Create a puzzle or game for which the easier levels can be solved by trial and error or intuition, but which also suggests a way of "cheating" by solving it "offline" using mathematics or computer science. Make it easy to export the information to solve it offline.
One idea: which polyhedron is bigger? Coordinates of vertices, lengths and dihedral angles of edges, angles in faces are available by clicking on them.
The math might not be entirely straightforward: the player is encouraged to develop mathematical techniques or algorithms (for example, a volume formula for an arbitrary polyhedron).
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