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Szilard's now-famous single-molecule engine was only the first of three constructions he introduced in 1929 to resolve several paradoxes arising from Maxwell's demon. We analyze Szilard's remaining two demon models. We show that the second one, though a markedly different implementation employing a population of distinct molecular species and semi-permeable membranes, is informationally and thermodynamically equivalent to an ideal gas of the single-molecule engines. Since it is a gas of noninteracting particles one concludes, following Boyd and Crutchfield, that (i) it reduces to a chaotic dynamical system---called the Szilard Map, a composite of three piecewise linear maps that implement the thermodynamic transformations of measurement, control, and erasure; (ii) its transitory functioning as an engine that converts disorganized heat energy to work is governed by the Kolmogorov-Sinai entropy rate; (iii) the demon's minimum necessary "intelligence" for optimal functioning is given by the engine's statistical complexity, and (iv) its functioning saturates thermodynamic bounds and so it is a minimal, optimal implementation. We show that Szilard's third model is rather different and addresses the fundamental issue, raised by the first two, of measurement in and by thermodynamic systems and entropy generation. Taken together, Szilard's suite of constructions lays out a range of possible realizations of Maxwellian demons that anticipated by almost two decades Shannon's and Wiener's concept of information as surprise and cybernetics' notion of functional information. This, in turn, gives new insight into engineering implementations of novel nanoscale information engines that leverage microscopic fluctuations and into the diversity of thermodynamic mechanisms and intrinsic computation harnessed in physical, molecular, biochemical, and biological systems.