This paper addresses problems of inferring the locations of moving agents from combinatorial data extracted by robots that carry sensors. The agents move unpredictably and may be fully distinguishable, partially distinguishable, or completely indistinguishable. The key is to introduce information spaces that extract and maintain combinatorial sensing information. This leads to monitoring the changes in connected components of the shadow region, which is the set of points not visible to any sensors at a given time. When used in combination with a path generator for the robots, the approach solves problems such as counting the number of agents, determining movements of teams of agents, and solving pursuit-evasion problems. An implementation with examples is presented.