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A Parking Problem

Consider a street of length L > 0. L is a real number. There are cars
of unit length that come and park anywhere they will fit along the
street (uniform distribution). (Assume that as long the available gap is
>= 1, they can laterally slide in). This process continues until no
more cars can be parked. What is the average number of cars that will
be parked at the end of the process?
Source:
Ravi Subramanianciting the following
web locations.

http://www.dse.nl/puzzle/complex/index.html#car_parking

http://www.thewizardofodds.com/math/ (#105)

Solution

Mail to Ken