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Lighting an Icosahedron

How many distinct figures are there with 3 light bulbs on the vertices of an
icosahedron? Place only 1 light bulb per vertex.

How many distinct figures are there with 3 light bulbs on the vertices of a
cube? 2 lightbulbs?

Source: POTW reader "Tulsa Mclain". Original cube extensions.

Solution

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