Let A, B, and C be spheres that are tangent pairwise and whose points of tangency are distinct. Let {D₁, D₂, ..., 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 = D₁).

What is the value of n?

If A, B, and C are allowed to be coincident, or let's say identical radii and identical centers, then you could have a string of as many D spheres as you want running around the outside of the A=B=C sphere.  n could be infinite

Probably the phrase "points of tangency are distinct" implies that A, B, and C can't be identical and coincident

Posted by Larry on 2005-11-03 23:52:11