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.

In agreement with those others who posted the correct solution, Alex is the doubleton, Bert is the liar, and Carl is the Knave.   

Examining the statements of Alex and Bert, one can eliminate all but one possible solution.  This single possibility is then confirmed by the statements of Carl: Alex is the doubleton, Bert is the liar, and Carl is the Knave. 

Posted by Dej Mar on 2007-09-25 04:55:36