In thinking about Bose-Einstein condensation, an apparent contradiction came to mind ... Take the usual "particle in a box" potential and start filling it with identical spin-1/2 particles, two at a time. Also impose the rule that each pair of particles added must have opposite spin, i.e. net spin of zero for the pair. Since the individual particles are fermions, they will occupy higher and higher energy levels, due to the exclusion principle. However, we can also view each inserted pair as a single boson. Since the occupation number of a boson state can rise as high as you want, it would seem that all the pairs fall into the ground state (at zero temperature), and their energies are all the same. So which picture of the system's energy is correct, Fermi, Bose, or some combination of the two? Quantum Mechanics must have an answer to this question, but I can't figure it out. Can anyone out there explain how to reconcile these two pictures of the system?