  The old open cluster M67 is an ideal testbed for current cluster evolution
models because of its dynamically evolved structure and rich stellar
populations that show clear signs of interaction between stellar, binary and
cluster evolution. Here we present the first truly direct N-body model for M67,
evolved from zero age to 4 Gyr taking full account of cluster dynamics as well
as stellar and binary evolution. Our preferred model starts with 12000 single
stars and 12000 binaries placed in a Galactic tidal field at 8.0 kpc from the
Galactic Centre. Our choices for the initial conditions and for the primordial
binary population are explained in detail. At 4 Gyr, the age of M67, the total
mass has reduced by 90% as a result of mass loss and stellar escapes. The mass
and half-mass radius of luminous stars in the cluster are a good match to
observations although the model is more centrally concentrated than
observations indicate. The stellar mass and luminosity functions are
significantly flattened by preferential escape of low-mass stars. We find that
M67 is dynamically old enough that information about the initial mass function
is lost, both from the current luminosity function and from the current mass
fraction in white dwarfs. The model contains 20 blue stragglers at 4 Gyr which
is slightly less than the 28 observed in M67. Nine are in binaries. The blue
stragglers were formed by a variety of means and we find formation paths for
the whole variety observed in M67. Both the primordial binary population and
the dynamical cluster environment play an essential role in shaping the
population. A substantial population of short-period primordial binaries (with
periods less than a few days) is needed to explain the observed number of blue
stragglers in M67.
