Section 3.5 Individual Research
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?
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?
