If you have 66 shake hands how many people in the party?

Answer 1

If there are n people, you have n*(n-1)/2 handshakes

That gives the equation n*(n-1)/2 = 66

or n*(n-1) = 132

n2 - n - 132 = 0

(n - 12)*(n + 11) = 0

The solution to this quadratic are n = 12 or n = -11

Since the number of people cannot be negative, n must be 12.