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Activity recognition of a single person in a smart space, using simple sensors, has been an ongoing research problem for the past decade, as simple sensors are cheap and non-intrusive. Recently, there is rising interest on multiple people activity recognition (MPAT) in a smart space with simple sensors, because it is common to have more than one person in real-world environments. We present the existing approaches of MPAT, such as Hidden Markov Models, and the available multiple people activities datasets. In our experiments, we show that surprisingly, without the use of existing approaches of MPAT, even standard classification techniques can yield high accuracy. We conclude that this is due to a set of assumptions that hold for the datasets that we used and this may be unrealistic in real life situations. Finally, we discuss the open challenges of MPAT, when these set of assumptions do not hold.