IMO Shortlist 1987 problem 10

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Dodao/la: arhiva
2. travnja 2012.
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1987