  The reader is reminded of several puzzles involving randomness. These may be
ill-posed, and if well-posed there is sometimes a solution that uses
probabilistic intuition in a special way. Various examples are presented
including the well known problem of the lost boarding pass: what is the
probability that the last passenger boarding a fully booked plane sits in the
assigned seat if the first passenger has occupied a randomly chosen seat? This
problem, and its striking answer of $\frac12$, has attracted a good deal of
attention since around 2000. We review elementary solutions to this, and to the
more general problem of finding the probability the $m$th passenger sits in the
assigned seat when in the presence of some number $k$ of passengers with lost
boarding passes. A simple proof is presented of the independence of the
occupancy status of different seats, and a connection to the Poisson--Dirichlet
distribution is mentioned.
