Fermi energy on a "fermion pre-gas model"

I'm having serious trouble while trying to follow an example from Callen's "Thermodynamics and an introduction to Thermostatistics" regarding the definition of the Fermi energy.

In said example one has a spin 1/2 fermion system with three spatial orbits with energies $\epsilon_1$, $\epsilon_2$, $\epsilon_3$ and each state can be empty or occupied, taking into account that the occupied state is 2-degenerate due to the spin. The mean number of particles in the system is found to be

$$\bar{N}=\frac{2}{e^{\beta(\epsilon_1-\mu)}+1}+\frac{2}{e^{\beta(\epsilon_2-\mu)}+1}+\frac{2}{e^{\beta(\epsilon_3-\mu)}+1}$$

So far so good. But then the example goes on, stating that:

• If we have four fermions and $\epsilon_1=\epsilon_2$, the Fermi level must lie somewhere between $\epsilon_2$ and $\epsilon_3$.
• If we have four fermions and $\epsilon_1<\epsilon_2=\epsilon_3$, the Fermi level coincides with $\epsilon_2$.
• If we have two fermions and $\epsilon_1<\epsilon_2=\epsilon_3$, the Fermi level lies between $\epsilon_1$ and $\epsilon_2(=\epsilon_3)$.

I don't understand these statements. Doesn't the Fermi energy coincide with the highest occupied energy level at zero temperature? I would say that in the first case $\epsilon_F=\epsilon_1$ since all the fermions fill the lowest energy levels, leaving the $\epsilon_3$-level empty; and that $\epsilon_F=\epsilon_1$ in the third.

• Thanks for answering! But I still don't get it. You said that the Fermi energy is such that all states with a energy same or lower are occupied. In the first case, for example, there are no fermions on any level above $\epsilon_2$. Why should the Fermi energy be there, since all levels above that are empty?