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A computational modeling approach was used to test one possible explanation for the limited capacity of the subitizing phenomenon. Most existing models of this phenomenon associate the subitizing span with an assumed structural limitation of the human information processing system. In contrast, we show how this limit might emerge as the combinatorics of the space of enumeration problems interacts with the human cognitive architecture in the context of an enumeration task. Subitizing-like behavior was generated in two different models of enumeration, one based on the ACT-R cognitive architecture and the other based on the principles of parallel distributed processing (PDP). Our results provide good qualitative fits to results obtained in a variety of empirical studies.