  The ONC appears to be unusual on two grounds: The observed constellation of
the OB stars of the entire Orion Nebula cluster and its Trapezium at its centre
implies a time-scale problem given the age of the Trapezium, and an IMF problem
for the whole OB star population in the ONC. Given the estimated crossing time
of the Trapezium, it ought to have totally dynamically decayed by now.
Furthermore, by combining the lower limit of the ONC mass with a standard IMF
it emerges that the ONC should have formed at least about 40 stars heavier than
5 M_sun while only ten are observed. Using N-body experiments we (i) confirm
the expected instability of the trapezium and (ii) show that beginning with a
compact OB-star configuration of about 40 stars the number of observed OB stars
after 1 Myr within 1 pc radius and a compact trapezium configuration can both
be reproduced. These two empirical constraints thus support our estimate of 40
initial OB stars in the cluster. Interestingly, a more-evolved version of the
ONC resembles the Upper Scorpius OB association. The N-body experiments are
performed with the new C-code CATENA by integrating the equations of motion
using the chain-multiple-regularisation method. In addition, we present a new
numerical formulation of the initial mass function.
