A girl says, "I'm 12 plus half my age," and "I can't give you my phone number, but I'll answer yes or no to...
logic/phone.number.question New
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Problem
A girl says, "I'm 12 plus half my age," and "I can't give you my phone number, but I'll answer yes or no to any question you ask." How old is she, and what is the maximum number of questions you need to ask her to find her phone number? I met this lovely girl the other day (in the library) and from here to there we started talking. I asked her how old she was and she goes: "I'm 12 plus half my age." WOW! That hit me in the face like an elbow-corner. She _was_ kinda sophisticated and unusual... Then we continued talking and I asked her for her phone number. She said: "I can't give you my number, but I'll answer yes or no to any question you ask." My questions to you people are the following: how old is the lovely girl, and what is the maximum number of questions I need to ask her in order to find her phone number? -- Ron <relkay01@solix.fiu.edu> [ Editor: the first paragraph is the editor's summary. ]
Show solution
Well, the girl is obviously 24. Assuming the girl is honest, you can find her phone number with one question: "Will your answer to this question be 'yes' if and only if you will recite your phone number within the next 30 seconds?" If she must answer and she must be truthful, she may answer this question either 'yes' or 'no', but either way, she has to recite her phone number within the next 30 seconds. The same technique works by replacing "you will recite your phone number within the next 30 seconds" with "you will spend the night with me", or whatever other devious requests you wish fulfilled. Guys, remember this technique, next time you encounter a totally truthful girl who promises to answer any question you put to her. -- Jonathan S. Haas <positron@neosoft.com>