  A particle in a one-dimensional delta-function potential and particle in a
box are two well-known pedagogical examples; their combination, particle in a
box with a delta-function potential V_\lambda(x)=\lambda\delta(x-x_0), too, has
been recently explored. We point out that it provides a unique example that is
solvable in the weak (\lambda->0) and the strong (1/\lambda->0) coupling
limits. In either limit, the attractive and repulsive potentials lead to
identical spectra, with the possible exception of a single negative-energy
state that is present when the potential is attractive. We numerically obtain
the spectra near the strong-coupling limit and discuss the consequences of the
degeneracy that arises when 1/|\lambda|=0.
