= Solution
Separation with Dirichlet walls gives
$$
\Psi_{n_xn_yn_z}=\sin\frac{n_x\pi x}{a}\sin\frac{n_y\pi y}{b}\sin\frac{n_z\pi z}{c},
$$
$$
E_{n_xn_yn_z}=\frac{\hbar^2\pi^2}{2m}\left(\frac{n_x^2}{a^2}+\frac{n_y^2}{b^2}+\frac{n_z^2}{c^2}\right),\qquad n_x,n_y,n_z\ge1.
$$
For $a<b<c$, the <ground state> $(1,1,1)$ has a <nondegenerate energy eigenvalue>[nondegenerate] energy. The cheapest <excited state>[excitation] changes the <quantum number> in the longest direction, so the <first excited state> $(1,1,2)$ also has a nondegenerate energy.
If $a<b=c$, the ground-state energy remains <nondegenerate energy eigenvalue>[nondegenerate], but $(1,2,1)$ and $(1,1,2)$ have equal first-excited energy, giving <state degeneracy>[degeneracy] two.
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