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Set of Spheres (Posted on 2005-11-03) Difficulty: 4 of 5
Let A, B, and C be spheres that are tangent pairwise and whose points of tangency are distinct. Let {D1, D2, ..., Dn} be a set of spheres each of which is tangent to spheres A, B, and C. For i = 1 to n, Di is externally tangent to Di+1 (where Dn+1 = D1).

What is the value of n?

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

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a coincidence | Comment 3 of 7 |
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
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