  In this paper, we investigate a problem concerning quartets, which are a
particular type of tree on four leaves. Loosely speaking, a set of quartets is
said to be `definitive' if it completely encapsulates the structure of some
larger tree, and `minimal' if it contains no redundant information. Here, we
address the question of how large a minimal definitive quartet set on n leaves
can be, showing that the maximum size is at least 2n-8 for all n>3. This is an
enjoyable problem to work on, and we present a pretty construction, which
employs symmetry.
