Boost your brain power !

In a small get-together, all the guests greeted themselves by shaking hands. The number of handshakes exchanged were 36
altogether.Can you guess how many guests were present ?
Answer follows.

Imagine that there are only 4 guests namely A,B,C,D.Okay.Now the exchanges were like this. That is,

A to B,   A to C ,  A to D, 
B to C , B  to D, and  C to D . that is 6 hand shakes.= 3! {FACTORIAL 3 =3*2*1.where * is meant for multiplication.}

If there were ' n ' persons, the number of hand shakes is {n-1}!. i .e ,{n-1}{n-2}..............3.2.1.=Sum of first n-1 natural numbers.
Sum of 1 to n terms=n{n+1}\2

So number of hand shakes={n-1}{n-1+1}\2
                                       ={n-1}n\2  =  36   given.

                                       =n2 -n -72 = 0
                                       ={n-9}{n+8}=0
                                    n   =   9.
  So  9 guests were present.