Math camp qualifying quiz 2014 Problem 3

Nov 2014
3
0
Amherst, MA
3. Let Pn be a regular n-sided polygon inscribed in a circle of radius 1. What is the minimum number of circles of radius
1/2 required to cover Pn completely? (Both Pn and the circles in this problem include the boundary as well as the
interior.) Note: in order to prove that something is the minimum, you need to prove both that it works and that nothing
smaller works.
 
Jun 2014
945
191
Earth
3. Let Pn be a regular n-sided polygon inscribed in a circle of radius 1. What is the minimum number of circles of radius
1/2 required to cover Pn completely? (Both Pn and the circles in this problem include the boundary as well as the
interior.) Note: in order to prove that something is the minimum, you need to prove both that it works and that nothing
smaller works.
(Repeat message)

If you're really gifted, then you need to demonstrate it here. Show some of your attempts here.
If you can't even show some of what you know about what you know here, then you're
probably not ready to pass that qualifying for that math camp. And you shouldn't go to the math camp.
 
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