Brain Teasers
Knights & Knaves
A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet two inhabitants: Amy and Brittany.
Amy tells you that Brittany is a knave. Brittany says, 'Neither Amy nor I are knaves.'
What are Amy and Brittany?
Amy tells you that Brittany is a knave. Brittany says, 'Neither Amy nor I are knaves.'
What are Amy and Brittany?
Hint
Guess and CheckAnswer
Take Amy's statement and assume it's true. If Brittany is a knave, that means that she is lying. That would mean that one of them is a knave, which would still be true. If Amy was lying, then Brittany would be telling the truth that neither of them were knaves, which would contradict Amy's lie. Therefore, Amy is a knight, and Brittany is a knave.Hide Hint Show Hint Hide Answer Show Answer
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Comments
My brain hurts! It was so obvious that it was confusing.
fun!
fun!
Very easy..even for me but on the other hand it was FUN
Very easy, but I enjoyed it!
I have seen this one in many variations over they ears, and it catches me scratching my head every durned time! But I keep coming back for more.
thats easy confusing and fun
A classic logic puzzle. Good fun!
actually that's wrong...lets use the author's answer first: amy=knight brittany=knave. if brittany is a knave and says "neither amy nor I are knaves" that means that brittany told the truth about amy not being a knave. if brittany is a knave she can only lie...so she couldn't say that amy isn't a knave. the only way this works is if brittany is a knight and amy lied to her and said that amy was a knight. so brittany, assuming that amy is a knight, can tell the truth by saying neither are knaves even though amy is a knave. otherwise it's unsolvable.
I love knight and knave puzzles. Rather than classifying knights as telling the truth and knaves as lying, I find it can be more helpful to classify knights as capable of making only true statements and knaves as capable of only making false statements.
@alexcunn:
B effectively says that A and B are both knights. If that statement is true, that means that A and B are both knights. If it is false, it could be the case that one of the two is a knight and the other a knave, or it could be that they are both knaves. This is to be differentiated from the case where two independent statements are made. If B says "Neither A nor B are knaves", that statement is what is known as the conjunction of two propositions: (1) A is not a knave, (2) B is not a knave. For a conjunction of two propositions in propositional calculus to be true, it must be the case that both propositions involved are true. If A is a knight and B is a knave, then A's statement must be true, and B's statement must be false. A's statement that B is a knave is true because B is a knave. B's statement that neither A nor B are knaves is false because it is not the case that neither A nor B is a knave. In general, for either/or, if one of the propositions is true, then the whole statement is true, and for neither/nor, if one of the propositions is false than the whole thing is false. The use of "neither P nor Q" is semantically equivalent to "Both (not P) and (not Q)".
@alexcunn:
B effectively says that A and B are both knights. If that statement is true, that means that A and B are both knights. If it is false, it could be the case that one of the two is a knight and the other a knave, or it could be that they are both knaves. This is to be differentiated from the case where two independent statements are made. If B says "Neither A nor B are knaves", that statement is what is known as the conjunction of two propositions: (1) A is not a knave, (2) B is not a knave. For a conjunction of two propositions in propositional calculus to be true, it must be the case that both propositions involved are true. If A is a knight and B is a knave, then A's statement must be true, and B's statement must be false. A's statement that B is a knave is true because B is a knave. B's statement that neither A nor B are knaves is false because it is not the case that neither A nor B is a knave. In general, for either/or, if one of the propositions is true, then the whole statement is true, and for neither/nor, if one of the propositions is false than the whole thing is false. The use of "neither P nor Q" is semantically equivalent to "Both (not P) and (not Q)".
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