The following two facts are known about Adam, Bert, and Carl:

1) Of Adam, Bert, and Carl, there is one knight, one knave, and one liar.
2) Adam said once, "Bert said that Carl isn't a knight."

Can you ask one yes/no question to one person and figure out who is who? If not, how many questions must you ask?

After initially reading the question the only thing you can say for sure is that Carl either is, or is not, a Knight and Adam and Bert are both telling the truth or one is lying.

The table below shows all possible cominations for the three men with (t) or (f) showing weather the Knave is lying or telling the truth according to the sentence given.

CARL    KNIGHT                CARL   KNIGHT
BERT    LIAR                     BERT   KNAVE(t)                               ADAM   KNAVE(t)              ADAM   LIAR

CARL    LIAR                    CARL    LIAR
BERT    KNIGHT                BERT    KNAVE(t)
ADAM   KNAVE(t)              ADAM   KNIGHT

CARL    KNAVE                 CARL    KNAVE
BERT    LIAR                    BERT    KNIGHT
ADAM   KNIGHT               ADAM    LIAR

The last two examples in the table identify Carl as a Knave. Carl cannot be a Knave however because the statement "Carl isn't a Knight" would be true and either Adam or Bert would by definition have to lie. Therefore Carl Must be either a Knight or a liar. Also, the table shows that since the Knave (in all examples) has told the truth, he will lie next.

The easiest solution to this problem would be to ask 2 questions. First ask Carl whether he is a Knave. If he says yes he is a Liar, and if he says no he is a Knight. Knowing that he is either lying or telling the truth I would then ask him the same question about Bert and use the process of elimination to ID Adam.

Still working on one question - I'm convinced it can be done but will take more time.

Posted by Robert Woods on 2005-02-17 00:37:57