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Turn off the light

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A Bright Star is a sphere, not just a point, that emits light in all directions from every point on its surface. A Dark Star is an opaque sphere whose dull black surface reflects no light. Dark Stars come in all sizes. Your assignment is to get and position a few of them around a given Bright Star in such a way as will absorb all its light, thus rendering it invisible from afar in every direction. What is the minimum number of Dark Stars required to carry out this task, and why?

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3 dark stars are enough to block all the light as shown below:

post-54025-0-66113200-1382112577_thumb.j

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3 dark stars are enough to block all the light as shown below:

attachicon.gifStars.JPG

Will that work in three dimensions?

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3 dark stars are enough to block all the light as shown below:

attachicon.gifStars.JPG

Will that work in three dimensions?

Good point.

Add 2 more dark stars then.

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3 dark stars are enough to block all the light as shown below:

attachicon.gifStars.JPG

Will that work in three dimensions?

Good point.

Add 2 more dark stars then.

Is that the least amount?

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I would start out with 4 Dark Stars in the shape of a polyhedron (three sided pyramid) large enough to contain the Bright star and touch each other, surrounded by another polyhedron of Dark Stars (rotated to cover the existing gaps) large enough to contain the inner polyhedron and touch each other.


Total of 8 Dark stars.

(Although the scale of the problem makes my head hurt)

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