Walk versus Wait: The Lazy Mathematician Wins

Details Walk versus Wait: The Lazy Mathematician Wins Walk versus Wait: The Lazy Mathematician Wins

2008-01-01

arxiv.org/abs/0801.0297v3

Mathematics

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3 pages

Scientific paper

In this recreational mathematics note, we address a simple, yet instructive question: Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the starting point. At each bus stop, Justin is faced with a choice: to walk or to wait. If he walks on, he can still catch a bus at the next bus stop--but if a bus passes him while he walks, he is almost assured a longer wait. We model Justin's decision constraint and completely solve the model in a special case. The answer is intuitive: the optimal strategy is the laziest.

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