If a and b are real numbers with a < b, an open interval (a, b) is the set of all real numbers x such that a < x < b. Prove that if I1,..., In is a set of n ≥ 2 open intervals such that each pair has a nonempty intersection, then
I1 ∩ I2 ∩ ........∩ In
is nonempty.
Flavius Josephus was a Jewish soldier and historian who lived in the first century (see [Graham, 1994; Schtimer]). He was one of the leaders of a Jewish revolt against Rome in the year 66. The following year, he was among a group of trapped soldiers who decided to commit suicide rather than be captured. One version of the story is that, rather than being captured, they formed a circle and proceeded around the circle killing every third person.
Josephus, being proficient in discrete math, figured out where he and a buddy should stand so they could avoid being killed.
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