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.

Alex is Doubleton.

Explanation:
Consider Carl's 1st statement. A liar or a knight can not
say that he is a liar himself.
So, Carl must be Knave or Doubleton.
If Carl is Doubleton, as his 1st statement is lie, 3rd
statement must be true.(he tells and lies in pairs)
Possibilities: (FTT),(FFT).
So, Bert is a knight must be true. But knight cannot declare
himself as knave. So, Carl is not doubleton. So, Carl is
a knave.

His second statement must be true, so Alex is Doubleton

Alex: Doubleton
Bert: Liar
Carl:Knave

Posted by Praneeth on 2007-09-21 01:27:11