A paper study is conducted on the detection of fissile material using neutron coincidence counters. Three unknown independent properties of assays of fissile material assays are identified to be the effective mass, the (alpha,n) production rate and the neutron multiplication rate. Singlet counting can only be implemented for very well-known assay samples. Doublet counting may be employed with calibration curves which reduce the number of unknowns from three to one. Multiplicity counting theoretically enables assay mass determination without calibration curves. Coincidence counting is most widely applied via active and passive well coincidence counters. Passive neutron well counters are well suited for determination of 240 Pu masses. Active neutron well counters are well suited for determination of fissile material masses. Active well counters are found to have relative mass errors of 4% for a highly enriched uranium (HEU) sample of mass of 1kg and 8% for a mass of 50g. Thermal neutron interrogation sources feature smaller relative errors in small assays than fast neutron interrogation sources.