  Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when
the beacon is a point required to be remain nonstrictly outside a polygon, and
the ball is a point always moving instantaneously and maximally toward the
beacon subject to staying nonstrictly within the same polygon? Kouhestani and
Rappaport [JCDCG 2017] gave an algorithm for determining whether a
ball-capturing beacon strategy exists, while conjecturing that such a strategy
always exists. We disprove this conjecture by constructing orthogonal and
general-position polygons in which the ball and the beacon can never be united.
