  Single-photon avalanche detectors (SPADs) are crucial sensors of light for
many fields and applications. However, they are not able to resolve photon
number, so typically more complex and more expensive experimental setups or
devices must be used to measure the number of photons in a pulse. Here, we
present a methodology for performing photon number-state reconstruction with
only one SPAD. The methodology, which is cost-effective and easy to implement,
uses maximum-likelihood techniques with a detector model whose parameters are
measurable. We achieve excellent agreement between known input pulses and their
reconstructions for coherent states with up to $\approx$ 10 photons and peak
input photon rates up to several Mcounts/s. When detector imperfections are
small, we maintain good agreement for coherent pulses with peak input photon
rates of over 40 Mcounts/s, greater than one photon per detector dead time. For
anti-bunched light, the reconstructed and independently measured pulse-averaged
values of $g^{(2)}(0)$ are also consistent with one another. Our algorithm is
applicable to light pulses whose pulse width and correlation time scales are
both at least a few detector dead times. These results, achieved with single
commercially available SPADs, provide an inexpensive number-state
reconstruction method and expand the capabilities of single-photon detectors.
