  The number of $\psi(3686)$ events collected by the BESIII detector during the
2021 run period is determined to be $(2259.3\pm 11.1)\times 10^6$ by counting
inclusive $\psi(3686)$ hadronic events. The uncertainty is systematic and the
statistical uncertainty is negligible. Meanwhile, the numbers of $\psi(3686)$
events collected during the 2009 and 2012 run periods are updated to be
$(107.7\pm0.6)\times 10^6$ and $(345.4\pm 2.6)\times 10^6$, respectively. Both
numbers are consistent with the previous measurements within one standard
deviation. The total number of $\psi(3686)$ events in the three data samples is
$(2712.4\pm14.3)\times10^6$.
