The Nature of Mathematics, 12th Edition
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Section 3.5 Individual Research

Individual Research Project 3.6

Convention Problem. A mathematician attended a convention of men and women scientists. The mathematician observed that if any two of them were picked at random, at least one of the two would be male. From this information, it is possible to deduce what percentage of the attendees were women?

Individual Research Project 3.7

A man is about to be electrocuted but is given a chance to save his lifE. In the execution chamber are two chairs, labeled 1 and 2, and a jailer.  One chair is electrified; the other is not.  The prisoner must sit on one of the chairs, but before doing so, he may ask the jailer one question, to which the jailer must answer "yes" or "no."  The jailer is a consistent liar or else a consistent truth teller, but the prisoner does not know which.  Knowing that the jailer either deliberately lies or faithfully tells the truth, what question should the prisoner ask?