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?

If Bert were a Liar and Carl a Knave, Bert could never have made the statement attributed to him by Adam, so Adam would be lying. But if this were the case, Adam would be the Knight among them and couldn't lie, so the combination of Bert as Liar, Carl as Knave and Adam as Knight is impossible.

That leaves five possibilities among the six permutations of Knight, Knave and Liar among Adam, Bert and Carl. This includes, for example, the possibility that Bert is a Knight, Carl is a Knave and Adam is a Liar, as, even though the statement attributed to Bert by Adam would be a possibility, it would not necessarily actually have taken place.

In order to differentiate among five possibilities, with yes/no questions, you'd need three such answers, so one yes/no question will not do.

Posted by Charlie on 2005-02-16 19:27:11