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Math Help - Distance measurement problem

  1. #1
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    Distance measurement problem

    Need help for this one too:

    Consider a square whose side has length 1. Suppose S is an arbitrarily chosen set of 5 distinct points from this square. Prove that S contains two points whose distance is at most 1/root 2.

    What will be the best way to answer such kind of question?
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  2. #2
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    Quote Originally Posted by faisalnet5 View Post
    Need help for this one too:

    Consider a square whose side has length 1. Suppose S is an arbitrarily chosen set of 5 distinct points from this square. Prove that S contains two points whose distance is at most 1/root 2.
    Divide the unit square into for congruent subsquares.
    How far apart can any two points within one of those subsquares be?
    Use the pigeon-hole principle.
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  3. #3
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    Thanks....but can u please tell me a bit more about how to use Pigeon-hole principle in this aspects?

    Regards
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  4. #4
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    Quote Originally Posted by faisalnet5 View Post
    Thanks....but can u please tell me a bit more about how to use Pigeon-hole principle in this aspects?
    If you have five points(pigeons) and only four squares(Pigeon-holes), then one hole has two pigeons in it.
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