  The colour-magnitude diagrams of resolved single stellar populations, such as
open and globular clusters, have provided the best natural laboratories to test
stellar evolution theory. Whilst a variety of techniques have been used to
infer the basic properties of these simple populations, systematic
uncertainties arise from the purely geometrical degeneracy produced by the
similar shape of isochrones of different ages and metallicities. Here we
present an objective and robust statistical technique which lifts this
degeneracy to a great extent through the use of a key observable: the number of
stars along the isochrone. Through extensive Monte Carlo simulations we show
that, for instance, we can infer the four main parameters (age, metallicity,
distance and reddening) in an objective way, along with robust confidence
intervals and their full covariance matrix. We show that systematic
uncertainties due to field contamination, unresolved binaries, initial or
present-day stellar mass function are either negligible or well under control.
This technique provides, for the first time, a proper way to infer with
unprecedented accuracy the fundamental properties of simple stellar
populations, in an easy-to-implement algorithm.
