  We consider a game in which a cop searches for a moving robber on a graph
using distance probes, studied by Carragher, Choi, Delcourt, Erickson and West,
which is a slight variation on one introduced by Seager. Carragher, Choi,
Delcourt, Erickson and West show that for any fixed graph $G$ there is a
winning strategy for the cop on the graph $G^{1/m}$, obtained by replacing each
edge of $G$ by a path of length $m$, if $m$ is sufficiently large. They
conjecture that the cop does not have a winning strategy on $K_n^{1/m}$ if
$m<n$; we show that in fact the cop wins if and only if $m\geqslant n/2$, for
all but a few small values of $n$. They also show that the robber can avoid
capture on any graph of girth 3, 4 or 5, and ask whether there is any graph of
girth 6 on which the cop wins. We show that there is, but that no such graph
can be bipartite; in the process we give a counterexample for their conjecture
that the set of graphs on which the cop wins is closed under the operation of
subdividing edges. We also give a complete answer to the question of when the
cop has a winning strategy on $K_{a,b}^{1/m}$.
