Earlier today I put five logical problems. Here they are again with solutions.
Planet doubtful
A certain planet inhabits two types of foreigners, Crick and chicks. Both types of foreigners – physically corresponding – have a strange way to speak. They only ask questions. The Cricice can only ask questions that are yes, while Goops can only ask questions that are not answered.
1.
solution no
If the answer is “no”, then the person should be a Goop because Gobs only asks these questions. But if the answer is “no”, they mention that they are not a compound. There is a contradiction, so this situation is impossible.
If the answer is “yes”, it is Crick. But if the answer is “Yes”, it is Goop! This situation is also impossible.
2. You meet two friends, Katsa and Anga. “Are we at least one of us?” I said. What is Katja and Anja?
solution Khatja is Creek and Anga Gob.
Say that the answer is “no”, then Khatja is Goop. But if not, then one of them will be Goop, nothing is Goops, and there is a contradiction. So this is impossible.
So the answer is “yes”, which means that Khatja Kreik. If someone is Goop, Katja should be.
3. I heard a conversation between two people. One of them asks, “Am I who can ask you if there is a processor on this planet?” What are the chances of a processor on this planet?
solution There is a processor on this planet
If the answer to this question is yes, then the liquid is Crick, and if they can ask whether there is a therapist on this planet, then this means that there is a processor on the planet, where the Cricks can only ask the questions that the answer is yes.
If the answer to this question is no, then the liquid is Goop. If they cannot ask if there is a processor on this planet, this means that there must be a processor on this planet, where Goops cannot ask questions unless their answer will be no. Because they cannot offer this answer, the answer should be yes.
Note: The question is the model “Am I who is the type that can ask you if it is x”, and X is correct, which is the strange type. This insight will be used in the following question.
4. Later you learn that there is exactly one processor on this planet of cricket and Goops. You want to know who he is. He met a foreigner named Andrew. “Am I who can ask if you are not a therapist?” He asks you. Do you have enough information to tell you who is definitely who is the processor now?
solution no
The exclusion is from the model “Am I who can ask you if it is x.” So we know that x is correct, that is, we know that Andrew is no Therapist. But we still do not know who He is Therapist.
5. A strange foreigner asks you, “Am I who is the type that can ask you the question I ask now?” What can be said about it?
solution She is Kreik
Suppose the answer is no. This means that the strange foreigner is Goop. But this also means that she cannot ask the question she asks. This does not have no meaning (because she asks her …) but this also means that the answer to the question is yes, because she cannot ask her while she is a job, and it is a direct contradiction. Suppose the answer to the question is yes. So it is Krick and it can ask the question she asks, so the answer to the question is yes. Everything is achieved.
Thanks to We solve problems Those who invented these puzzles. WSP runs free mathematics departments for high school students (in the United Kingdom from 7 to 11) in nine cities in the United Kingdom. If you want to subscribe to the next academic year You can advance here.
I have prepared a mystery here on Mondays since 2015. I have always been aware of the wonderful puzzles. If you want one suggestion, Send me.
