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Pile of Cannonballs (Posted on 2004-08-03) Difficulty: 3 of 5
If one stacks 10 cannonballs of diameter d in a pile (tetrahedron), what is the height of the pile?

No Solution Yet Submitted by ThoughtProvoker    
Rating: 3.0000 (2 votes)

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to richard | Comment 8 of 12 |
(In reply to re: 10 balls by Richard)

i did think it was a 'given'. (and i forgot to write "centers")

but how to prove it's a regular tetrahedron? good point.

may we consider the top ball and the three supporting it, and then assume the relationship holds through the rest of the structure?

the three balls supporting the top ball are tangent to one another. they have the same diameter thus their centers create an equilateral triangle with sides of length d.
the top ball resting upon these three is tangent to each of them and its center is the same distance (d) from the centers of the three.
of the four balls, no matter which three you consider, an equilateral triangle with sides of length d is created by their centers.

that seems 'regular' to me. i'm not a mathematician so i know no other way to prove it.
  Posted by rixar on 2004-08-04 19:49:06

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