  We examine the initial mass functions (IMFs) of stars produced by different
molecular core mass functions. Simulations suggest that more massive cores
produce more stars, so we propose a model in which the average number of stars
formed in a core is equal to the initial number of Jeans masses in that core.
Small-$N$ systems decay through dynamical interactions, ejecting low-mass stars
and brown dwarfs which populate the low-mass tail of the IMF. Stars which
remain in cores are able to competitively accrete more gas and become more
massive. We deduce the forms of the core mass functions required to explain the
IMFs of Taurus, Orion, IC 348 and NGC 2547. These core mass functions fall into
two categories - one which peaks at a few $M_\odot$ to explain Taurus and NGC
2547, and one that peaks at around $0.2 M_\odot$ to explain Orion and IC 348.
