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Thread: please help me prove this problem.

  1. #1
    rcs
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    please help me prove this problem.

    there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

    thank you.
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  2. #2
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    Re: please help me prove this problem.

    Quote Originally Posted by rcs View Post
    there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

    thank you.
    Do you mean "there are five points inside a square of side two length 2"?
    Your statement as is makes no sense at all.
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  3. #3
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    Re: please help me prove this problem.

    Quote Originally Posted by rcs View Post
    there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.

    thank you.
    Seems like a pidgeon hole. You can hide 4.
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    Re: please help me prove this problem.

    Quote Originally Posted by rcs View Post
    there are five points of side two length 2. prove that there exists two of them having a distance not more than square root of 2.
    Lets assume that this concerns a square that is $2\times 2$.
    Suppose we have four smaller squares that are each $1\times 1$. The length of the diagonal of any one the the smaller squares is $\sqrt2$.
    Question: Is it possible to use the four smaller squares to completely cover the larger square?
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