We consider the problem of counting a set of discrete point targets using a network of sensors under a minimalistic model. Each sensor outputs a single integer, the number of distinct targets in its range, but targets are otherwise indistinguishable to sensors: no angles, distances, coordinates, or other target-identifying measurements are available. This minimalistic model serves to explore the fundamental performance limits of low-cost sensors for such surveillance tasks as estimating the number of people, vehicles or ships in a field of interest to first degree of approximation, to be followed by more expensive sensing and tion if needed. This simple abstract setting allows us to explore the intrinsic complexity of a fundamental problem, and derive rigorous worst-case performance bounds. We show that even in the 1-dimensional setting (for instance, sensors counting vehicles on a road), the problem is non-trivial: target count can be estimated within relative accuracy of factor 2 an...