Brain teaser!!! handshakes!!

Number of People is 12......... every person will handshake with 11 people ...... 12x11 / 2 = 66 ;) m i right?

Answer is 12.....

  n

     C              =        66

          2

N = 12

ITS 12 AS PROVED BELOW

With two people (A and B), there is one handshake
   (A with B).

With three people (A, B, and C), there are three handshakes
  (A with B and C;   B with C).

With four people (A, B, C, and D), there are six handshakes
  (A with B, C, and D;   B with C and D;   C with D).

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n²+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.