Smart object interfaces enable a computer to respond to a group of users' manipulations of a physical environment. This unobtrusive interface is especially well suited for providing guidance as students attempt to solve mathematical and scientific puzzles. This paper introduces a formalism for describing arrangements of smart objects on a 2D surface, and suggests a strategy for efficiently representing such arrangements in a computer application. It then shows how these techniques are implemented in a Tangram with a smart objects interface, which provides multimedia feedback as children play with the puzzle pieces.