Given some points in the plane, draw the minimum Traveling Salesman's Path. Or, Euclidean Steiner Tree. These seem pretty easy to make into competitive games: whoever has the current best solution earns points based on time until someone else finds a better one.
For Euclidean Steiner, the player draws a topology and the computer automatically does local minimization to compute the total edge length. Perhaps no one earns points until the approximate tree based on locally optimizing the minimum spanning tree is beaten.
In 3D with VR.
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