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 reply to
answer by K Sengupta)
A liar or a knight will never identify himself as a liar. Thus, Carl's first statement is false and, accordingly, he must be a Knave or Doubleton.
Assume that Carl is a Doubleton. Then his first statement that Alex is a Doubleton is false. Accordingly, his third statement must be true. So, Bert is the Knight, However, Bert's first statement that he is a knave must be false as no Knight will identify himself as a Knave. This leads to a contradiction.
Accordingly, Carl must be a Knave. Then, by his truly spoken 2nd statement it follows that Alex is the Doubleton. So, Bert must be a knight or liar. However, Bert's first statement implies that he cannot be a knight, and accordingly, he must be the liar.
Consequently, summarizing the foregoing, we have:
Individual Truth Value Type
---------------- -------------------- ----------
Alex F, F, T Doubleton
Bert F, F, F Liar
Carl F, T, F Knave
Edited on September 8, 2022, 12:50 am
explanation to puzzle answer
