MathDB

Let

S_1

and

S_2

be two spheres with distinct radii that touch externally. The spheres lie inside a cone

C

, and each sphere touches the cone in a full circle. Inside the cone there are

n

additional solid spheres arranged in a ring in such a way that each solid sphere touches the cone

C

, both of the spheres

S_1

and

S_2

externally, as well as the two neighboring solid spheres. What are the possible values of

n

?
Proposed by Iceland.

Problem Statement