  Scattershot photon sources are known to have useful properties for optical
quantum computing and boson sampling purposes, in particular for scaling to
large numbers of photons. This paper investigates the application of these
scattershot sources towards the metrological task of estimating an unknown
phase shift. In this regard, we introduce three different scalable multimode
interferometers, and quantify their quantum Fisher information performance
using scattershot sources with arbitrary system sizes. We show that two of the
interferometers need the probing photons to be in certain input configurations
to beat the classical shot-noise precision limit, while the remaining
interferometer has the necessary symmetry which allows it to always beat the
classical limit no matter the input configuration. However, we can prove all
three interferometers gives the same amount of information on average, which
can be shown to beat the classical precision limit. We also perform Monte Carlo
simulations to compare the interferometers in different experimentally relevant
regimes, as a function of the number of samples.
