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Spherplex (Posted on 2019-11-25) Difficulty: 3 of 5
A sphere is reconstituted into n identical smaller spheres, keeping the total volume constant.

Let a be the ratio of the total surface area of the smaller spheres to the surface area of the original sphere.

Let b be the ratio of the radius of the original sphere to the radius of each of the smaller spheres.

Let c be the ratio of the volume of the original sphere to the volume of each of the smaller spheres.

What is the minimum integer value of a+b+c?

No Solution Yet Submitted by Danish Ahmed Khan    
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re: solution Comment 3 of 3 |
(In reply to solution by Charlie)

right again on both counts!

At least I got n=8 right.

I had the bad luck to test my answer with the case n=1 which checked-out (a+b+c=3) even though incorrect!

Edited on November 25, 2019, 1:08 pm
  Posted by Steven Lord on 2019-11-25 11:11:11

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