Create a puzzle with a large number of magnetic spheres or discs (these already exist), and a large metal sphere of a very precise size. The goal is to place all the magnets touching the surface of the large sphere. Only a careful sphere covering pattern will do.
There are probably some nice looking coverings based on the geodesic sphere for some sizes, but for very difficult puzzles, use one of the sizes for which the pattern is more random looking.
Minimum sphere that can be tangent to (kiss) N unit spheres.
Minimum sphere onto which can be drawn N non-overlapping unit circles.
Something bad might happen with so many magnet poles aligned radially.
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