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.

All the three individuals lied in their respective first statements. The remaining individuals with the exception of Carl lied in their second statements. Of the three third statements, only Alex's was spoken truly.

Thus Alex is the doubleton, Carl is the knave and Bert is the liar.

Edited on September 21, 2007, 5:55 am

Posted by K Sengupta on 2007-09-21 05:53:20