  Consider the following problem: how many collinear triples of points must a
transversal of (Z/nZ)^2 have? This question is connected with venerable issues
in discrete geometry. We show that the answer, for n prime, is between (n-1)/4
and (n-1)/2, and consider an analogous question for collinear quadruples. We
conjecture that the upper bound is the truth and suggest several other
interesting problems in this area.
