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?
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 20051103 23:52:11 