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In this paper, we present a new task that investigates how people interactwith and make judgments about towers of blocks. In Experiment~1, participantsin the lab solved a series of problems in which they had to re-configure threeblocks from an initial to a final configuration. We recorded whether they usedone hand or two hands to do so. In Experiment~2, we asked participants onlineto judge whether they think the person in the lab used one or two hands. Theresults revealed a close correspondence between participants' actions in thelab, and the mental simulations of participants online. To explainparticipants' actions and mental simulations, we develop a model that plansover a symbolic representation of the situation, executes the plan using ageometric solver, and checks the plan's feasibility by taking into account thephysical constraints of the scene. Our model explains participants' actions andjudgments to a high degree of quantitative accuracy.

Physical problem solving: Joint planning with symbolic, geometric, and dynamic constraints