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 transfroms 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 ℤ3-Gauss law to restrict the dynamics to sectors with the required center charge in $V$.