Samedi 9 Janvier 2016

Suppose two right circular cones and one right circular cylinder mutually interpenetrate, with the base of each cone and both bases (i.e., both ends) of the cylinder sealed by precisely fitting flat circular surfaces. What is the maximum number of pieces (i.e., completely bounded volumes) that can thus be formed, considering only the surfaces of these three figures as boundaries and counting only pieces that are not further subdivided?

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