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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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Solution Solution | Comment 5 of 6 |
Without Brollís efficiency, but along the same lines..

Scale down the given rectangle and its circles by halving the dimensions. It will then appear as a quarter of the original rectangle covered now by 100 circles with r=1. This pattern of covering can then be used for each quarter of the given rectangle using 400 such circles altogether.
There will be some covering of the covered, as Broll hinted at.

  Posted by Harry on 2012-01-31 12:12:22
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