  The combination of asteroseismologically-measured masses with abundances from
detailed analyses of stellar atmospheres challenges our fundamental knowledge
of stars and our ability to model them. Ancient red-giant stars in the Galactic
thick disc are proving to be most troublesome in this regard. They are older
than 5 Gyr, a lifetime corresponding to an initial stellar mass of about
$1.2{\mathrm{M}_{\odot}}$. So why do the masses of a sizeable fraction of
thick-disc stars exceed $1.3{\mathrm{M}_{\odot}}$, with some as massive as
$2.3{\mathrm{M}_{\odot}}$ ? We answer this question by considering duplicity in
the thick-disc stellar population using a binary population-nucleosynthesis
model. We examine how mass transfer and merging affect the stellar mass
distribution and surface abundances of carbon and nitrogen. We show that a few
per cent of thick-disc stars can interact in binary star systems and become
more massive than $1.3{\mathrm{M}_{\odot}}$. Of these stars, most are single
because they are merged binaries. Some stars more massive than
$1.3{\mathrm{M}_{\odot}}$ form in binaries by wind mass transfer. We compare
our results to a sample of the APOKASC data set and find reasonable agreement
except in the number of these thick-disc stars more massive than
$1.3{\mathrm{M}_{\odot}}$. This problem is resolved by the use of a
logarithmically-flat orbital-period distribution and a large binary fraction.
