  Since its publication, Aharonov and Vaidman's three-box paradox has undergone
three major advances: i). A non-counterfactual scheme by the same authors in
2003 with strong rather than weak measurements for verifying the particle's
subtle presence in two boxes. ii) A realization of the latter by Okamoto and
Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with
disappearance and reappearance of the particle. We now combine these advances
together. Using photonic quantum routers the particle acts like a quantum
"shutter." It is initially split between Boxes A, B and C, the latter located
far away from the former two. The shutter particle's whereabouts can then be
followed by a probe photon, split in both space and time and reflected by the
shutter in its varying locations. Measuring the former is expected to reveal
the following time-evolution: The shutter particle was, with certainty, in
boxes A+C at t1, then only in C at t2, and finally in B+C at t3. Another branch
of the split probe photon can show that boxes A+B were empty at t2. A Bell-like
theorem applied to this experiment challenges any alternative interpretation
that avoids disappearance-reappearance in favor of local hidden variables.
