  Recent measurement of mass of PSR J1614-2230 rules out most of existing
models of equation of state (EOS) of dense matter with high-density softening
due to hyperonization, based on the recent hyperon-nucleon and hyperon-hyperon
interactions, leading to a "hyperon puzzle".
  We study a specific solution of "hyperon puzzle", consisting in replacing a
too soft hyperon core by a sufficiently stiff quark core. We construct an
analytic approximation fitting very well modern EOSs of 2SC and CFL color
superconducting phases of quark matter. This allows us for simulating continua
of sequences of first-order phase transitions from hadronic matter to the 2SC,
and then to the CFL state of color superconducting quark matter.
  We obtain constraints in the parameter space of the EOS of superconducting
quark cores, resulting from M_max> 2 M_sol. We also derive constraints that
would result from significantly higher measured masses. For 2.4 M_sol required
stiffness of the CFL quark core should have been close to the causality limit,
the density jump at the phase transition being very small.
  Condition M_max > 2 M_sol puts strong constraints on the EOSs of the 2SC and
CFL phases of quark matter. Density jumps at the phase transitions have to be
sufficiently small and sound speeds in quark matter - sufficiently large. A
strict condition of thermodynamic stability of quark phase results in the
maximum mass of hybrid stars similar to that of purely baryon stars. Therefore,
to get M_max>2 M_sol for stable hybrid stars, both sufficiently strong
additional hyperon repulsion at high density baryon matter and a sufficiently
stiff EOS of quark matter would be needed. However, it is likely that the high
density instability of quark matter (reconfinement) indicates actually the
inadequacy of the point-particle model of baryons in dense matter at very high
densities.

Solar and Stellar Astrophysics;Nuclear Theory