The airplane problem (generative recursion)?
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Passengers are lined up at the airport to board a full flight to
Dallas.  Each passenger is assigned a seat, and every passenger is
planning to sit in his or her assigned seat.  Except one: Joe is
afraid of Texas Rangers, and he has been drinking so heavily that he
can no longer grasp the concept of an assigned seat.

Here's the procedure:

  - When Joe boards, he picks an unoccupied seat at random and sits in
    it.

  - When any other passenger boards, he or she sits in their assigned
    seat if it is available.  If the assigned seat is already
    occupied, he or she picks an unoccupied seat at random and sits in
    it.

They're traveling by the new SouthBlue discount carrier, and places in
the boarding line are assigned at random.  Write a program to answer
the following question:

  - If there are $N$ total passengers, what is the probability that
    the last passenger gets his or her assigned seat?


The chain problem (generative recursion)
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A chain is composed of $N$ links, where $N$ is an even number at least
$6$.

  - A link is chosen at random from somewhere in the middle of the
    chain (not at either end).  That link is cut and thrown away,
    leaving two pieces of chain.

  - The larger of the two remaining pieces is cut at random in the
    same way.

  - What is the probability that the three pieces of chain can be
    fully extended to form a triangle?