  In order to understand the puzzle of the free energy of an individual quark
in QCD, we explicitly construct ensembles with quark numbers $N_V\neq 0\!\mod
3$, corresponding to non-zero triality in a finite subvolume $V$ on the
lattice. We first illustrate the basic idea in an effective Polyakov-loop
theory for the heavy-dense limit of QCD, and then extend the construction to
full Lattice QCD, where the electric center flux through the surface of $V$ has
to be fixed at all times to account for Gauss's law. This requires introducing
discrete Fourier transforms over closed center-vortex sheets around the spatial
volume $V$ between all subsequent time slices, and generalizes the construction
of 't Hooft's electric fluxes in the purge gauge theory. We derive this same
result from a dualization of the Wilson fermion action, and from the transfer
matrix formulation with a local $\mathbb Z_3$-Gauss law to restrict the
dynamics to sectors with the required center charge in $V$.
