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Math Help - problem with area

  1. #1
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    Thumbs up problem with area

    Problem # 9
    Consider any 5 points all of which are in, or on , a square of side 1 . Prove that there must be at least one pair of them who will be no further than 22 apart.



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  2. #2
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    Quote Originally Posted by rlarach View Post
    Problem # 9
    Consider any 5 points all of which are in, or on , a square of side 1 . Prove that there must be at least one pair of them who will be no further than 22 apart.



    THANKS FOR THE HELP
    22 what apart??

    -Dan
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  3. #3
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    Quote Originally Posted by rlarach View Post
    Problem # 9
    Consider any 5 points all of which are in, or on , a square of side 1 . Prove that there must be at least one pair of them who will be no further than 22 apart.



    THANKS FOR THE HELP
    The 22 should be sqrt(2)/2.

    Let me explain. Partition the square into 4 smaller squares by drawing two lines down the middles. Now there are 5 point being placed into 4 boxes. Pigeonholing we get 2 points are the same smaller square. The maximum distance from those two points is sqrt(2)/2.
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