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Covering a rectangle by circles (Posted on 2012-01-30) Difficulty: 2 of 5
Prove, that if a given rectangle can be covered by 100 circles each of r=2, then it can be covered by 400 circles each of r=1.

See The Solution Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

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re: Possible solution | Comment 3 of 6 |
(In reply to Possible solution by broll)

Broll:


I don't get your last post at all.  The area of the rectangle is necessarily less than the total area of the circles, because the circles cover the rectangle.  So if "efficiency" x is less than 1, then the area of the rectangle = 400pi * x.

And the area of the r=1 circles is the same as the area of the r=2 circles, so if they cover the rectangle, they also do so with "efficiency" x

  Posted by Steve Herman on 2012-01-31 10:21:50
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