= Solution
Both in-plane orientations minimize the one-site <energy>. Since every <adsorption site> is occupied, the sites label independent choices even though the molecules are chemically identical. The <ground state> of the whole system therefore has
$$
\boxed{U_{\min}=-N\varepsilon,\qquad\Omega_0=2^N.}
$$
The <ground-state degeneracy> is extensive: independently choosing either in-plane orientation at each site costs no <energy>. There is no extra vacancy or free-translational contribution in this model.
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