(How was the pinecone? I imagine the taste wasn't that bad but the texture was difficult to get through)
Happy early Halloween!
Here are a few puzzles paraphrased from What is the Name of This Book? by Raymond Smullyan. These are from the chapter on the Island of Knights and Knaves. Knights always tell the truth and knaves always lie (and every person on the island is one or the other).
1. Inhabitants of the island A, B, and C were hanging out. A stranger asked A, "Are you a knight or a knave?" A mumbled the answer and the stranger couldn't hear. The stranger asked B, "What did A say?" B responded, "A said that he is a knave." C interjected: "Don't believe B; he is lying!" Is B a knight or a knave? What about C? AnswerB must be a knave, since neither a knight nor a knave can say that they are a knave. Therefore, C must be a knight.
2. C's answer isn't needed to solve the above problem. Here's a version where C's answer is necessary. The stranger instead asks A, "How many knights are among you?" A mumbles the answer. The stranger asks B, "What did A say?" B replies, "A said that there is one knight among us." Then C says, "Don't believe B; he is lying!" What are B and C? AnswerB is a knave and C is a knight.
3. There are two inhabitants, A and B, who are each either a knight or a knave. A says, "At least one of us is a knave." What are A and B? AnswerA is a knight and B is a knave.
4. Suppose A says, "Either I am a knave or B is a knight." What are A and B? (The meaning of either/or this book uses is this: if the statement "either P or Q" is true, at least one of P or Q is true. [Both can be true.] On the other hand, if the statement "either P or Q" is false, both P and Q are false.) AnswerIf A is a knave, the sentence is false, meaning that A is not a knave and B is not a knight. That would mean that A is a knave and not a knave at the same time. So he must be a knight. His statement must be true and at least one of the phrases must be true. Since A isn't a knave, B must be a knight. They are both knights.
5. Suppose A says, "Either I am a knave or else two plus two equals five." What would you conclude? AnswerThis is a trick question. Neither a knight nor a knave could say that sentence.
6. There are three people, A, B, and C, who are each either a knight or knave. A says "All of us are knaves" while B says "Exactly one of us is a knight." What are A, B, and C? AnswerA is a knave, B is a knight, and C is a knave.
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Happy early Halloween!
Here are a few puzzles paraphrased from What is the Name of This Book? by Raymond Smullyan. These are from the chapter on the Island of Knights and Knaves. Knights always tell the truth and knaves always lie (and every person on the island is one or the other).
1. Inhabitants of the island A, B, and C were hanging out. A stranger asked A, "Are you a knight or a knave?" A mumbled the answer and the stranger couldn't hear. The stranger asked B, "What did A say?" B responded, "A said that he is a knave." C interjected: "Don't believe B; he is lying!" Is B a knight or a knave? What about C?
Answer
B must be a knave, since neither a knight nor a knave can say that they are a knave. Therefore, C must be a knight.2. C's answer isn't needed to solve the above problem. Here's a version where C's answer is necessary. The stranger instead asks A, "How many knights are among you?" A mumbles the answer. The stranger asks B, "What did A say?" B replies, "A said that there is one knight among us." Then C says, "Don't believe B; he is lying!" What are B and C?
Answer
B is a knave and C is a knight.3. There are two inhabitants, A and B, who are each either a knight or a knave. A says, "At least one of us is a knave." What are A and B?
Answer
A is a knight and B is a knave.4. Suppose A says, "Either I am a knave or B is a knight." What are A and B? (The meaning of either/or this book uses is this: if the statement "either P or Q" is true, at least one of P or Q is true. [Both can be true.] On the other hand, if the statement "either P or Q" is false, both P and Q are false.)
Answer
If A is a knave, the sentence is false, meaning that A is not a knave and B is not a knight. That would mean that A is a knave and not a knave at the same time. So he must be a knight. His statement must be true and at least one of the phrases must be true. Since A isn't a knave, B must be a knight. They are both knights.5. Suppose A says, "Either I am a knave or else two plus two equals five." What would you conclude?
Answer
This is a trick question. Neither a knight nor a knave could say that sentence.6. There are three people, A, B, and C, who are each either a knight or knave. A says "All of us are knaves" while B says "Exactly one of us is a knight." What are A, B, and C?
Answer
A is a knave, B is a knight, and C is a knave.