  We describe the preparation of atom-number states with strongly interacting
bosons in one dimension, or spin-polarized fermions. The procedure is based on
a combination of weakening and squeezing of the trapping potential. For the
resulting state, the full atom number distribution is obtained. Starting with
an unknown number of particles $N_i$, we optimize the sudden change in the
trapping potential which leads to the Fock state of $N_f$ particles in the
final trap. Non-zero temperature effects as well as different smooth trapping
potentials are analyzed. A simple criterion is provided to ensure the robust
preparation of the Fock state for physically realistic traps.
