Time to get those brains warmed up!
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Question
I am thinking of an integer n with 0 = n = 15. To figure out what number I'm thinking of, you can ask me 7 yes-or-no questions -- questions that can only be answered with either "yes" or "no". The questions must be independent of each other, their answers, and the order in which they are answered. (So you can't ask a question like, "if the answer to the previous question was "yes", then is n larger than 10, otherwise is n even?") When you ask me your seven questions, I am allowed to LIE about at most one of the answers. What seven questions can you ask to determine n?
Good luck!
I don't think this works because he says the answers have to be "independent" of each other. Therefore, you essentially submit all the questions at once and then he answers all 7 yes or no.
The other problem is that he could tell the truth both the first and second time you ask if it is odd, and then lie later on about one of the subsets, but you won't know which one. This is a tough one...
It's done through binary. I'm not in the mood to stimulate my mind this much though as my mind is ready to shut off in about 29 minutes.
The way that I took it as independent given the information provided I couldn't ask, if the number is bigger than or equal to 7, is the number bigger than or equal to 9? But I could ask is the number bigger than or equal to 7. I could also ask is the number bigger than or equal to 9.
But reading it over again, I guess that method wouldn't work.
But if he lied about when I asked if the number was greater than or equal to a certain number I would figure it out in the subsequent questions and still be able to solve the question.
Using binary I think I can figure out the number in only 5 questions:
Will M: If they answer "Yes" to your first question, then that isn't a lie. You therefore cannot solve if any of the other answers are lies.
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