  In this Letter we demonstrate that any interaction of pressureless dark
matter with holographic dark energy, whose infrared cutoff is set by the Hubble
scale, implies a constant ratio of the energy densities of both components thus
solving the coincidence problem. The equation of state parameter is obtained as
a function of the interaction strength. For a variable degree of saturation of
the holographic bound the energy density ratio becomes time dependent which is
compatible with a transition from decelerated to accelerated expansion.
