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points or pigeons in square? (Posted on 2019-08-05) Difficulty: 2 of 5
Given 5 points inside a square of side 10 cm, what is the probability that at least two of the points are within 8cm of each other?

No Solution Yet Submitted by Danish Ahmed Khan    
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re: what? | Comment 3 of 8 |
(In reply to what? by Charlie)

here is how you can picture such a situation:


the square is 10cm on a side so place the first 4 at the 4 corners and then draw circles of radius 8cm centered at each of these points, there is a small area in the center that is not covered by an of the circles so the 5th point can go anywhere inside there.  Now this allows allows you to move the first 4 slightly and still leave room for the 5th.  Of course this may not be the only possible configuration but it does show how it is at least possible.

  Posted by Daniel on 2019-08-05 18:51:02
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