Question 1178310
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<pre>

If "n" is the number of persons, and if each shakes hand with every other person,

then the number of handshakes is  {{{(n*(n-1))/2}}}.


So, you have this equation


    {{{(n*(n-1))/2}}} = 36,


which gives


    n*(n-1) = 2*36 = 72;


hence,  n = 9.


<U>ANSWER</U>.  There are 9 persons at the party.
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Solved.