  We analyze the proposal of Aharonov, Popescu, Rohrlich and Skrzypczyk [New.
J. Phys. 15, 113015] of disembodying physical properties from particles. We
argue that a different criterion, based on the cross-average $\langle
\mathrm{`}cat\ somewhere \mbox{'}\times \mathrm{`}grin\ somewhere\
else\mbox{'}\rangle$ should be used to detect the disembodiment, rather than
the local averages $\langle \mathrm{`}cat\ somewhere \mbox{'}\rangle$ and
$\langle\mathrm{`}grin\ somewhere\ else\mbox{'}\rangle$. Here, the exact
probability distribution and its characteristic function are derived for
arbitrary coupling strength, preparation and post-selection. This allows to
successfully hunt down the quantum Cheshire cat, showing that it is a
consequence of interference, that it is present also for intermediate-strength
measurements, and that it is a rather common occurrence in post-selected
measurements.
