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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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Hints/Tips mathworld link | Comment 5 of 7 |

If two of the spheres A,B,C are internal to the third the situation is as:

http://mathworld.wolfram.com/Hexlet.html

And the solution is n=6

If A,B,C are are externally tangent, I think the solution can also be 6 counting a sphere at infinity

Related is the Steiner Chain:

http://mathworld.wolfram.com/SteinerChain.html

but the number of circles is not limited.


  Posted by Jer on 2005-11-04 12:47:40
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