleton L, L, T

Bert: Liar: L, L, L

Carl: Knave: L, T, L

 

Posted by Leming on 2007-09-20 10:50:17