Question 1092322
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For  "n"  persons the number of hand shakes with each other is    {{{(n*(n-1))/2}}}.


So,  you need find  "n"  from the equation


{{{(n*(n-1))/2}}} = 66.


=====>    n*(n-1) = 2*66 = 132.


The only two consecutive positive integers that multiplied to  132  are  11  and  12.


So,  the answer to your problem is:    The number of guests in the party is  12.