  The number partitioning problem can be interpreted physically in terms of a
thermally isolated non-interacting Bose gas trapped in a one-dimensional
harmonic oscillator potential. We exploit this analogy to characterize, by
means of a detour to the Bose gas within the canonical ensemble, the
probability distribution for finding a specified number of summands in a
randomly chosen partition of an integer n. It is shown that this distribution
approaches its asymptotics only for n > 10^10.
