  This paper solves a pursuit-evasion problem in which a prince must find a
princess who is constrained to move on each day from one vertex of a finite
graph to another. Unlike the related and much studied `Cops and Robbers Game',
the prince has no knowledge of the position of the princess; he may, however,
visit any single room he wishes on each day. We characterize the graphs for
which the prince has a winning strategy, and determine, for each such graph,
the minimum number of days the prince requires to guarantee to find the
princess.
