In this paper, we present a new task that investigates how people interact with and make judgments about towers of blocks. In Experiment 1, participants in the lab solved a series of problems in which they had to re-configure three blocks from an initial to a final configuration. We recorded whether they used one hand or two hands to do so. In Experiment 2, we asked participants online to judge whether they think the person in the lab used one or two hands. The results revealed a close correspondence between participants’ actions in the lab, and the mental simulations of participants online. To explain participants’ actions and mental simulations, we develop a model that plans over a symbolic representation of the situation, executes the plan using a geometric solver, and checks the plan’s feasibility by taking into account the physical constraints of the scene. Our model explains participants’ actions and judgments to a high degree of quantitative accuracy.
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