There is an east-west street of length L units. And we park cars of unit length along the north side until we can't place any more cars. Each car is placed randomly (uniformly).

What is the expected number of cars that can be parked (as a function of L)?
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I'll start you off...

For 0 <= L < 1, F(L) = 0
For 1 <= L < 2, F(L) = 1

Okay... now the easy ones are out of the way, can you describe the function for L>=2?

This one is google-able using "cars of unit length" (quotes included) as the search string.  One of the best results is

http://mathworld.wolfram.com/RenyisParkingConstants.html

Posted by Richard on 2004-07-05 16:59:07