Puzzles & Paradoxes

March 13, 2007 7:40pm CST
On the fictional island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights are honest and virtuous, and always tell the truth. Knaves are base and shameful, and always lie. A stranger comes to the island and encounters three inhabitants, referred to as A, B and C. The visitor asks A whether he' s a knight or a knave. Inhabitant A mumbles an answer the stranger cannot understand. B then says: "A said that he is a knave" while C says: "Don' t believe B, he is lying!" It is not possible to determine A' s type from this conversation, but it is possible to tell what type B and C are.
2 people like this
5 responses
@Denmarkguy (1845)
• United States
14 Mar 07
It's a process of elimination puzzle. Inhabitant A MUST have said "I'm a Knight." We know this because Knights do not lie, so a knight could ONLY have said "I'm a Knight." On the other hand, a Knave always lies, so saying "I'm a Knave" would have been truthful, so it could not have been said by a Knave. Therefore we KNOW that A said "I'm a Knight." When we KNOW this, and are told that Inhabitant B says "A said that he is a knave" we can extrapolate that Inhabitant B MUST be a Knave, because he just lied. Inhabitant C then states "Don' t believe B, he is lying!" and is telling the truth-- and therefor MUST be a Knight. Therefore: Inhabitant A said "I'm a Knight," but we don't know which type he is. Inhabitant B is a Knave Inhabitant C is a Knight
• Turkey
2 Jan 08
Wow. I couldn't think of that. I think yours is the right answer.
@AndriaToh (1268)
• Malaysia
13 Sep 07
B is a knave. A could not have said that he was a knave, since that would be telling the truth about himself. C is then a knight, since he has stated that B is lying. But it is true that A's type cannot be determined. If he was either a knight or a knave, he would still say that he is a knight both ways, and what B said would still be a lie in both cases.
• United States
14 Mar 07
It is not possible to determine any of the three inhabitant's types. If person A is a Knight then that means person B is lying (Knave) and person C is telling the truth (Knight). If person A is a Knave then that means person B is telling the truth (Knight) and person C is lying (Knave). I do not know how you all went about reaching your conclusions, but it is not possible to whether any of the inhabitants are knights or knaves.
@NatureBoy (493)
• Singapore
14 Mar 07
Ha ha. It is possible for me to determine the visitors type. He is NAIVE if he believes and of them. To tell the truth, I can't tell A B C's type from the conversation too. LOL So I think A is the smartest, by not saying anything he doesn't lie (not knave) nor does he tell the truth (not knight) Ha Ha.
@aries_0325 (3062)
• Philippines
14 Mar 07
I reached a different conclusion I detemined A, but couldnĀ“t determine B, and C. Maybe you confused yourself there. A is a knave, but for B and C there are two possibilities. Possibility 1 A. Knave B. Knight C. Knave Possibility 2 A. Knave B. Knave C. Knight Possibility 3 - Both cannot be knights togheter, because one of them says that the other is lying, if both say just truth they must agree. Possibility 4 - Both cannot be Knaves togheter, because C would be saying the truth when he says that B is lying.