Quiz

Hermit, yes, noted. Sooner or later, the polyhedron will simply minimize potential energy. The physical approach is much simpler here than the mathematical one, through the projection of the center of gravity ;) In this regard, Mort correctly pointed out that it's easier to achieve on the edge. Actually, where I found this problem, they simply stated: "A perpetual motion machine is impossible => this is impossible." But it seemed insufficient to me. What if there's some kind of paradox...? Or maybe this system isn't actually a perpetual motion machine (a hydroelectric power station might also seem like a perpetual motion machine: the river flows endlessly, and we get free energy. But in reality, there's no perpetual motion machine there. Maybe there's some external energy source here too?). I considered potentials to be the optimal explanation. Hermit, make a wish.