SOLUTION: every two persons shakes hand with each other in a party and the total number of hand shakes is 66.the number of guests in party is

Algebra ->  Permutations -> SOLUTION: every two persons shakes hand with each other in a party and the total number of hand shakes is 66.the number of guests in party is      Log On


   

Question 1092322: every two persons shakes hand with each other in a party and the total number of hand shakes is 66.the number of guests in party is
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
For  "n"  persons the number of hand shakes with each other is   %28n%2A%28n-1%29%29%2F2.

So,  you need find  "n"  from the equation

%28n%2A%28n-1%29%29%2F2 = 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.