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Thread: handshake equation

  1. #1
    Sep 2008

    Question please help!!! need for tmw!!!

    ok so I have to create an equation to explain how many handshakes you get if you input any number of people. for instance, i came up with this equation:
    n=number of people

    so we know it would take 15 handshakes for 6 people to all shake everyones hand...and 21 for 7 people, and 28 for 8 people and 36 for 9 people and so on. so when you put 7 in as n, you get 42, then you divide by 2 and get 21, which is the number of handshakes.

    but the other part of the problem is that the equation has to be manipulated to be true for (x+1)

    therefore; (x+1)((x+1)-1)

    kind of like that. except for that then it isn't true. so i have to manipulate an equation to be true for x=1 and x=x+1
    which is causing a serious problem
    and i have to show how i manipulated it to get there.
    so if anyone can help, please do!!
    Last edited by fhcchick90; Sep 10th 2008 at 05:26 PM.
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  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    you are using induction to prove that the number of handshakes is

    $\displaystyle h = \frac{n(n-1)}{2} = \frac{n^2}{2} - \frac{n}{2}$

    you assume it's true for $\displaystyle n$, then prove true for $\displaystyle n+1$

    if you add one more person, then he/she shakes hands with n people. making the total number of handshakes $\displaystyle h + n$

    so ... for $\displaystyle n+1$ people

    $\displaystyle \frac{(n+1)(n)}{2} = \frac{n^2}{2} + \frac{n}{2} = \frac{n^2}{2} + n - \frac{n}{2} = \frac{n^2}{2} - \frac{n}{2} + n = h + n$
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