  P\'or and Wood conjectured that for all $k,l \ge 2$ there exists $n \ge 2$
with the following property: whenever $n$ points, no $l + 1$ of which are
collinear, are chosen in the plane and each of them is assigned one of $k$
colours, then there must be a line (that is, a maximal set of collinear points)
all of whose points have the same colour. The conjecture is easily seen to be
true for $l = 2$ (by the pigeonhole principle) and in the case $k = 2$ it is an
immediate corollary of the Motzkin-Rabin theorem. In this note we show that the
conjecture is false for $k, l \ge 3$.
