3

Prove that you can't arrange 100 points inside a $13\times18$ rectangle so that the distance between any two points is at least 2.

I tried many ways to divide the rectangle, but I can't get the parts to be small enough, and also less than 100.

VividD
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user92366
  • 31

1 Answers1

8

Draw a circle of radius 1 around each point and imagine a "frame" around the rectangle of width 1. How much of the expanded rectangle will the (non-overlapping) circles fill?

Barry Cipra
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