Let A, B, and C be spheres that are tangent pairwise and whose points of tangency are distinct. Let {D_{1}, D_{2}, ..., D_{n}} be a set of spheres each of which is tangent to spheres A, B, and C. For i = 1 to n, D_{i} is externally tangent to D_{i+1} (where D_{n+1} = D_{1}).
What is the value of n?