How many people were at the party?

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At a party, everyone shook hands with everybody else. There were 66 handshakes.

How many people were at the party?

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    Best answer

    Total Number of people – 12

    EXPLANATION-
    If there are n people,

    the first person will shake hand with n-1 persons,
    the second with n-2,
    the third with n-3,
    and
    the (n-1)th person with n-(n-1)=1 person means the last person.

    Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1
    Which can be equated using n(n-1)/2=66
    Hence, n=12

    Detective Expert Answered on 7th September 2015.
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