At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Choose the correct option
A) 14	B) 18	C) 11	D) 17	E) 12
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.   correct answer is 12)12
<result>E</result>
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?