  We study the equation of state of a mixture of (quasi-)free constituent
quarks and nucleons with hard-core repulsion at zero temperature. Two opposite
scenarios for the realization of the Pauli exclusion principle are considered:
(i) a Fermi sea of quarks surrounded by a shell of baryons -- the quarkyonic
matter, and (ii) a Fermi sea of nucleons surrounded by a shell of quarks which
we call \emph{baryquark matter}. In both scenarios, the sizes of the Fermi sea
and shell are fixed through energy minimization at fixed baryon number density.
While both cases yield a qualitatively similar transition from hadronic to
quark matter, we find that baryquark matter is energetically favored in this
setup and yields a physically acceptable behavior of the speed of sound without
the need to introduce an infrared regulator. In order to retain the
theoretically more appealing quarkyonic matter as the preferred form of dense
QCD matter will thus require modifications to the existing dynamical generation
mechanisms, such as, for example, the introduction of momentum-dependent
nuclear interactions.
